Conceptual-Science-Labmanual.Pdf

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CONCEPTUAL PHYSICS

Laboratory Manual

Paul Robinson San Mateo High School San Mateo, California Illustrated by Paul G. Hewitt

Needham, Massachusetts Upper Saddle River, New Jersey Glenview, Illinois CP02_SE_LAB_ FM 6/20/08 9:24 AM Page ii

Contributors Consultants

Roy Unruh Kenneth Ford University of Northern Iowa Germantown Academy Cedar Falls, Iowa Fort Washington, Pennsylvania

Tim Cooney Jay Obernolte Price Laboratory School University of California Cedar Falls, Iowa Los Angeles, California

Clarence Bakken Gunn High School Palo Alto, California

Cover photograph: Motor Press Agent/Superstock, Inc.

Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. When such a designation appears in this book and the publisher was aware of a trademark claim, the designation has been printed in initial capital letters (e.g., Macintosh).

Copyright © 2002 by Prentice-Hall, Inc., Upper Saddle River, New Jersey 07458. All rights reserved. Printed in the United States of America. This pub- lication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department.

ISBN 0-13-054257-1 22 V 031 13 12 11

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Acknowledgments

Most of the ideas in this manual come from teachers who share their ideas at American Association of Physics Teachers (AAPT) meetings that I have attended since my first year of teaching. This sharing of ideas and coopera- tive spirit is a hallmark of our profession. Many more individuals have contributed their ideas and insights freely and openly than I can mention here. The greatest contributors are Roy Unruh and Tim Cooney, principal authors of the PRISMS (Physics Resources and Instructional Strategies for Motivating Students) Guide. I am especially thankful to them and others on the PRISMS team: Dan McGrail, Ken Shafer, Bob Wilson, Peggy Steffen, and Rollie Freel. For contributions and feedback to the first edition, I am grateful to Brad Huff, Bill von Felten, Manuel Da Costa, and Clarence Bakken, as well as the students of Edison Computech High School who provided valuable feedback. I am especially indebted to my talented former student Jay Obernolte, who developed computer software that originally accompanied this manual. For helpful lab ideas I thank Evan Jones, Sierra College; Dave Wall, City College of San Francisco; David Ewing, Southwestern Georgia University; and Sheila Cronin, Avon High School, CT, for her adaptations of CASTLE curriculum. Thanks go to Paul Tipler; Frank Crawford, UC Berkeley; Verne Rockcastle, Cornell University; and the late Lester Hirsch for their inspiration. I am especially grateful to Ken Ford, who critiqued this third edition and to my talented and spirited students at San Mateo High School who constantly challenge and inspire me. For suggestions on integrating the computer in the physics laboratory, I am grateful to my AAPT colleagues Dewey Dykstra, Robert H. Good, Charles Hunt, and Dave and Christine Vernier. Thanks also to Dave Griffith, Kevin Mather, and Paul Stokstad of PASCO Scientific for their professional assistance. I am grateful to my computer consultant and long time friend Skip Wagner for his creative expertise on the computer. For production assistance I thank Lisa Kappler Robinson and Helen Yan for hand-lettering all the illustrations. Love and thanks to my parents for their encouragement and support, and to my children—David, Kristen, and Brian—and my dear Ellyn—for being so patient and understanding! Most of all, I would like to express my gratitude to Paul Hewitt for his illustrations and many helpful suggestions. Paul Robinson

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Contents

To the Student x Goals, Graphing, Use of the Computer, Lab Reports, Safety in the Physics Laboratory, Emergency Procedures The laboratory activities and experiments are listed here with the lab topic in italics and the purpose of each lab is stated under the title of the lab.

1 Making Hypotheses – Inquiry Method 1 To practice using observations to make hypotheses. 2 The Physics 500 – Measuring Speed 3 To compute the average speed of at least three different races and to participate in at least one race. 3 The Domino Effect – Maximizing Average Speed 5 To investigate the ways in which distance, time, and average speed are interrelated by maximizing the speed of falling dominoes. To become familiar with elementary graphing techniques. 4 Merrily We Roll Along! – Acceleration Down an Incline 9 To investigate the relationship between distance and time for a ball rolling down an incline. 5 Conceptual Graphing – Graphical Analysis of Motion 17 To make qualitative interpretations of motion from graphs. 6 Race Track – Acceleration 23 To introduce the concept of constantly changing speed. 7 Bull’s Eye – Projectile Motion 25 To investigate the independence of horizontal and vertical components of motion. To predict the landing point of a projectile. 8 Going Nuts – Inertia 29 To explore the concept of inertia. 9 Buckle Up! – Inertia 31 To demonstrate how Newton’s first law of motion is involved in collisions. 10 24-Hour Towing Service – Statics and Vectors 33 To find a technique to move a car when its wheels are locked. 11 Getting Pushy – Variables Affecting Acceleration 35 To investigate the relationship among mass, force, and acceleration. 12 Constant Force and Changing Mass – Mass and Acceleration 39 To investigate the relationship of mass on an accelerating system. 13 Constant Mass and Changing Force – Force and Acceleration 43 To investigate how increasing the applied force affects the acceleration of a system.

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14 Impact Speed – Effect of Air Friction on Falling Bodies 47 To estimate the speed of a falling object as it strikes the ground. 15 Riding with the Wind – Components of Force 51 To investigate the relationships between the components of the force that propels a sailboat. 16 Balloon Rockets – Action and Reaction 55 To investigate action-reaction relationships. 17 Tension – Action and Reaction 57 To introduce the concept of tension in a string. 18 Tug-of-War – Action and Reaction 61 To investigate the tension in a string, the function of a simple pulley, and a simple “tug-of-war.” 19 Go Cart – Two-Body Collisions 65 To investigate the momentum imparted during elastic and inelastic collisions. 20 Tailgated by a Dart – Momentum Conservation 69 To estimate the speed of an object by applying conservation of momentum to an inelastic collision. 21 Making the Grade – Mechanical Energy 73 To investigate the force and the distance involved in moving an object up an incline. 22 Muscle Up! – Power 75 To determine the power that can be produced by various muscles of the human body. 23 Cut Short – Conservation of Energy 77 To illustrate the principle of conservation of energy with a pendulum. 24 Conserving Your Energy – Conservation of Energy 79 To measure the potential and kinetic energies of a pendulum in order to see whether energy is conserved. 25 How Hot Are Your Hot Wheels? – Efficiency 83 To measure the efficiency of a toy car on an inclined track. 26 Wrap Your Energy in a Bow – Energy and Work 85 To determine the energy transferred into an archer’s bow as the string is pulled back. 27 On a Roll – Friction and Energy 89 To investigate the relationship between the stopping distance and height from which a ball rolls down an incline. 28 Releasing Your Potential – Conservation of Energy 93 To find quantitative relationships among height, speed, mass, kinetic energy, and potential energy. 29 Slip-Stick – Coefficients of Friction 97 To investigate three types of friction and to measure the coefficient of friction for each type. 30 Going in Circles – Centripetal Acceleration 103 To determine the acceleration of an object at different positions on a rotating turntable. 31 Where’s Your CG? – Center of Gravity 107 To locate your center of gravity.

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32 Torque Feeler – Torque 111 To illustrate the qualitative differences between torque and force. 33 Weighing an Elephant – Balanced Torques 113 To determine the relationship between masses and distances from the fulcrum for a balanced see-saw. 34 Keeping in Balance – Balanced Torques 117 To use the principles of balanced torques to find the value of an unknown mass. 35 Rotational Derby – Rotational Inertia 121 To observe how objects of various shapes and masses roll down an incline and how their rotational inertias affect their rate of rotation. 36 Acceleration of Free Fall – Acceleration of Gravity 125 To measure the acceleration of an object during free fall with the help of a pendulum. 37 Computerized Gravity – Acceleration of Gravity 129 To measure the acceleration due to gravity, using the Laboratory Interfacing Disk. 38 Apparent Weightlessness – Free Fall 133 To observe the effects of gravity on objects in free fall. 39 Getting Eccentric – Elliptical Orbits 135 To get a feeling of the shapes of ellipses and the locations of their foci by drawing a few. 40 Trial and Error – Kepler’s Third Law 137 To discover Kepler’s third law of planetary motion through a procedure of trial and error using the computer. 41 Flat as a Pancake – Diameter of a BB 139 To estimate the diameter of a BB. 42 Extra Small – The Size of a Molecule 141 To estimate the size of a molecule of oleic acid. 43 Stretch – Elasticity and Hooke’s Law 143 To verify Hooke’s law and determine the spring constants for a spring and a rubber band. 44 Geometric Physics – Scaling 147 To investigate the ratios of surface area to volume. 45 Eureka! – Displacement and Density 153 To explore the displacements method of finding volumes of irregularly shaped objects and to compare their masses with their volumes. 46 Sink or Swim – Archimedes’ Principle and Flotation 157 To introduce Archimedes’ principle and the principle of flotation. 47 Weighty Stuff – Weight of Air 161 To recognize that air has weight. 48 Inflation – Pressure and Force 163 To distinguish between pressure and force, and to compare the pressure that a tire exerts on the road with the air pressure in the tire. 49 Heat Mixes: Part I – Specific Heat of Water 167 To predict the final temperature of a mixture of cups of water at different temperatures. 50 Heat and Mixes: Part II – Specific Heat of Nails 171 To predict the final temperature of water and nails when mixed.

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51 Antifreeze in the Summer? – Specific Heat and Boiling Point 175 To determine what effect antifreeze has on the cooling of a car radiator during the summer. 52 Gulf Stream in a Flask – Convection 179 To observe liquid movement due to temperature differences. 53 The Bridge Connection – Linear Expansion of Solids 181 To calculate the minimum length of the expansion joints for the Golden Gate Bridge. 54 Cooling Off – Comparing Cooling Curves 185 To compare the rates of cooling objects of different colors and surface reflectances. 55 Solar Equality – Solar Energy 189 To measure the sun’s power output and compare it with the power output of a 100-watt light bulb. 56 Solar Energy – Solar Energy 193 To find the daily amount of solar energy reaching the earth’s surface and relate it to the daily amount of solar energy falling on an average house. 57 Boiling Is a Cooling Process – Boiling of Water 197 To observe water changing its state as it boils and then cools. 58 Melting Away – Heat of Fusion 201 To measure the heat of fusion from water. 59 Getting Steamed Up – Heat of Vaporization 205 To determine the heat of evaporation for water. 60 Changing Phase – Changes of Phase 209 To recognize, from a graph of the temperature changes of two systems, that energy is transferred in changing phase even though the temperature remains constant. 61 Work for Your Ice Cream – Energy Transfer 211 To measure the energy transfers occurring during the making and freezing of homemade ice cream. 62 The Drinking Bird – Heat Engines 213 To investigate the operation of a toy drinking bird. 63 The Uncommon Cold – Estimating Absolute Zero 217 To use linear extrapolation to estimate the Celsius value of the temperature of absolute zero. 64 Tick-Tock – Period of a Pendulum 221 To construct a pendulum with the period of one second. 65 Grandfather’s Clock – Period of a Pendulum 223 To investigate how the period of a pendulum varies with its length. 66 Catch a Wave – Superposition 225 To observe important wave properties. 67 Ripple While You Work – Wave Behavior 229 To observe wave phenomena in a ripple tank. 68 Chalk Talk – Nature of Sound 233 To explore the relationships between sound and the vibrations in a material.

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69 Mach One – Speed of Sound 235 To determine the speed of sound using the concept of resonance. 70 Shady Business – Formation of Shadows 237 To investigate the nature and formation of shadows. 71 Absolutely Relative – Light Intensity 239 To investigate how the light intensity varies with distance from the light source. 72 Shades – Polarization 243 To investigate the effects of polarized light. 73 Flaming Out – Atomic Spectra 247 To observe the spectra of some metal ions. 74 Satellite TV – Parabolic Reflectors 249 To investigate a model design for a satellite TV dish. 75 Images – Formation of Virtual Images 251 To formulate ideas about how reflected light travels to your eyes. 76 Pepper’s Ghost – Multiple Reflections 253 To explore the formation of mirror images by a plate of glass. 77 The Kaleidoscope – Multiple Reflections 255 To apply the concept of reflection to a mirror system with multiple reflections. 78 Funland – Images Formed by a Curved Mirror 257 To investigate the nature, position, and size of images formed by a concave mirror. 79 Camera Obscura – Pinhole Camera 261 To observe images formed by a pinhole camera and to compare images formed with and without lens. 80 Thin Lens – Convex and Concave Lenses 263 To explore concave and convex lenses. 81 Lensless Lens – Pinhole “Lens” 265 To investigate the operation of a pinhole “lens.” 82 Bifocals – Images Formed by a Convex Lens 267 To investigate the nature, position, and size of images formed by a converging lens. 83 Where’s the Point? – Focal Length of a Diverging Lens 271 To measure the focal length of a diverging lens. 84 Air Lens – Refraction in Air 273 To apply knowledge of lenses to a different type of lens system. 85 Rainbows Without Rain – Thin-Film Interference 275 To observe and develop a hypothesis about the phenomenon of light interference. 86 Static Cling – Static Electricity 277 To observe some of the effects of static electricity. 87 Sparky, the Electrician – Simple Series and Parallel Circuits 279 To study various arrangements of a battery and bulbs and the effects of those arrangements on bulb brightness. 88 Brown Out – Capacitors 283 To investigate charging and discharging a capacitor.

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89 Ohm Sweet Ohm – Ohm’s Law 285 To investigate how current varies with voltage and resistance. 90 Getting Wired – Current Flow in Circuits 289 To build a model that illustrates electric current. 91 Cranking Up – Series and Parallel Circuits 293 To compare work done in series and parallel circuits. 92 3-Way Switch – Household Circuits 297 To explore ways to turn a lightbulb on or off from one of two switches. 93 3-D Magnetic Field – Magnetic Field Lines 299 To explore the shape of magnetic fields. 94 You’re Repulsive – Force on Moving Charges 301 To explore the force on a charge moving through a magnetic field, and the current induced in a conductor moving in a magnetic field. 95 Jump Rope Generator – Electromagnetic Induction 305 To demonstrate the generator effect of a conductor cutting through the earth’s magnetic field. 96 Particular Waves – Photoelectric Effect 307 To observe the photoelectric effect. 97 Nuclear Marbles – Nuclear Scattering 311 To determine the diameter of a marble by indirect measurement. 98 Half-Life – Half-Life 315 To develop an understanding of half-life and radioactive decay. 99 Chain Reaction – Chain Reaction 317 To simulate a simple chain reaction. Appendix – Significant Figures and Uncertainty in Measurement

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To the Student

ALSO LIKE A GAME, TO FULLY YOU NEED TO KNOW THE RULES OF UNDERSTAND PHYSICS, YOU A GAME BEFORE YOU CAN FULLY NEED TO KNOW HOW TO KEEP ENJOY IT. LIKEWISE WITH THE SCORE. THIS INVOLVES PHYSICAL WORLD———TO FULLY OBSERVING, MEASURING, AND APPRECIATE NATURE YOU NEED TO EXPRESSING YOUR FINDINGS IN KNOW ITS RULES———WHAT PHYSICS NUMBERS. THAT’S WHAT THIS IS ABOUT. READ YOUR TEXTBOOK LAB MANUAL IS ABOUT. DO AND ENJOY! PHYSICS AND UNDERSTAND!

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Goals

The laboratory part of the Conceptual Physics program should 1) Provide you with hands-on experience that relates to physics concepts. 2) Provide training in making measurements, recording, organizing, and analyzing data. 3) Provide you with the experiences in elementary problem solving. 4) Show you that all this can be interesting and worthwhile—doing physics can be quite enjoyable!

This lab manual contains 61 activities and 38 experiments. Most activities are designed to provide you with hands-on experience that relates to a specific concept. Experiments are usually designed to give you practice using a particular piece of apparatus. The goals for activities and experiments, while similar, are in some ways different. The chief goal of activities is to acquaint you with a particular physical phenomenon which you may or may not already know something about. The emphasis during an activity is for you to observe relationships, identify variables, and develop tentative explanations of phenomena in a qualitative fashion. In some cases, you will be asked to design experiments or formulate models that lead to a deeper understanding. Experiments are more quantitative in nature and generally involve acquiring data in a prescribed manner. Here, a greater emphasis is placed on learning how to use a particular piece of equipment, making measurements, identifying and estimating errors, organizing your data, and interpreting your data.

Graphing

When you look at two columns of numbers that are related some way, they probably have little meaning to you. A graph is a visual way to see how two quantities are related. You can tell at an instant what the stock market has been doing by glancing at a plot of the Dow Jones Industrial Average plotted as a function of time. Often you will take data by changing one quantity, called the independent variable, in order to see how another quantity, called the dependent variable, changes. A graph is made by plotting the values of the independent variable on the horizontal axis, or x-axis with values of the dependent variable on the vertical axis, or y-axis. When you make a graph, it is always important to label each of the axes with the quantity and units used to express it. The graph is completed by sketching the best smooth curve or straight line that fits all the points. To eliminate confusion and increase learning efficiency, your teacher will guide you before each experiment as to how to label the axes and choose a convenient scale. Often you will work in groups and graph your data as you perform the experiment. This has the chief advantage of pro- viding immediate feedback if an erroneous data point is made. This gives you time to adjust the apparatus and make the necessary adjustments so that your data are more meaningful. Everyone in the class can be easily compared by simply overlapping the graphs on an overhead projector. This method also has the added benefit of eliminating graphing as a homework assignment!

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Use of the Computer

The computer provides a powerful tool in collecting and analyzing your data and displaying it graphically. Data plotting software enables you to input data easily and to plot the corresponding graph in minutes. With the addition of a printer, your graphs can be transferred to paper and included with your lab report. Because of the computer’s ability to calculate rapidly and accurately, it can help you analyze your data quickly and efficiently. The interrela- tionships between variables become more apparent than if you had to plot the data by hand. In this course you will be encouraged to use the computer (if it is available in your lab room) as a laboratory instrument that can measure time and temperature and sense light. You can convert the computer into a timer, a light sensor, and a thermometer by connecting to it one or more variable resistance probes. Though not required for any of the labs, the use of probeware greatly facilitates data collection and processing.

Lab Reports

Your teacher may ask that you write up a lab report. Be sure to follow your teacher’s specific instructions on how to write a lab report. The general guideline for writing a lab report is: Could another student taking physics at some other school read your report and understand what you did well enough to replicate your work?

Suggested Guidelines for Lab Reports Lab number and title Write your name, date, and period in the upper right-hand corner of your report. Include the names of your partners underneath. Purpose Write a brief statement of what you were exploring, verifying, measuring, investigating, etc. Method Make a rough sketch of the apparatus you used and a brief description of how you planned to accomplish your lab. Data Show a record of your observations and measurements, including all data tables. Analysis Show calculations performed, any required graphs, and answers to questions. Summarize what you accomplished in the lab.

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Safety in the Physics Laboratory

By following certain common sense in the physics lab, you can make the lab safe not only for yourself but for all those around you.

1. Never work in the lab unless a teacher is present and aware of what you are doing. 2. Prepare for the lab activity or experiment by reading it over first. Ask questions about anything that is unclear to you. Note any cautions that are stated. 3. Dress appropriately for a laboratory. Avoid wearing bulky or loose- fitting clothes or dangling jewelry. Pin or tie back long hair, and roll up loose sleeves. 4. Keep the work area free of any books and materials not needed for what you are working on. 5. Wear safety goggles when working with flames, heated liquids, or glassware. 6. Never throw anything in the laboratory. 7. Use the apparatus only as instructed in the manual or by your teacher. If you wish to try an alternate procedure, obtain your teacher’s approval first. 8. If a thermometer breaks, inform your teacher immediately. Do not touch either the mercury or the glass with your bare skin. 9. Do not force glass tubing or thermometer into dry rubber stopper. The hole and the glass should both be lubricated with glycerin (glyc- erol) or soapy water, and the glass should be gripped through a paper towel to protect the hands. 10. Do not touch anything that may be hot, including burners, hot plates, rings, beakers, electric immersion heaters, and electric bulbs. If you must pick up something that is hot, use a damp paper towel, a pot holder, or some other appropriate holder. 11. When working with electric circuits, be sure that the current is turned off before making adjustments in the circuit. 12. If you are connecting a voltmeter or ammeter to a circuit, have your teacher approve the connections before you turn the current on. 13. Do not connect the terminals of a dry cell or battery to each other with a wire. Such a wire can become dangerously hot. 14. Report any injuries, accidents, or breakages to your teacher immediately. Also report anything that you suspect may be malfunctioning. 15. Work quietly so that you can hear any announcements concerning cautions and safety. 16. Know the locations of fire extinguishers, fire blankets, and the nearest exit. 17. When you have finished your work, check that the water and gas are turned off and that electric circuits are disconnected. Return all materials and apparatus to the places designated by your teacher. Follow your teacher’s directions for disposal of any waste materials. Clean the work area.

* See page xiv for descriptions of the safety symbols you will see throughout this laboratory manual.

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Safety Symbols These symbols alert you to possible dangers in the laboratory and remind you to work carefully.

Safety Goggles Corrosive Chemical

Lab Apron Poison

Breakage Physical Safety

. Heat-Resistant Gloves Flames

Heating No Flames

Sharp Object Fumes

General Safety Electric Shock Awareness

Emergency Procedures

Report all injuries and accidents to your teacher immediately. Know the locations of fire blankets, fire extinguishers, the nearest exit, first aid equipment, and the school’s office nurse.

Situation Safe Response

Burns Flush with cold water until the burning sensation subsides. Cuts If bleeding is severe, apply pressure or a compress directly to the cut and get medical attention. If cut is minor, allow to bleed briefly and wash with soap and water. Electric Shock Provide fresh air. Adjust the person’s position so that the head is lower than the rest of the body. If breathing stops, use artificial resuscitation. Eye Injury Flush eye immediately with running water. Remove contact lenses. Do not allow the eye to be rubbed. Fainting See Electric Shock. Fire Turn off all gas outlets and disconnect all electric circuits. Use a fire blanket or fire extinguisher to smother the fire. Caution: Do not cut off a person’s air supply. Never aim fire extinguisher at a person’s face.

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Name Period Date

Chapter 1: About Science Inquiry Method

1 Making Hypotheses

Purpose

To practice using observations to make hypotheses. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy 2 1-gallon metal cans Mathematical Level: none 2 2-hole #5 stoppers glass funnel or thistle tube glass tubing rubber tubing 500-mL beaker Adapted from PRISMS.

Discussion

Science involves asking questions, probing for answers, and inventing

simple sets of rules to relate a wide range of observations. Intuition and Activity inspiration come into science, but they are, in the end, part of a system- atic process. Science rests on observations. These lead to educated guesses, or hypotheses. A hypothesis leads to predictions, which can then be tested. The final step is the formulation of a theory that ties together hypotheses, predictions, and test results. The theory, if it is a good one, will suggest new questions. Then the cycle begins again. Sometimes this process is brief, and a successful theory that explains existing data and makes useful predictions is developed quickly. More often, success takes months or years to achieve. Scientists must be patient people! Procedure

Step 1: Observe the operation of the mystery apparatus (shown in Observe apparatus. Figure A) set up by your teacher. © Addison-Wesley Publishing Company, Inc. All rights reserved. All rights Inc. Company, Publishing © Addison-Wesley

Fig. A Chapter 1 About Science 1 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage2 2 Propose explanations. Laboratory ManualLaboratory (Activity 1) reach aconsensusabouthow itworks. Record theconsensushere. and how itworks. Write ofhow adescription you thinkitworks. Step 2: Step 3: Students willbeexpectedtoofferanexplanationaswhythe liquid up the tube. The waterin the funnelincreasesairpressureincan,forcing several paragraphs. apparatus workedthewayitdid.Explanationsmayvaryfromoneto Report your findingstothe rest oftheclass. The classshould apparatusAttempt toexplainwhatishappeninginthemystery

Name Period Date

Chapter 2: Linear Motion Measuring Speed

2 The Physics 500

Purpose

To compute the average speed of at least three different races and to par- Setup: <1 ticipate in at least one race. Lab Time: 1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: easy Mathematical Level: easy meterstick stopwatch string equipment brought by students for their races Adapted from PRISMS.

Discussion

In this activity, you will need to think about what measurements are necessary to make in order to compute the average speed of an object. How

does the average speed you compute compare with the maximum Activity speed? How could you find the maximum speed of a runner or a car between stoplights? Procedure

Step 1: Work in groups of about three students. Select instruments to Measure average speed. measure distance and time. Develop a plan that will enable you to determine speed. Two students race each other in races such as hopping on one foot, rolling on the lawn, or walking backward. The third student collects and organizes data to determine the average speed of each racer. Repeat this process until each member of your group has a chance to be the timer. For the race in which you are the timer, record your plan and the type of race.

When measurements are to be made in an experiment, a good experimenter organizes a table showing all data, not just the data that “seem to be right.” Record your data in Data Table A. Show the units you used as well as the quantities. For each measurement, record as many digits as you can read directly from the measuring instrument, plus one

Chapter 2 Linear Motion 3 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage4 4 Compute unknowndistance. Laboratory ManualLaboratory (Activity 2) Data TableA Step 1. usingtheaverageamphitheater orthelengthofacorridor), speedfrom Then, computethedistancecovered (suchasthedistanceacross the oneofyour eventsoverthen askyou toperform anunknown distance. 2. 1. Analysis Step 2: 4. 3. No. Average meanstheaverage of thehigh,middle, andthe low for eachevent?Explain. Should therecorded average speedrepresent themaximumspeed The averagespeedisthetotaldistancedividedbytime. taken fortravel? How doesaverage speedrelate tothedistancecovered andthetime fastest speed attained duringit. No, thistechniquemeasures theaveragespeedforevent,not anevent? the fastestspeedattained during Does your measurement techniqueforspeed enableyou tomeasure Answers willvary. Themaximumshouldbeabout20milesperhour. hour (1.00m/s=2.24mi/h)? Which eventhadthegreatest average speedintheclassmilesper values. Upon completingStep 1,report toyour teacher. Your teacherwill distance = ______= distance ______= speed average ______event:

Name Period Date

Chapter 2: Linear Motion Maximizing Average Speed

3 The Domino Effect

Purpose

To investigate the ways in which distance, time, and average speed are Setup: <1 interrelated by maximizing the speed of falling dominoes. To become Lab Time: 1 familiar with elementary graphing techniques. Learning Cycle: concept development Required Equipment/Supplies Conceptual Level: easy Mathematical Level: easy approximately 50 dominoes stopwatch meterstick Thanks to Clarence Bakken for his ideas and suggestions for this lab.

Discussion

A central property of motion is speed—the rate at which distance is covered. By rate, we mean how much or how many of something per unit of

time: how many kilometers traveled in an hour, how many feet moved in Activity a second, how many raindrops hitting a roof in a minute, how much interest earned on a bank account in a year. When we measure the speed of an automobile, we measure the rate at which this easily seen physical thing moves over the ground—for instance, how many kilometers per hour. But when we measure the speed of sound or the speed of light, we measure the rate at which energy moves. We cannot see this energy. We can, however, see and measure the speed of the energy pulse that makes a row of dominoes fall.

Procedure

Step 1: Set up 50 dominoes in a straight row, with equal spacing Set up string of dominoes. between them. The dominoes must be spaced at least the thickness of one domino apart. Your goal is to maximize the speed at which a row of dominoes falls down. Set the dominoes in a way you think will give the greatest speed.

Step 2: Measure the total length of your row of dominoes.

Chapter 2 Linear Motion 5 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage6 6 Graph data. Repeat fordifferentspacings. speed. Compute averagetoppling from either end. light probesseveral dominoes caution them to position the computer photogatesystem, (2) If students are using the getting the “answer.” tance of method rather than inconclusive—stress impor- (1) Studentresultsmaybe Laboratory ManualLaboratory (Activity 3) Data TableA be exactlyatoneofyour measured points). whereon thecurve thespeedismaximum orminimum(thisneednot by through your datapoints. sketchingasmoothcurve Identify thepoint Step 8: Data TableA. produce toppling.Record in your data(including dataforthefirsttrial) pling andaspacingthatisaboutaslarge asyou canmakeitandstill spacing thatisaboutassmallyou canmakeitandstillproduce top- Step 7: Step 4: of thelastone, anddividethisby thenumberofdominospacings. thelengthfrom themiddleoffirstdominoto measuring Step 3: Step 6: Step 5: Using aseparate pieceofgraph paper, makeagraph ofyour data Repeat Steps 5and6foratleastthree more spacings. Include a Compute theaverage topplingspeedforyour row ofdominoes. Measure thetimeittakesforyour row ofdominoestofall down. Measure thelengthofadomino. Compute theaverage spacingdistancebetween dominoesby average distancebetween dominoes= ______time = ______= time spacing distance=______dominolengths ______= domino of length average speed = ______= speed average

© Addison-Wesley Publishing Company, Inc. All rights reserved. 3. 2. 1. Analysis Name to topple. cannot bedefinedatasmaller“instant”thanthetime foronedomino interval forwhichaspeedcanbedefinedisonedomino spacing.Speed therefore variessomewhatasthepulsetravelsalong. (b) Thesmallest (a) Dominoescan’t besetupwithexactlyequal spacing. Speed speed? noes rather thaninstantaneous speed Why dowe useaverage and compositionofthedominoes. The factors include the spacing;tablesurface;andheight,uniformity, What are thefactorsthataffectspeedoffallingdominoes? Average speedisthetotaldistancedividedbytime. What isadefinitionofaverage speed? for the pulse running downfor thepulserunning thedomi- i.A Fig. Period Chapter 2Linear Motion Date 7 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage8 8 mentation required! nificant role.Futureexperi- table surfacealsoplaysasig- between thedominoand possible thatthefriction are thereforeinconclusive.Itis that gaveaminimum;results mum andlightwoodenones tic dominoesthatgaveamaxi- real effectofusingheavyplas- 0.6 dominolengths.Thisisa minimum ataspacingof0.5to but otherdominoesgivea spacing of0.6dominolengths, maximum speedarounda Some dominoesgiveanice Chapter 2Linear Motion 4. 6. 5. Heavy plasticdominoesshowmaximumspeedsaround100–110cm/s. speed? From your graph, whatisthemaximumorminimumtoppling gives thedistance,whichwilllikelybeinrange50to65m. Substituting thespeedv thattakesoneminutetofall? string noes, how longarow ofdominoeswouldberequired tomakea At themaximumorminimumtopplingspeedofrow ofdomi- spacing of0.3to0.5dominolengths. dominoes givingaminimumspeed,theoccurstypicallyat typically ataspacingofaround0.55–0.60dominolengths.Forlighter For heavierdominoesgivingamaximumspeed,theoccurs the lengthofadomino? maximum orminimumspeed? What istheratio ofthisspacingto What spacingbetween dominoesdoyou predict wouldgivethe Light woodendominoesshowminimumspeedsaround80cm/s. and thetimet = 60sintotheequation d =vt

Name Period Date

Chapter 2: Linear Motion Acceleration Down an Incline

4 Merrily We Roll Along!

Purpose

To investigate the relationship between distance and time for a ball Setup: 1 rolling down an incline. Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: difficult 2-meter ramp Mathematical Level: moderate steel ball bearing or marble wood block stopwatch tape meterstick protractor overhead transparencies

Optional Equipment/Supplies

computer 3 light probes with interface 3 flashlights or other light sources 6 ring stands with clamps

Discussion

Measurement of the motion of a freely falling object is difficult because the speed increases rapidly. In fact, it increases by nearly 10 m/s every second. The distance that the object falls becomes very large, very quickly. Galileo slowed down the motion by using inclined planes. The component of gravity acting along the direction of the inclined plane is less than the full force of gravity that acts straight down—so the change of speed happens more slowly and is easier to measure. The less steep the incline, the smaller the acceleration. The physics of free fall can be understood by first considering the motion of a ball on an inclined plane. This experiment will require you to make many timing measurements using a stopwatch or, if available, a computer. If you use a stopwatch, develop good timing techniques so as to minimize errors due to reaction time. The computer-photogate system is a powerful stopwatch because it not only eliminates reaction time, but can be used in a variety of timing modes. Since the diameter of the ball can be measured directly, its speed can be found by dividing the diameter by the amount of time it © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 2 Linear Motion 9 CP02_SE_LAB_Ch01-13 3/5/01 11:32 AM Page 10

takes to pass through the beam striking the light probe. Strictly speaking, since the ball’s speed is increasing as it rolls through the light beam, it exits the beam slightly faster than it enters the beam. The width of the ball divided by the time the ball eclipses the light beam gives the average speed of the ball through the light beam, not the instantaneous speed. But once the ball has picked up speed partway down the incline, its percentage change in speed is small during the short time that it eclipses the light. Then its measured average speed is practically the same as its instantaneous speed. Procedure

Set up ramp. Step 1: Set up a ramp with the angle of the incline at about 10° to the horizontal, as shown in Figure A.

Fig. A

Divide ramp into equal parts. Step 2: Divide the ramp’s length into six equal parts and mark the six positions on the board with pieces of tape. These positions will be your release points. Suppose your ramp is 200 cm long. Divide 200 cm by 6 to get 33.33 cm per section. Mark your release points every 33.33 cm from the bottom. Place a stopping block at the bottom of the ramp to allow you to hear when the ball reaches the bottom.

Data Table A

Time the ball down the incline. Step 3: Use either a stopwatch or a computer to measure the time it takes the ball to roll down the ramp from each of the six points. (If you use the computer, position one light probe at the release point and the If using the “Chronometer” program, select Event Timer other at the bottom of the ramp.) Use a ruler or a pencil to hold the ball and then “off” mode. at its starting position, then pull it away quickly parallel to incline to release the ball uniformly. Do several practice runs with the help of your partners to minimize error. Make at least three timings from each position, and record each time and the average of the three times in Data Table A.

Graph data. Step 4: Graph your data, plotting distance (vertical axis) vs. average time (horizontal axis) on an overhead transparency. Use the same scales reserved. All rights Inc. Company, Publishing © Addison-Wesley

10 Laboratory Manual (Experiment 4) CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage11

© Addison-Wesley Publishing Company, Inc. All rights reserved. Record your datainData Table B. Graph your dataasinStep 4. Step 5: compare results. on thecoordinate axesastheothergroups inyour classsothatyou can Name the ramp tobeabout10°. and 160cmfrom thestoppingblock,asinFigure B. Set the inclineof Step 6: 3. 2. 1. gravitational forcealongtherampisgreater. The accelerationincreaseswithlargerangles.componentof What happenstotheacceleration iftheangleoframp isincreased? Yes, theball coverseachadditionaldistanceinlesstime. your answer. Does theballaccelerate down theramp? Citeevidencetodefend Acceleration istherateatwhichvelocitychanges. What isacceleration? eetSes24wt h nln e ta nl °steeper. Repeat Steps 2–4withtheinclinesetatanangle5° Remove thetapemarks andplacethemat10cm,4090 Period in lessadditionaltime. covers eachadditionaldistance time unitbutrather the ball in multiplesofthe“natural” spaced distancesdonotresult balls rolledfromequally Students shoulddiscoverthat repeat. Change thetiltoframpand ramp. Reposition thetapemarkerson Chapter 2Linear Motion i.B Fig. Data TableB Date 11 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage12 Study yourdata. 12 Graph data. equal intervalsoftime. tances resultin(moreorless) the progressivelylargerdis- Students shoulddiscoverthat Time theballdownramp. Laboratory ManualLaboratory 4) (Experiment Data TableC also 4. unit oftime. Column 4now containstherolling timesasmultiplesofthe “natural” difference between t call this average time interval one call thisaverage timeinterval “natural” unit oftime. Note that Do asGalileo withinclinedplanesand didinhisfamousexperiments another, findtheiraverage by addingthefourvalues anddividingby 4. Step 10: Column 3ofData Table C. 5. class andcompare them. Step 11: difference Step 9: as theothergroups inyour classsothatyou cancompare results. zontal axis)onanoverhead transparency. Use thesamecoordinate axes Step 8: that already listedasone “natural” unitinColumn 4of Table C.Doyou see difference between t Column 2ofData Table C. of thefourpositionsandrecord eachaverage ofthethree timesin each ofthefourrelease positions. Make atleastthree timingsfrom each Step 7: you cite to support youryou answer? citetosupport Does itincrease, decrease, orremain constant? What evidencecan What happenstothespeed overhead projector. No. This is clearly evident when student graphsare compared onthe Do ballsofdifferent masshavedifferent accelerations? (longer) section. The speedincreases. The balltakesthesametimetorolldowneach t t 3 2 and will equal—more orless—twounitsinColumn 4?Record this, and Look atthedatainColumn 2alittlemore closely. Notice thatthe Graph axis) vs. your data,plottingdistance(vertical time(hori- Measure thetimeittakesforballtoroll down theramp from If your values inColumn 3are slightlydifferent from one Overlay your transparency graph withothergroups inyour between t 4 in “natural” units, rounded offtothenearest integer. t 2 4 3 and and and t t t 1 3 2 ? Record thesethree in timeintervals is approximately thesameast is alsonearlythesameast of theballasitrolls down theramp? 1 . What aboutthe 1 itself. The t 1 is

© Addison-Wesley Publishing Company, Inc. All rights reserved. 7. “natural” timeunitsandthedistancerolled intime 8. Record your datainData Table E. Step 14: cluded thatthedistanced tomeasure through a smallopeningserves drips the time. Galileo con- 400 years ago!He useda “water clock,” inwhichtheamountofwaterthat Galileo’s geniusasanexperimenter. Remember, there were nostopwatches columnofData the timesinfourth Table C.For example, that Galileo isstillfamousformakingitfirst!Compare thedistanceswith Step 13: 6. ball in Table D. Fill intheblanksofColumns 2and3toseethepattern. Step 12: great asthedistancerolled intimet Name ural” unitoftime? Is thedistanceballrolls tothesquare proportional ofthe “nat- The accelerationincreases with increasingangle. is increased? What happenstotheacceleration oftheballasangle oftheramp The sizes errors ofyour mayhelpyou experimental appreciate time. Yes, to the squareof the “natural”unitof thedistance is proportional tothesquaresof thefirstfourintegers. The distancesareproportional of the first four integers? What istherelation between thedistancestraveled andthesquares You are now bigdiscovery—so big,infact, aboutto makeavery eetSes61 ihteiciesta nage5 steeper. Repeat Steps 6–10withtheinclinesetatan angle 5° Investigate more carefully thedistancestraveled by therolling is proportional tothesquareis proportional ofthetime d ~ 1 . t 2 t 2 is 2 2 , or4,timesas t 2 is two t Table D . Period Increase tiltoframp. Chaper 2Linear Motion Date 13 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage14 14 ately greateraccelerations. shorter timesandproportion- the largerangleresultsin Students shoulddiscoverthat probes. Set upcomputerwithlight Laboratory ManualLaboratory 4) (Experiment Data TableE recorded inData Table E. axis). (horizontal Data TableC. each distancefrom therelease recorded point,from theinformation in the table. Also record theaverage rolling timeittookfortheballtotravel divide thediameterofballby theeclipsetime. Record thespeedsin approximate theinstantaneousspeedofballatthree positions, eclipse timesforeachprobe, andrecord your timings inData Table F. To is justthediameterofball.Measure thediameter oftheball. back oftheballleavesit. The distancetraveled thistimeinterval during val between whenthefront oftheballenterslightbeamand byball asitpassesaprobe canbedetermined thetimeinter- measuring 40 cm,and90cmfrom therelease pointontheramp. The speedofthe using lightprobes. Onewayistopositionthree lightprobes 10cm, rolling down theramp. This canbeaccomplishedseveral different ways You canusethecomputer toinvestigatethespeedballacquires the BallDownRamp InvestigatingtheSpeedof Going Further: 9. eetwt h apa nage5 steeper. Use therolling times Repeat withtheramp atanangle5° Make axis) vs. aplotofinstantaneousspeed(vertical rolling time With theinclinesetatanangle ofabout10°,measure therespective 10 would fall5 In 2secondsitwouldfall far woulditfreely fallin2seconds?510 dropped it.It thefirstsecond.How wouldfallabout5metersduring Instead ofreleasing theballalongramp, supposeyou simply 2 as far, or100x(5 m) =500m(ifairresistance is neglected). 2 as far, or25x(5m)=125m.In10secondsitwouldfall diameter of ball = ______= ball of diameter 2 as far, or4x(5m)=20m.In5seconds,it

© Addison-Wesley Publishing Company, Inc. All rights reserved. 12. 11. 10. Name Yes, theupperlimitisaccelerationofgravity, the balldown theramp? What isit? increased. Doyou thinkthere isanupperlimittotheacceleration of As theangleoframp increased, theacceleration oftheball time interval. it. Studentsareactuallydeterminingtheaveragespeedoverthatshort enters thefirstpartoflightbeamandtimewhenballleaves No, the lightprobe is usedtomeasurethe time betweenwhen theball were you really instantaneousspeed?Explain. determining thespeedofballwithlightprobes,When you determined accelerations ofthe balls aregreater. The slopes of the speed vs. time graphs are greaterwhen the to theacceleration oftheballdown theramp? How dotheslopesoflinesinyour graphs ofspeedvs. timerelate g. Period Chapter 2Linear Motion Date Data TableF 15 CP02_SE_LAB_Ch01-13 3/5/01 11:32 AM Page 16 CP02_SE_LAB_Ch01-13 3/5/01 11:32 AM Page 17

Name Period Date

Chapter 2: Linear Motion Graphical Analysis of Motion

5 Conceptual Graphing

Purpose

To make qualitative interpretations of motions from graphs. Setup: <1 Lab Time: >1 Learning Cycle: concept Required Equipment/Supplies development sonic ranger Conceptual Level: moderate computer Mathematical Level: none masking tape marking pen ring stand large steel ball Thanks to Bob Tinker and Ron Thornton for their ideas and soup can suggestions for this lab. board pendulum clamp

Discussion Activity

Have you ever wondered how bats can fly around in the dark without bumping into things? A bat makes squeaks that reflect off walls and objects, return to the bat’s head, and are processed by its brain to give clues as to the location of nearby objects. The automatic focus on some cameras works on very much the same principle. The sonic ranger is a device that measures the time that ultra-high-frequency sound waves take to go to, and return from, a target object. The data are fed to a computer, where they are graphically displayed on the monitor. Data plotting software can display the data in three ways: distance vs. time, velocity vs. time, and acceleration vs. time. Procedure

Step 1: Your teacher will set up the sonic ranger and the computer for you. Check to see that the sonic ranger appears to be functioning Check sonic ranger. properly.

Step 2: Place the sonic ranger on a desk or table so that its beam is chest high. A floor stand is very useful for this purpose, if available. Affix 5 An alternative method is to meters of masking tape to the floor in a straight line from the sonic use string instead of tape as a ranger, as shown in Figure A. rule. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 2 Linear Motion 17 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage18 18 monitor. Observe graphsoncomputer Calibrate thefloor. Laboratory ManualLaboratory (Activity 5) i.A Fig. 3. quickly. Step 6: 2. thegraph plotted. observe thegraphranger plotted. Repeat, andobserve walkingfaster, and Step 5: 1. thegraph made.observe the graph made. Repeat, backingawayfrom thesonicranger faster, and watch themonitor. Back awayfrom thesonicranger slowly andobserve Step 4: isters 1m,2andsoon. mark of the tape. Calibrate thetapeby marking where thecomputerreg- time plot.Point thesonicranger atastudentstandingthe5-meter Step 3: Sketch theshapeofresulting graph. graph withasteeperdownward(morenegative)slope. downward totheright.Walking fastertowardthesonicrangergivesa Both distancevs.timegraphsshouldbestraightlinesthatslope How dothegraphs compare? with asteeperslope. to theright.Walking faster awayfromthesonicrangergivesagraph Both distancevs.timegraphsshouldbestraightlinesthatslopeupward How dothegraphs compare? Back awayfrom thesonicranger slowly; stop;thenapproach Stand atthefarendoftape. Slowly approach thesonic Stand onthe1-metermark. Alwaysfacethe sonicranger and Adjust thesonicranger software sothatitdisplaysadistance vs.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 6. Step 8: 5. Step 7: 4. Name farther belowthetimeaxis. start-up period)belowthetimeaxis.Walking awayfastergivesaline Both velocityvs.timegraphsarehorizontalstraightlines (afteraninitial How dothetwonewgraphs compare? axis. period).Walkingstart-up awayfastergivesalinefartherabovethetime Both velocityvs.timegraphsarehorizontalstraightlines(afteraninitial How dothegraphs ofvelocityvs. timecompare? Figure E:Receding;standingstill;etc.;approaching;etc. Figure D:Standingstill;receding;standingetc. Figure C:Approaching;thenstandingstill;receding. speed thanbefore. Figure B:Recedingfromthesonicranger;thenapproachingatagreater Figures B, C,D, andE. whatwalkingmotionsresultDescribe inthegraphs shown in i.B Fig. Repeat Step 5,usingthevelocityvs. timeplotter. Repeat Step 4,butuseavelocityvs. timeplotter. i.C Fig. i.D Fig. Period Chapter 2Linear Motion Date i.E Fig. 19 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage20 20 Analyze motiononanincline. a straight line than a ball. easier to roll up the incline in soup with no dent. It is much a newcanofBean with Bacon a smoothlaminated board and For bestresults,besuretouse i.F Fig. Laboratory ManualLaboratory (Activity 5) 7. Step 9: 10. 9. Now thetwographs, observe distancevs. timeandvelocityvs. time. Predictions will vary. 8. graphs willlooklikeforthecanorballrolled upanddown theincline. Predict whattheshapesofdistancevs. timeandvelocityvs. time the canatleast40cm(theminimumrange) from thesonicranger. motion ofacanorlarge steelballrolled upanincline. Initially position Step 10: Going Further Sketch theshapeofresulting graph. Sketch theshapeofvelocityvs. timegraph. Sketch theshapeofdistancevs. timegraph. Sketch your predicted shapesinthefollowing space. Repeat Step 6,usingthevelocityvs. timeplotter. Set upthesonicranger asshown inFigure F, toanalyze the

© Addison-Wesley Publishing Company, Inc. All rights reserved. 14. 13. lapped, students can comparethedistanceand velocity simultaneously. zero of time is put at maximum velocity). If these last two graphs are over- The velocityvs.timegraphwill look likeacosineor sine curve(cosineif the 12. zero of time is put at zero displacement). The distancevs.timegraphwill look likeasineorcosinecurve(sineifthe 11. ment andanswer thefollowing questions. lyze the motion ofapendulumbasedonFigure G.Perform your experi- Step 11: Name The speedisleastatthetopofswing(ateitherend). Where isthespeedleastforaswingingpendulumbob? direction). The speedisgreatestatthebottomofswing(formotionineither Where isthespeedgreatest foraswingingpendulumbob? Sketch theshapeofvelocityvs. timegraph. Sketch theshapeofdistancevs. timegraph. Devise an experimental setupthatusesthesonicrangerDevise an experimental toana- Period bob. works wellforapendulum An oldbilliardballorgolf Analyze motionof a pendulum. Chapter 2Linear Motion i.G Fig. Date 21 CP02_SE_LAB_Ch01-13 3/5/01 11:32 AM Page 22 CP02_SE_LAB_Ch01-13 3/5/01 11:32 AM Page 23

Name Period Date

Chapter 2: Linear Motion Acceleration

6 Race Track

Purpose

To introduce the concept of constantly changing speed. Setup: <1 Lab Time: 1 Learning Cycle: concept Required Equipment/Supplies development race grid in Figure A Conceptual Level: easy colored pencil or pen Mathematical Level: none graph paper (optional)

Discussion

A car can accelerate to higher speed at no more than a maximum rate determined by the power of the engine. It can decelerate to lower speed at no more than a maximum rate determined by the brakes, the tires, and the road surface. This simple but fun game will quickly teach you the meaning of fixed acceleration. Activity Race Track is a truly remarkable simulation of automobile racing. Its inventor is not known. It is described in the column “Mathematical Games” in the journal Scientific American, January 1973, p. 108. Procedure

Step 1: Each contestant should have a pencil or pen of a different color. Use the race grid in Figure A. Each player draws a tiny box just below a grid point on the starting line. The players then move in order. Getting started.

Step 2: Contestants must obey the following rules. (1) The first move must be one square forward: horizontally, verti- Rules of the road. cally, or both (diagonally). (2) On each succeeding move a car can maintain its latest velocity or increase or decrease its speed by one square per move in the horizontal or vertical direction or both. For example, a car going 2 squares per move vertically can change to 2 squares per move vertically and 1 square to the left or right; 1 or 3 squares per move vertically; or 1 or 3 squares per move vertically and 1 square to the left or right. (3) The new grid point and the straight-line segment joining it to the preceding grid point must lie entirely within the track. (4) No two cars may simultaneously occupy the same grid point. That is, no collisions are allowed! © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 2 Linear Motion 23 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage24 24 Lay outnewcourse. credit. up atournament for extra want tohavestudentsset challenging. You may This gameisparticularly Laboratory ManualLaboratory (Activity 6) i.A Fig. S

1. Analysis 3. 2. at astraight ofthetrack. portion interesting, Draw thetrack shouldbestrongly line curved. astart/finish at least3squares widerthanthenumberofcars. To makethegame on apieceofgraph paper. butshouldbe The widthofthetrack canvary Step 3: more thanoneeachturn. To summarize, thespeedineitherx

T AR

per movebeforecrashing. Answers willvary, butitispossibletogetupspeedsof6or7squares race? What wasthefastestanyplayer thecourseof everwent during important toslowdown asitistospeedup. important Possibly. Driverswhocrashdonottakeinto account thatitisas Did anybodycrash? If so, whydoyou thinktheydid? speed—not theirinstantaneousspeed. Probably not.Generallywinnersaredriverswhomaximize theiraverage Did thatplayer wintherace? (5) The firstplayer tocross thefinishlinewins! T If you wanttoplaythegameagain,you candraw anewrace grid or y

direction canchangeby no

IS H

Name Period Date

Chapter 3: Projectile Motion Projectile Motion

7 Bull’s Eye

Purpose

To investigate the independence of horizontal and vertical components Setup: 1 of motion. To predict the landing point of a projectile. Lab Time: >1

Learning Cycle: application Experiment Required Equipment/Supplies Conceptual Level: difficult Mathematical Level: difficult ® ramp or Hot Wheels track Using a stopwatch instead of 1/2-inch (or larger) steel ball photogates or light probes empty soup can greatly reduces the accuracy meterstick students can achieve and like- plumb line wise diminishes their ability to stopwatch, ticker-tape timer, or land the ball in the can. computer There are two advantages of light probes with interface having students do the com- light sources puter simulation: (1) it tutors students needing both conceptual help and help with the math; (2) you can then require students to first acquire their Discussion data and get a “Bull’s Eye” on the computer before attempt- Imagine a universe without gravity. In this universe, if you tossed a rock ing to land the ball in the can. where there was no air, it would just keep going—forever. Because the rock would be going at a constant speed, it would cover the same amount of distance in each second (Figure A). The equation for distance traveled when motion is uniform is

x = vt Fig. A

The speed is x v = — t Coming back to earth, what happens when you drop a rock? It falls to the ground and the distance it covers in each second increases (Figure B). Gravity is constantly increasing its speed. The equation of the vertical distance y fallen after any time t is 1 y = —gt2 2 where g is the acceleration of gravity. The falling speed v after time t is Fig. B v = gt © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 3 Projectile Motion 25 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage26 26 Compute thehorizontalspeed. at aconstantspeedand negligible, theballshouldroll ramp islevelandthefriction probe isre-illuminated.Ifthe ing balltowhenthesecond is re-illuminiatedbythepass- from whenthefirst light probe you aremeasuringthetime T time is used withLabTools eclipse time.Iftwoprobesare diameter oftheball by the probes, thendividingthe eclipse eitheroneortwo light is estimatedbyhavingtheball tal projectionspeed of theball In thisexperiment,thehorizon- between thetwophotogates. with thetime it takes toroll to landafterleavingthetable fuse thetimeittakes the ball It’s easyforstudentstocon- tical, however). (don’t expectthemtobeiden- i.D Fig. 3 should benearlythesame Laboratory ManualLaboratory 7) (Experiment T 2 + T 3 . Thisisbecause , thetotal T 1 and i.C Fig. zontal speedofthethree runs. runs. from thesamepoint(marked withtape)on theramp foreachofthree (from speed.Release pointAtoB)findthehorizontal theball distanceontheramp intothehorizontal D). Divide thistimeinterval (point AinFigure D)tothetimeitleavestabletop(pointBinFigure ball totravel, from thefirstmomentitreaches theleveloftabletop Step 2: height oftheramp shouldbeat least30cm. Make oftheramp part thehorizontal atleast20cmlong. The vertical should notswayorbend. The ballmustleavethetable balls roll smoothlyandreproducibly, asshown inFigure D. The ramp Step 1: Procedure so thattheballlandsincanfirst measurements andcomputationswillbetopositionanempty soupcan when released heightonanincline. from acertain The finaltestofyour . • When thinkingabouthow fast,thinkaboutv=gt • When thinkingabouthow far,thinkabouty Vertical motion • When thinkingabouthow fast,thinkaboutv • When thinkingabouthow far,thinkaboutx=vt. Horizontal motion sets of “books”: onethattreats motionaccording thehorizontal to does not. The secret toanalyzingprojectile motionistokeeptwoseparate undergoes theacceleration duetogravity, motion whilethehorizontal andtheotherhorizontal. line motions:onevertical motion The vertical motion thatresults asthecombinationoftwostraight- canbedescribed and theotherthattreats motionaccording thevertical to Do Your istopredict goalinthisexperiment where asteelballwillland What happenswhenyou tosstherock sideways(Figure C)? The curved not Use astopwatch orlightprobe tomeasure thetimeittakes Assemble your ramp. Make itassturdy aspossiblesothesteel permit the ball to strike thefloor!Record theballtostrike permit theaverage hori- horizontal speed = ______= speed horizontal x y = = — vt 1 2 gt 2 time! = (12) = xt. gt 2 horizontally .

© Addison-Wesley Publishing Company, Inc. All rights reserved. Place thecanonfloorwhere you predict itwillcatchtheball. dicted range. Predict therange oftheball. Write theequationyou usedandyour pre- Step 5: Show your work inthefollowing space. in thecan. Write theequationthatrelates h time Step 4: 1. an emptysoupcanonthefloor. the ballmustdrop from thebottomendoframp inorder tolandin Step 3: Name likely hittheside of the can. measured fromthetrackto horizontal speedoftheballislarge.Theverticalheight The heightofthecanmakesavery distance the vertical Should theheightofcanbetakenintoaccountwhenmeasuring t it takestheballtofallfrom thebottomendoframp andland The range distanceoftravel isthehorizontal foraprojectile. Using equationfrom theappropriate thediscussion,find Using measure aplumblineandstring, distanceh thevertical equation for vertical distance:______equation forvertical predicted range R equation forrange: ______t h = ______= = ______= h? If so, makeyour measurements accordingly. top = ______= big of the can or the ball willmorethan difference—particularly ifthe and t. h should be Period Chapter 3Projectile Motion Measure the vertical distance. Predict therange. Date 27 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage28 28 Horizontally launchball. available. pendulum to launch the ball, if from aramp or use a ballistic Students caneitherrollaball Laboratory ManualLaboratory 7) (Experiment 2. Analysis initial speedsyou don’t know. to calculatespeedsingeneral! Do thisforoneortwofired ballswhose work backward and calculatetheball’s initialspeed. This isagoodway and fire it, and thenmeasure itsrange rather thanpredicting it,you can Suppose you don’t know speedofthesteelball.If you thefiring goahead Going Further 4. 3. percentage error.) Compute thepercentage error. (See Appendix 1onhow tocompute Compare theactualrange oftheballwithyour predicted range. their idealparabolictrajectories. This isthesamereasonthatline-drivegolfandbaseballstailofffrom target islocated,becauseairfrictionincreaseswithincreasingspeed. The ballismorelikelytomissthetargetfartherdownrange air resistance hadinthisexperiment? on therelease pointoftheballonramp. What role doyou think tothespeedatwhichitleftramp.proportion The speeddepends You probably noticedthatthe range oftheballincreased indirect error inmeasuringtheverticaldistance. Misses canbecausedbyairfriction,misalignmentofthetrack,and What maycausetheballtomisstarget? attainable. Answers willvary;typicallyapercentageerrorof5%orlessis

© Addison-Wesley Publishing Company, Inc. All rights reserved. 1. Analysis touching thehoopwithonlyonehand. hoop. The ideaistogetasmanynutspossibleintothebottleby the mouthofanarrow-mouth bottle. Stack thenutsontopof The gameissimple. Carefully on hoopvertically balance anembroidery Procedure toit? trick neath anentire placesetting?Can thatreally bedone, oristhere some Have you everseenmagicianson whipatableclothoutfromTV under- Discussion 12 1/4-inchnuts narrow-mouth bottle hoop 12-inch woodenembroidery Required Equipment/Supplies To explore theconceptofinertia. Purpose hpe :Newton’s FirstLawofMotion—Inertia Chapter 4: Name flicking yourwristtowhiskthehoopoutfromunder nuts. far Swing (say)yourrightarmhorizontallyacrossbody, grabbingthe The besttechniqueistofacethehoopsothatyousee thefullcircle. thewinner’sDescribe technique. 8 side (e.g.,leftside)of the hoopwhileyourarmisinmotionand Going Nuts Chapter 4Newton’s First Law ofMotion—Inertia Period Mathematical Level:none Conceptual Level:easy Learning Cycle:exploratory Lab Time: 1 Setup: <1 Date Inertia 29

Activity CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage30 30 Laboratory ManualLaboratory (Activity 8) 2. The motionofthehoopisnottransferredtonutsbecausewhen Explain why thewinner’s techniquewassuccessful. down intothebottle. mouth ofthebottle.Withhoopnolongerinplace,theydropstraight friction betweenthenutsandhoop.Inertiakeepsover part ofthehoopjustbelownutsgoes side ofthehoopispulledoutwardsharplyatstartswing, down, so thereisalmostno

© Addison-Wesley Publishing Company, Inc. All rights reserved. ate toward thetable’s edge. Step 3: belt foroneofthem. Step 2: of eachpulley. onthetable.floor andthecarts Place awoodblockonthetableinfront the tableedgeandhangmassesover themwiththemasseson a 200-gmasstotheotherendofeachstrings. Attach thepulleysto Step 1: Procedure lawisignored.what happenswhenthatimportant Newton’s firstlawofmotion. This activitydemonstrates inminiature belts inautomobilesandothervehiclesare apractical response to ing withconstantvelocityuntilaforce isappliedtothatobject. Seat Newton’s firstlawofmotionstatesthatanobjectinkeeps mov- Discussion 2 woodblocks 2 pulleys 2 smalldolls band rubber 2 200-ghookmasses 2 dynamicscarts 4 mofstring Required Equipment/Supplies collisions. To demonstrate how Newton’s firstlawofmotionisinvolvedin Purpose hpe :Newton’s FirstLawofMotion—Inertia Chapter 4: Name 9 Pull backside by thecarts sideandrelease themsotheyacceler- UsePlace onedolloneachcart. asaseat bandtoserve arubber Attach toeachoftwosmalldynamicscarts. 2mofstring Attach Buckle Up! Chapter 4Newton’s First Law ofMotion—Inertia Period without “seat belts.” Crash doll oncartwithand Adapted fromPRISMS. Mathematical Level:none Conceptual Level:easy Learning Cycle:application Lab Time: 1 Setup: <1 Date Inertia 31

Activity CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage32 32 Laboratory ManualLaboratory (Activity 9) 1. Analysis 2. cart crashedcart toastop? What stoppedthemotionofdollwithoutaseatbeltwhen The dollwiththeseatbeltremainedoncart. Was there anydifference forthedollwithaseatbelt? The dollwithouttheseatbeltkeptmovinguntilithitfloor.

© Addison-Wesley Publishing Company, Inc. All rights reserved. Show the appliedforce andtheotherforces witharrows. is theonlyenergy source you canuse. Make asketchof your method. and where theforce isuptoyour imagination. is exerted Your own body forceexerting onarope, chain,orcabletiedtothecar’s front end.How Step 2: locked, andthegearselectorseton “park” orinfirstgear. Step 1: Procedure force withbrains thanwithbrawn. Inexert. thisactivity, toshow you willtry afargreater thatyou canexert possibilities. Even withoutusingpulleys, you canmultiplytheforces you with your bare hands. You can dothesamewitharope, butwithmore You aforce canexert onaparked automobile if you push orpullonit Discussion automobile orotherlarge movable mass tree support orotherstrong vertical 7 mto10ofchainorstrong rope Required Equipment/Supplies To findatechniquetomove acarwhenits wheelsare locked. Purpose hpe :Newton’s FirstLawofMotion—Inertia Chapter 4: Name 10 Your goalistomove thecarclosertotree. You willdothisby Park withatree acaronlevelsurface infront ofit,thebrakes 24-Hour TowingService Chapter 4Newton’s First Law ofMotion—Inertia Period parked car. Devise techniquetomove demonstration. Try itandsee! a studentlaborasclass students whetheritbedoneas This isapopularactivitywith end isrecommended. hook (3inchesorso)oneach A heavychainwithalarge Mathematical Level:moderate Conceptual Level:difficult Learning Cycle:exploratory Lab Time: 1 Setup: <1 Statics and VectorsStatics Date 33

Activity CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage34 34 i.A Fig. Laboratory ManualLaboratory (Activity 10) 1. Analysis 3. 2. A becomessmaller, theforces F weight of thebook,issmall,whileF Look atFigure A.Suppose aforce F exerted onthestumpbyaverticalforcechainasinFigureA. stump andattemptingto pull it outdirectly, amuchgreaterforcecanbe For example, instead of connecting a large chain from a tractor to a tree how thismightbepossible. stumps, straighten dentsincarfenders, andpulllooseteeth!Explain This methodformakingalarge force isusedtofelltrees, pull appliances, beamsinconstruction,etc. Bow andarrow, stringtighteners(fortennisrackets,etc.),dental cation.” List othersituationsthatcouldusethistechniquefor “force multipli- the car. to explainhow asmallsidewaysforce canresult inalarge pullon inChapter4ofyour text.Useexplained further avectordiagram must adduptozero. The force strongman. forF The sameistrue force onwhateveritisattachedto, inthiscase, handofthe theright vectors angles tothehorizontal. Tension inthechaincanthenbeshown as F 1 and F 2 . Since thesystemisnotaccelerating, allforces F 1 1 and 2 is thetensioninchainand . The force . The 3 1 is appliedtoachainatright and F 2 become larger. This ideais F 2 are large. Astheangle F 3 , inthiscasethe

© Addison-Wesley Publishing Company, Inc. All rights reserved. released. aconstantpullingforceand exert ontheskater whentheskateris Step 3: balance byThe skaterholdsaspring itshook. Another studentmuststandbehindthe0-mmark andhold the skater. Step 2: straight, andlevel.Gym areas orhallwayswork well. 0 m,510and15m. The pathalongthefloorshouldbesmooth, Step 1: Procedure activity, you thatinfluence acceleration. willinvestigatesomevariables backasaccelerating arunning throughdescribe thedefensiveline. In this negative acceleration whenitcomestoastop. We hearsportscasters Most ofushavefelttheacceleration ofacarasitleavesstopsignorthe Discussion tape meterstick stopwatch balance spring roller skates orskateboard Required Equipment/Supplies To investigatetherelationship between mass, force, andacceleration. Purpose hpe :Newton’s SecondLawofMotion— Chapter 5: Name 11 With piecesoftape, of mark positionsontheflooratintervals A third studentmustgrasp balance theotherendofspring A studentmustputontheskatesandstand0-m mark. Force and Acceleration Force Getting Pushy Chapter 5Newton’s Second LawofMotion—Force andAcceleration Period Pull onskater. . . catchskater. Mark offdistances. Adapted fromPRISMS. Mathematical Level:easy Conceptual Level:moderate Learning Cycle:exploratory Lab Time: >1 Setup: <1 Variables Affecting Date Acceleration 35

Activity CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage36 36 Laboratory ManualLaboratory (Activity 11) Data TableB Data TableA skaters asbefore. Record your results inData Table B. throughout thedistanceskaterispulled,butusingsamethree Step 5: directions thetrial. slightlyduring tochange skater maynotbeholdingtheskatesparallel ormaybetrying mass, butkeepingtheforce thesame. If theresults are inconsistent,the Step 4: Data Table Aalongwiththereadings balance. onthespring takes togetthe5-m,10-m,and15-mmarks, andrecord thisdatain the skaterispulled.Donotpullharder to “get going.” Time how longit The pullermustmaintainaconstantforce throughout thedistance Repeat withthepullermaintainingadifferent Repeat twice, theexperiment usingdifferent the skaterstovary constant force

© Addison-Wesley Publishing Company, Inc. All rights reserved. 6. 5. 4. 3. 2. 1. Analysis Name There mustbeanother3-N force results. How canthisbeexplained? Suppose a3-Nforce isappliedtotheskater and nomovement The greatertheforce is, the greater theaccelerationis. depend upontheforce? When themassofskaterissame, how doestheacceleration The greaterthemassis,smalleraccelerationis. the mass? When theforce isthesame, how doestheacceleration dependupon without measurements. The accelerationisprobablythesame,butthistoosubtletoshow alongthemeasuredyou andfarther proceed farther distances? What happenstotherate ofincrease inspeed—theacceleration—as The speedincreases. the measured distances? along What happenstothespeedasyou andfarther proceed farther goes faster and fasterwhen pulled. Student observations should cause them to reject this notion. The skater or reject thisnotion? required toproduceconfirm aconstantspeed.Doyour observations Until thetimeofGalileo, peoplebelievedthataconstantforce is opposing Chapter 5Newton’s Second LawofMotion—Force andAcceleration the 3-Nforceapplied. Period Date 37 CP02_SE_LAB_Ch01-13 3/5/01 11:32 AM Page 38 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage39

© Addison-Wesley Publishing Company, Inc. All rights reserved. tance themasscanfallfrom thetable tothefloor. Step 2: ways pullonthecart. the direction oftheforce from adownward pullonthemass intoaside- Step 1: Procedure relationship between massandacceleration shouldbecomeevident. asystem and thehangingweight comprise You willapplytheforce by suspending aweight over apulley. The cart dynamics cart. You willapplythesameforce ofdifferent tocarts mass. same force isappliedtoeach.In you willaccelerate this experiment a ple undergo greater acceleration thanmore massivepeople when the affect theseaccelerations? speed. Andwhentheycometoastop, theydecelerate. How doesmass off speed.Cars accelerate from astopsignuntiltheyreach cruising Airplanes accelerate from rest untiltheyreach ontherunway theirtake- Discussion stopwatch, ticker-tape timer, or graph paperoroverhead transparencies masking tape paper clipsorsmallweights string balance triple-beam pulley withtableclamp 1 50-ghookmass 4 500-gmasses(2comewithPasco carts) 2 Pasco andtrack dynamicscarts meterstick Required Equipment/Supplies To investigatetheeffectofincreases inmassonanaccelerating system. Purpose hpe :Newton’s SecondLawofMotion— Chapter 5: Name 12 In Activity 11, “Getting Pushy,” you discovered thatlessmassivepeo- light sources light probes withinterface computer Mark thanthe dis- offadistanceonthetabletopslightlyshorter Fasten apulley over theedgeoftable. The pulleywillchange Force and Acceleration Force Changing Mass Constant Force and and accelerate together. A Chapter 5Newton’s Second LawofMotion—Force andAcceleration Period Set uppulley-and-cartsystem. masses workwell). masses (either500-gor1-kg gle cartloadedwith 5 identical the Pascocartsbyusingasin- can easilybesubstitutedfor ball-bearing dynamicscarts with thecarts.Thetraditional additional massesthatcome the samemassas500-g added featureofhavingabout results. Thecartsalsohavethe track systemgiveexcellent The Pascodynamicscartsand Mathematical Level:difficult Conceptual Level:moderate development Learning Cycle:concept Lab Time: >1 Setup: <1 Mass and Acceleration Mass Date 39

Experiment CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage40 40 Compute theacceleration. and repeat. Remove massesfromthecart Set uptimingsystem. the pulley. small woodblocktoprotect a pieceof foam orevena using the Pasco setup, position collide with the pulleys. If not track sothatthe carts don’t stopping baronthePasco Remind studentstoadjustthe i.A Fig. Laboratory ManualLaboratory 12) (Experiment Data TableA accelerating systemthatrelates distanced,acceleration a,andtimet. pute theaccelerations ofthesystem. To dothis, usetheequationforan Step 8: Table A,alongwiththeaverage timeforeachmass. each time(thelastremoving Record thetopcart). thetimesinData Step 7: and record theaverage time. The timerstopswhenthesecondlightprobe iseclipsed. that asitisreleased, thetimer. iteclipsesthefirstlightprobe andstarts distance isthebetween twolightprobes. Position so thecart teacher how tooperate thisdevice),oracomputerwithlightprobes. The falling weight. You coulduseastopwatch, aticker-tape timer(askyour Step 6: theexperiment. falling weight thesameatalltimesduring ment. AddKeep a50-ghookmasstothepaperclipcounterweight. this Step 5: bying theexperiment adjustingthestopbarondynamics track.) your teacher abreak! Stop before thecart itcrashes intothepulleydur- ispushedslightlyitmovesthat whenthecart ataconstantspeed.(Give so add enoughpaperclipsorsmallweights totheotherendofstring thread itover thepulley, asshown inFigure A. To effects, offsetfrictional withmaskingtape.and carts Tie and tothecart oneendofthestring It tosecure500-g massesonthetopcart. maybenecessary themasses Step 4: paper clipcounterweight. Data Table A.Donotincludethe50-ghangingmassor mass ofthe Record andthefouradditionalmassesin thetotalmassofcart(s) Step 3: Repeat three times, recording thetimesinData Table A.Compute Use theaverage timesforeachmassfrom Steps 5and6tocom- Repeat Step 5fivetimes, removing a500-gmassfrom thecart There are andthe ofwaystotimethemotioncart avariety Practice accelerating afewtimestoensure thecart proper align- Nest ontopofoneanother, thetwodynamicscarts andstackthe Use themassofcarts. balancetodetermine atriple-beam d = — 1 2 at 2

© Addison-Wesley Publishing Company, Inc. All rights reserved. 2. 1. Analysis and your distanceinmeters, your unitsofacceleration willbem/s the acceleration, a.Provided you express your massunitsin kilograms Rearrange thisequationtoobtaintheacceleration. acceleration axis)vs. (vertical axis). mass(horizontal Step 9: Name For constantappliedforce,accelerationdecreasesasmassincreases. tion? force, how doesincreasing themassofanobjectaffectitsaccelera- Share your results withotherclassmembers. For aconstant applied increases isacceptable. suggests thatandshowstheaccelerationdecreasingasmass The graphshouldlooklikesomekindofhyperbola.Anythat graph oracurve? yourDescribe graph ofacceleration vs. mass. Is itastraight-line alwaysacceleratesThe cart through thesamedistanced.Calculate Record your accelerations inData Table A. Using anoverhead transparency orgraph paper, makeagraph of a = 2d — t 2 Chapter 5Newton’s Second LawofMotion—Force andAcceleration 2 Period . Graph yourdata. Date 41 CP02_SE_LAB_Ch01-13 3/5/01 11:32 AM Page 42 CP02_SE_LAB_Ch01-13 3/5/0111:32AMPage43

© Addison-Wesley Publishing Company, Inc. All rights reserved. it onthehangingweight. without changingthemass by removing andplacing massfrom thecart keeping themassofsystem constant. The appliedforce isincreased force systemaffectsits acceleration onacart-and-falling-weight while mass—to seehow itaffectstheacceleration oftheentire system. accidental, however. In doingso, you changedonlyonevariable— system actually addingmasstothecart-and-falling-weight moving exactlythesameamount.By you were addingmasstothecart, asystem. together form doesn’tThe cart move withoutthefallingweight and thefallingweight cart But isreallymass ofthecart. the cart ofasystem part how theacceleration wasaffectedby ofadynamicscart increasing the the other, asystem. thetwosoconnectedtogetherform same amount.Since motorcan’t theelectric move onewithoutmoving Thus, theelevator doesn’t move moving withoutthecounterweight the areThe elevator andthecounterweight connectedby astrong cable. up Have you sitegoes evernoticedwhenanelevator cageataconstruction Discussion stopwatch, ticker-tape timer, or graph paperoroverhead transparency paper clips string 6 20-ghookmasses pulley withtableclamp masking tape Pasco andtrack dynamicscart Required Equipment/Supplies of asystem. To investigatehow increasing theappliedforce affectstheacceleration Purpose hpe :Newton’s SecondLawofMotion— Chapter 5: Name that a large counterweight (usuallymadeofconcrete)that alarge counterweight comesdown? 13 In you willinvestigate how thisexperiment, increasing theapplied Adding rather masstothecart thantothefallingweight was In 12, Experiment “Constant Force andChangingMass,” you learned light sources light probes withinterface computer Force and Acceleration Force Changing Force Constant Massand —just astheelevator andthecounterweight Chapter 5Newton’s Second LawofMotion—Force andAcceleration consisting ofthe . not Period attach themassestostring. dents improviseamethodto will do.Inthatevent,havestu- tutes (suchasslottedmasses) masses, any20-gmasssubsti- If youdon’t have6hooked 100-g, and 200-gmasses. cartloadedwith50-g, single the Pascocartbyusinga cart caneasilysubstitutedfor tional ball-bearingdynamics results. However, thetradi- track systemgiveexcellent The Pascodynamicscartand Mathematical Level:difficult Conceptual Level:difficult development Learning Cycle:concept Lab Time: >1 Setup: <1 Force and Acceleration Force Date 43

Experiment CP02_SE_LAB_Ch01-13 3/5/0111:33AMPage44 44 the massconstant. after usingitinordertokeep each massbackonthecart string. Besure masses ontheend of the Some trials willrequiretwo 250-g massesonthestring. Step 6 for 150-g, 200-g, and 50 gramseachtrial. Repeat mass of the hanging weight by string, soastoincrease the place it on the end of the 100-g massfromthecartand it backonthecartand take a mass from thestringand place dents must remove the 50-g If usinga ball-bearing cart,stu- Increase theappliedforce. Measure theaccelerationtime. just asitisreleased. cart sothatitstartsthetime Students shouldreleasethe Set uptimingsystem. weight system. Set upcart-and-hanging- Laboratory ManualLaboratory 13) (Experiment students return Data TableA your datainData Table A. withtheother20-g mass.of thestring Make several andrecord runs Step 6: data andcomputetheaverage ofyour three inData trials Table A. and damagesthepulley!Repeat atleasttwice. eachtrial Record your before time ittakestoaccelerate toward your cart the pulley. Catch thecart Step 5: andhangitontheendofstring. the cart Step 4: the secondlightprobe iseclipsed. thetimer.it eclipsesthefirstlightprobe andstarts The timerstopswhen tance between twolightprobes. Position sothatasitisreleased, thecart device works), oracomputerwithlightprobes. The distanceisthedis- stopwatch, aticker-tape timer(your teacherwillshow you how this Step 3: theexperiment. atanytimeduring terweight rolls onthe track ortablewithconstantspeed.Donotremove thiscoun- ismoved sothatwhenthecart the endofstring by asmalltap, it tional effects, placejustenoughpaperclipsorothersmallweights on pulley, andtiealarge papercliptotheendofstring. To offsetfric- Step 2: Masking tapemayberequired toholdthemassesinposition. 12, except withsix20-gmasses. thatyou should loadthedynamicscart pute theacceleration usingtheformula: 12,youExperiment measured accelerated thetotaltimecart tocom- The samegeneral procedure 12willbeusedhere. usedinExperiment In Step 1: Procedure it crashes intothepulleyandspewsyour massesallover thefloor With your timingsystemallset,release andmeasure thecart the You ofways. cantimethesystem inavariety You couldusea Remove andplaceitontheend another20-gmass from the cart For remove thefirsttrial, oneofthehooked20-gmassesfrom passtheotheroverAttach tothecart, oneendofthestring the Set upyour apparatus muchthesameasyou didinExperiment a = 2d — t 2

© Addison-Wesley Publishing Company, Inc. All rights reserved. in metersandyour acceleration willhaveunitsofm/s “2F,” andsoon. caused by thesingle20-gmass “F,” theforce causedby two20-gmasses 4. 3. 2. 1. Analysis the samedistanced,acceleration equals2d/t axis) vs. force axis).Since (horizontal alwaysaccelerates thecart through use anoverhead transparency tomakeagraph ofacceleration (vertical Step 8: Data TableA. weight by 20grams eachtime. Make several andrecord runs your datain Step 7: Name proportional totheforceandinversely proportional tothemass(a The experimentalfindingsshouldshowthattheacceleration isdirectly mass increases. The acceleration is stant force isapplied,theacceleration ofthesystemdecreases In (orshouldhave!)thatwhen acon- 12,you Experiment learned Yes; atleast itshouldbe! same ineachcase? Was themassofaccelerating +fallingweight) the system(cart The accelerationincreaseswithincreasingforce. increases? Does theacceleration increase ofthecart ordecrease astheforce The graphisastraight-linegraph. produce astraight-line graph? graph oracurved yourDescribe graph ofacceleration vs. force. Doyour datapoints eration. come upwithageneral relationship between force, mass, andaccel- the appliedforce. Combine theresults 12and13to ofExperiments masses) increases. That is, theacceleration is system increases astheforce appliedtoit(theweights ofthefalling mass ofthesystem.Here 13,theacceleration inExperiment ofthe With thehelpofyour teacher, calculatetheaccelerations and Repeat Step 5fivetimes, increasing themassoffalling inversely proportional Chapter 5Newton’s Second LawofMotion—Force andAcceleration 2 directly proportional . Express your distance 2 . Call theforce to the as its Period ~ m — F to ). Graph yourdata. Date 45 CP02_SE_LAB_Ch01-13 3/5/01 11:33 AM Page 46 CP02_SE_LAB_Ch14-20 3/5/01 11:34 AM Page 47

Name Period Date

Chapter 5: Newton’s Second Law of Motion— Effect of Air Friction Force and Acceleration on Falling Bodies

14 Impact Speed

Purpose

To estimate the speed of a falling object as it strikes the ground. Setup: <1 Lab Time: >1

Required Equipment/Supplies Learning Cycle: application Experiment Conceptual Level: difficult stopwatch Mathematical Level: difficult string with a rock tied to one end object with a large drag coefficient, such as a leaf or feather ® ® Thanks to Verne Rockcastle for Styrofoam plastic foam ball or Ping-Pong table-tennis ball this lab.

Discussion

The area of a rectangle is its height multiplied by its base. The area of a triangle is its height multiplied by half its base. If the height and base are measured in meters, the area is measured in square meters. Consider the area under a graph of speed vs. time. The height represents the speed measured in meters per second, m/s, and the base represents time measured in seconds, s. The area of this patch is the speed times the time, expressed in units of m/s times s, which equals m. The speed times the time is the distance traveled. The area under a graph of speed vs. time represents the distance traveled. This very powerful idea underlies the advanced mathematics called integral calculus. You will investigate the idea that the area under a graph of speed vs. time can be used to predict the behavior of objects falling in the presence of air resistance. If there were no air friction, a falling tennis ball or Styrofoam ball would fall at constant acceleration g so its change of speed is This lab is very sophisticated v – v = gt f i conceptually but very elegant and relatively simple to per- where vf = final speed form. Challenge your best stu- vi = initial speed dents to try it! g = acceleration of gravity t = time of fall

A graph of speed vs. time of fall is shown in Figure A, where vi = 0. The y-axis represents the speed vf of the freely falling object at the end of any time t. The area under the graph line is a triangle of base t and 1 — height vf , so the area equals 2 vft. To check that this does equal the distance traveled, note the follow- – ing. The average speed v is half of vf . The distance d traveled by a con- © Addison-Wesley Publishing Company, Inc. All rights reserved. All rights Inc. Company, Publishing © Addison-Wesley

Chapter 5 Newton’s Second Law of Motion—Force and Acceleration 47 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage48 48 for Talent Contestin1988. by theWestinghouse Search 1986, andJaywasrecognized California StateScienceFairin Physics Divisionofthe program wonfirstprizeinthe Obernolte. Theheart of this same titleprogrammedbyJay the computersimulationby This labisgreatlyenhancedby Laboratory ManualLaboratory 14) (Experiment tal axisupto the theoretical speedvs. timeline. (In Figure B, thisline is time, draw line from thetheoretical avertical timeoffallonthehorizon- time line. time curvemustbethesame asthearea under thetheoretical speed vs. same withorwithoutairresistance. Thearea undertheactualspeedvs. for noairresistance. The height distance fallenandthetime offall?Calculate thetheoretical timeoffall awayfrom thetheoreticalcurves straight line. and greater withtheincreasing speed. The graph ofactualspeedvs. time difference is smallatfirst,butgrows asairresistance becomesgreater value of9.8m/s (say from thetwelfth floorofabuilding),thefalltakes3.5s, stantly accelerating bodyisitsaverage speed tion fall looks like the curve inFigurefall lookslikethecurve B. objects, includingtennisballs. Agraph oftheactualspeedvs. thetimeof the theoretical timeof2.96s. is Airfriction i.B Fig. i.A Fig. Is there awaytosketchtheactualspeed vs. from onlythe timecurve Since airresistance reduces the acceleration tobelow thetheoretical If you timeatennisballfallingfrom rest adistanceof43.0minair t of travel. It isthe distancefallen.Onagraph oftheoretical speedvs. 2 , thefallingspeedislessthantheoretical speed. The d = v – t or d = from whichtheobjectisdropped isthe — 1 2 v f t not negligible v – multiplied by thedura- for most longer than

© Addison-Wesley Publishing Company, Inc. All rights reserved. the object’s probable impactspeed. pled region over tothespeedaxis. Where itintersectsthespeedaxisis Step 8: the samemass. again. and try Your approximation isdonewhenthetworegions have regions. If theirmassesare notthesame, adjustyour actualspeedcurve the cardboard andcutthemout. Then measure themassoftwo wall andproject your transparency ontoit. Trace your tworegions onto region. your stippledregion shouldbethesameasthatofcross-hatched time line, usingtheexamplementionedindiscussion. The area of actual speedvs. timecurve, outtothepointwhere itcrosses theactual Step 7: the theoretical speedvs. timeline. time line. Draw linefrom theactual theothervertical the leaving outtheactualspeedvs. timecurve. Draw linefrom onevertical Step 6: ball toreach theground ifthere were noairresistance. cal timeoffallforyour ball.Remember, thisisthetimeitwouldtake Step 5: tennis ball. lineoftheactualtimegivesprobable impactspeedofthe vertical the actualspeedvs. timecurve. The pointwhere crosses the thiscurve areas underthetwographs are thenequal. cal speedvs. timelineduetodecreased speed(cross-hatched area). of fall(stippledarea) equalsthearea subtracted from below thetheoreti- Sketch sothatthearea thiscurve addedbelow itduetoincreased time linebelowcrosses the secondvertical thetheoretical speedvs. timeline. time line” inFigure B.) Sketch ofactualspeedvs. acurve timethat the approved methodsofSteps 1and2. Step 4: Step 3: measure thedistanceobjectfalls. Step 2: associated withthetimeryou use. long-fall drop site, releasing various techniques, andreaction times Styrofoam ballandclockitstimeoffallwithin 0.1sorbetter. Consider a Step 1: Procedure the labeled “theoretical timeline.”) Draw lineupward anothervertical from Name theoretical actual One possiblewaytodothisistapeapieceofcardboard tothe Your group shouldchooseastrategy todrop aPing-Pong ball or Draw ofyour stip- corner linefrom ahorizontal theupperright Starting sketchyour from approximation theorigin, forthe Using anoverhead transparency orgraph paper, trace Figure B, Using your measured value fortheheight,calculatetheoreti- Measure theheightandfallingtimesforyour objectusing Submit your plantoyour teacherforapproval. Devise amethodthateliminatesasmucherror aspossibleto time of fall on the horizontal axis. (This lineislabeled “actual axis.time offallonthehorizontal (This time offallforyour heightuptothetheoretical speedvs. theoretical time = ______= time theoretical actual time of fall = ______= fall of time actual height = ______= height This isafairapproximation to Chapter 5Newton’s Second LawofMotion—Force andAcceleration time offallupto Period The Predict probableimpactspeed. Sketch curve on graph. speed lines. Draw theoretical andactual time. Compute theoretical falling times. Measure height and falling Submit proposaltoteacher. Measure falling height. Devise droppingstrategy. Date 49 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage50 50 Laboratory ManualLaboratory 14) (Experiment 1. Analysis 5. 4. 3. 2. 6. does your actualspeedvs. compare timecurve withtheirs? Have your teacheroverlap your graph withthoseofothers. How before itbecamehorizontal. take muchlongerandwould arrive atamuchhighervalue of speed It wouldquicklybecomehorizontal. The baseball’s would speed curve that ofabaseball? would itsspeedvs. timegraph looklike?How mightitdifferfrom If you dropped alarge leaffrom theEmpire State Building, what greater. d =v different-sized symbolssuchasthoseusedonpage66ofyour text. speeds andtimescompare withandwithoutairfriction? Try touse Howfallen isthesamewithorwithoutairfriction. dotheaverage The equationfordistancetraveled is The height from whichthe object isdropped. What doesthearea underyour speedvs. timegraph represent? These objectsencountersmallairresistance. close tothetheoretical speedvs. timeline? What canyou sayaboutobjectswhosespeedvs. are timecurves Answers willvarydependingontheobjectdropped. so theobjecthasreacheditsterminalspeed. If thegraphishorizontal,it’s becausethespeed isnolongerchanging, speedbyterminal glancingatanactualspeedvs. timegraph? accelerating. How couldyou tellwhetheranobjecthadreached its The – terminal t = v – t; theaveragespeedwithairfrictionisless,buttime speed ofafallingobjectistheatwhichitstops d = v – t. In thislab, thedistance

Name Period Date

Chapter 5: Newton’s Second Law of Motion— Components of Force Force and Acceleration 15 Riding with the Wind

Purpose

To investigate the relationship between the components of the force that Setup: 1 propels a sailboat. Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: difficult dynamics cart fitted with an aluminum or cardboard sail Mathematical Level: moderate protractor electric fan ruler pulley mass hangers Adapted from PRISMS. set of slotted masses string Pasco has an excellent fan cart that can be used as a sailboat. However, students must still use some kind of handheld fan, Discussion not the one on the cart!

In this experiment, you will use a small model sailboat and an electric fan. The physics of sailing involves vectors—quantities that have both magnitude and direction. Such directed quantities include force, velocity, acceleration, and momentum. In this lab, you will be concerned with force vectors. In Figure A, a crate is being pulled across a floor. The vector F represents the applied force. This force causes motion in the horizontal direction, and it also tends to lift the crate from the floor. The vector can be “resolved” into two vectors—one horizontal and the other vertical. The horizontal and vertical vectors are components of the original vector. The components form two sides of a rectangle. The vector F is the diagonal of this rectangle. When a vector is represented as the diagonal of a rectangle, its components are the two sides of the rectangle. Whatever the direction of wind impact on a sail, the direction of the resulting force is always perpendicular to the sail surface. The magni- Fig. A tude of the force is smallest when the wind blows parallel to the sail— when it goes right on by without making any impact. The force is largest when the sail is perpendicular to the wind—when the wind makes full impact. Even if the wind hits the sail at another angle, the resulting force is always directed perpendicular to the sail. The keel of a sailboat is a sort of fin on the bottom of the boat. It helps prevent the boat from moving sideways in the water. The wind force on the sail can be resolved into two components. One component, K (for keel), is parallel to the keel. The other component, T (for tip), is perpendicular to the keel, as shown in Figure B. Only the component K contributes to the motion of the boat. The component T tends to move

Chapter 5 Newton’s Second Law of Motion—Force and Acceleration 51 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage52 52 Sail theboatatanangle. Sail theboatdirectlydownwind. upwind. Try tosailtheboatdirectly i.C Fig. Laboratory ManualLaboratory 15) (Experiment Do notlethairorfingersgetinthebladesoffan. fan.Do tric CAUTION: In thefollowing procedure, you willbeworking withanelec- tacking. points intheforward direction. The procedure ofgoingupwind iscalled wind. But aboatcanangle 3. behind, parallel tothewheels. 2. keeping thesailperpendiculartowheels, asshown inFigure C. 1. blowing onthefront from the fan.Position thesailperpendiculartowheels. Start thefan the keelisblown straight backward. No boatcansail the wind. wind force becomeszero. The fastestspeeddownwind isthespeedof If theboat isgoingasfastthewind,thensailsimplysags. The as thewind.Asboatgoesfaster, thewindforce onthesaildecreases. Step 3: Step 2: Step 1: Procedure pendicular tothesail.Remember thatthelength Step 4: What happenstothecart? How move? doesthecart What happenstothecart? A boatpointeddirectly anglesto intothewindwithitssailatright Any boatwithasailcandownwind, that is, inthesamedirection The cartgoesforwardalthoughsomewhatslowerthan inStep2. The cartgoesforward. The cartgoesbackward. eoiintesi ta4°angletothewheels. Direct thewind Reposition thesailata45° Direct thewindfrom behind Position withitswheels(thekeel)parallel thecart tothewind Use todraw aruler avectorthatrepresents thewindforce per- of the cart withthewindparallelof thecart tothe wheels. into thewindsothatacomponentofforce K the cart andparallelthe cart tothewheels, of thevectoryou draw directly into the

© Addison-Wesley Publishing Company, Inc. All rights reserved. mass of1kghasaweight of10N. from thepulley. Record themassrequired tobalancethecart. the pulleyandremoving tomove thesmallestmasscauses cart away tomovewhen addingthesmallestmassyou havecausesthecart toward just balancesthewindforce onthecart. The windforce isbalanced adding themuntiltheweight ofthemasses(includingmass hanger) the sail.Slowly force depends onhow closethefanistosail.Place thefan closeto 90°. Holding thefanonitshighestspeed setting. turn thecart, The wind sothatthefullforcethe pulleyandcart thesailat ofthewindstrikes perpendicular tothedirection Place thefandirectly ofthecart. between other endover thepulley. Attach Set amasshangertothestring. thesail Attach andthread tothecart oneendofapiecelightweight string the Step 7: K 4. from the front, asshown inFigure D. Step 6: vector diagram forthiscase. Step 5: nents. Labeltheforces andeachcomponentonthediagram. represents thesize oftheforce. Split thevectorintoits Name components. Calculate theweight ofthismass, usingtheapproximation that a Draw avectorrepresenting thewindforce, andsplititintoits It sailsagainstthewind(atanangle). sailagainstorwiththewind? Does thecart Set upapulleyontheedgeoftable, asshown inFigure E. eetSe u iettewn ta6°angletothewheels Repeat Step 3butdirect thewindata60° Repeat Step 3withthefanperpendiculartowheels. Make a The vectordiagramshouldbeidenticaltothatinStep4. add very smallmassestothe masshanger.add very Continue weight = ______= weight mass = ______= mass Chapter 5Newton’s Second LawofMotion—Force andAcceleration T and K compo- T Period and i.D Fig. i.E Fig. Change thewinddirection. Change thewinddirection. Date 53 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage54 54 Laboratory ManualLaboratory 15) (Experiment 6. the cart. wind. Record themassandcalculateweight required tobalance 5. 8. 7. Analysis Step 8: uration? What istheamountofwindforce actingonthesailinthisconfig- Answers willvary;abalancingmassof100gistypical,sotheforce uration? What istheamountofwindforce actingonthesailinthisconfig- force whenthewind is perpendiculartothesail.Ittakestwovector tothe wind, the wind force isgreater than halfthe wind For asail45° Justify your answer withavectordiagram. than half,equaltoorgreater thanhalfthewindforce at90°? tothewind,iswindforce less at45° When thesailisoriented When thesailisperpendiculartowind,windforcelargest. greatest windforce? ofthesailwithrespectWhich orientation tothewindprovided the Step 7.Thecorrectanswershouldbe0.707timestheof6. Answers willvary;studentsmaymeasureabouthalftheanswerof would beabout1N. other, toequalaresultantvector1unitlong. components, 0.707 (orabout 0.7) unitslongandperpendicular toeach eetSe ,btti ieoin h ala 5 angletothe Repeat Step thesailata45° 7,butthistimeorient weight = ______= weight mass = ______= mass

Name Period Date

Chapter 6: Newton’s Third Law of Motion— Action and Reaction Action and Reaction

16 Balloon Rockets

Purpose

To investigate action-reaction relationships. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy balloons Mathematical Level: none paper clips guide wire or string Adapted from PRISMS. tape straws

Discussion

Early in this century, the physicist Robert Goddard proposed that rockets would someday be sent to the moon. He met strong opposition from people who thought that such a feat was impossible. They thought that a Activity rocket could not work unless it had air to push against (although physics types knew better!). Your mission is a less ambitious one—to construct a balloon rocket system that will travel across the room! Scientists look for the causes of observed effects. As you construct your balloon rockets and improve upon the design, think about how you would explain to a friend how and why your design works. Procedure

Step 1: String the guide wire or string across the room. Make a rocket Devise a rocket system. system that will propel itself across the classroom on the wire or string. Use a balloon for the rocket power, and the straw, paper clips, and tape to make a guidance system. Draw a sketch or write a description of your design. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 6 Newton’s Third Law of Motion—Action and Reaction 55 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage56 56 Modify systemdesign. Laboratory ManualLaboratory (Activity 16) 2. 1. Analysis wire requires both technique and ingenuity. two balloon “fuel tanks” propel across the room without snagging the guide This activityisnotunlikethe work ofthe astronauts—challenging! Making will getacross theroom andthencomeback Step 2: write a description ofyour design. adescription write more difficulttimegettingtothemooniftherewereair inouterspace. the balloonwouldhaveagreateracceleration.Rockets resistance actuallyhindersaccelerationoftheballoon,andwithoutit, balloon, notthesurroundingair. Thesurroundingairwithits Yes, itisthe airthatissqueezedoutoftheballoonpushes Would therocket actionstilloccur ifthere were nosurrounding air? (reaction). and theairthatissqueezedoutinturnpushesbackonballoon The stretchedballooncollapsesandforcesairoutthenozzle(action) Explain whyaninflatedballoonmoves whentheairescapes. Getting there isonlyhalftheproblem! Make arocket systemthat again. Draw asketchor

Name Period Date

Chapter 6: Newton’s Third Law of Motion— Action and Reaction Action and Reaction

17 Tension

Purpose

To introduce the concept of tension in a string. Setup: <1 Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development 3 large paper clips Conceptual Level: moderate 3 large identical rubber bands Mathematical Level: none 1 m of strong string 500-g hook mass ring stand spring scale Rubber bands should be thick enough so that the percentage ruler stretching is relatively small for marking pen the forces applied in the experiment.

Discussion

When you put bananas on a hanging scale at the supermarket, a spring is stretched. The greater the weight of the bananas (the force that is exerted), the more the spring is stretched. Rubber bands act in a similar way when stretched. For stretches that are not too great, the amount of the stretch is directly proportional to the force. If you hang a load from a string, you will produce a tension in the string and stretch it a small amount. The amount of tension can be measured by attaching the top end of the string to the hook of a spring scale hanging from a support. The scale will register the tension as the sum of the weights of the load and the string. The weight of the string is usually small enough to be neglected, and the tension is simply the weight of the load. Is this tension the same all along the string? To find the tension at the lower end of the string you could place a second scale there, but the weight of the added scale would increase the tension in the top scale. You need a scale with a tiny mass. Since a rubber band stretches propor- tionally with the force, you could use it to measure the tension at the lower end of the string. Its tiny weight will not noticeably affect the reading in the top scale. In this activity, you will use rubber bands to investigate the tensions at different places along short and long strings supporting the same load.

Procedure

Step 1: Without stretching them, place three identical large rubber Mark rubber bands.

© Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley bands flat on a table. Carefully mark two ink dots 1 cm apart on each of the rubber bands. Chapter 6 Newton’s Third Law of Motion—Action and Reaction 57 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage58 58 bands. Hang loadfromstringandtwo string. Hang loadfromonebandand 3-rubber-band stretch. Cut string. i.A Fig. Laboratory ManualLaboratory 17) (Experiment Record your findings. bytom ofthestring thestretches measuring bands. ofthetworubber stretch ofthe addedband.Compare thetensionsattopandbot- band,mentallypredictattaching thebottomrubber theamountof andtheload,asshownend ofthestring inFigure E. While you are Step 7: band. the marks oftherubber in Figure D. Record reading thespring-scale andthedistancebetween band.Suspendrubber asshown theloadonotherendofstring, totheremainingclip hook,connectoneendofa25-cmlengthstring Step 6: of thethree bands. Record your results. three bandsconnectedasshown rubber inFigure C.Measure thestretch Step 5: scale.the spring between band.Alsorecord theinkmarks ontherubber thereading on scale. insidethespring bandandthespring both therubber band asshown inFigure B. Note thattheweight oftheloadstretches the scalehook.Suspend the500-gloadfrom thelower endoftherubber extends over theedgeoftable. bandover Place oneendofarubber Step 4: Step 3: 50 cm. Tie intoaloop. eachendofstring Step 2: While theloadissuspended,measure andrecord thedistance distance between marks ofbottomband=______With theuseofpaper-clip hooks, repeat theprevious stepusing Using apaper-clip bandbetween thelower arubber hook,insert bands.Disconnect theloadandtwoofrubber Using apaper- Suspend standsuchthatit scalefrom thetopofaring thespring Bend the paperclipsintodoublehooks, asshown inFigure A. Cut into2lengthsof25cmeach,and1length a1-meterstring distance between marks oftopband=______distance between marks ofbottomband=______distance between marks ofmiddleband=______distance between marks oftopband=______tension (spring-scale reading)tension (spring-scale ______= distance between marks ofband=______tension (spring-scale reading)tension (spring-scale ______= distance between marks =______tension (scalereading) =______

© Addison-Wesley Publishing Company, Inc. All rights reserved. i.BFg i.DFg i.FFg i.H Fig. G Fig. F Fig. E Fig. D Fig. C Fig. B Fig. 1. Analysis After your prediction, measure andrecord your findings. are substituting,mentallypredict how theinkmarks willbe. farapart withthetensionatitsends.tension atthemiddleofastring While you in Figure G)forthe50-cmstring. This arrangement istocompare the joined by paper-clip bandinthemiddle(asshown hookswitharubber Step 9: findings. Makestring. amentalprediction before you measure andrecord your F, dependsonthelengthof toseewhetherthetensioninstring Step 8: Name readings ofSteps5and7. string’s weightisnegligible).Evidenceforthis isthesamescale spring scalehasnoeffectonthespring-scalereading (because the The lengthofthestringthattransmitsweight loadtothe scale? spring What evidencecanyou cite? haveanyeffectonthereadingDoes thelengthofstring ofthe distance between marks ofbottomband=______distance between marks ofmiddleband=______distance between marks ofbottomband=______distance between marks oftopband=______distance between marks oftopband=______Repeat theprevious step, substitutingtwo25-cmpiecesofstring Repeat Step asshown 7usingthe50-cmpieceofstring, inFigure Chapter 6Newton’s Third LawofMotion—Action andReaction Period 4.9 N. scale shouldread500-gor same. Fora500-gloadthe scale shouldalwaysbethe sion asrecordedonthespring all the rubberbands.Theten- marks should be thesamefor The distance betweenthe strings. Add rubber band between two Repeat usinglongerstring. Date 59 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage60 60 Laboratory ManualLaboratory 17) (Experiment 2. 4. 3. The length of the string hasno effect on the magnitude of the force What evidencecanyou cite? dependonthelengthof string? Does thetensioninstring is halfthe normal stretching distance when a singlerubberband distance betweenthe ink marks is greaterthan 1 cmbyan amountthat amount ofstretchis therefore halfasmuchitwasbefore.(The each isreducedbyhalf.Eachbandsupportshalftheloadand When twoside-by-siderubberbandssupporttheload,tensionin your prediction, Explain your thensetuptheexperiment. result. suspended by twoside-by-side bandsasshown inFigure H?Make How bandstretch muchwouldeachrubber ifthe500-gloadwere by thesameamountofstretchrubberbandsinStep8. The tensionisthesameallalongastretchedstring.Thisevidenced compare? What evidencecanyou cite? How doesthetensionatdifferent distances alongastretched string load.) bands, paperclips, and stringare negligible in comparison tothe500-g on the scale throughout the different steps.(Theweights of therubber transmitted throughit as tension.Evidenceforthis is the same reading supports theload.) predicted stretch =______actual stretch = ______= stretch actual

Name Period Date

Chapter 6: Newton’s Third Law of Motion— Action and Reaction Action and Reaction 18 Tug-of-War

Purpose

To investigate the tension in a string, the function of a simple pulley, and Setup: <1 a simple “tug-of-war.” Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate 5 large paper clips 2 low-friction pulleys Mathematical Level: none 2 large identical rubber bands 2 ring stands 2 m of strong string spring scale 2 500-g hook masses measuring rule

Discussion

Suppose you push on the back of a stalled car. You are certainly aware that you are exerting a force on the car. Are you equally aware that the car is exerting a force on you? And that the magnitudes of the car’s force on you and your force on the car are the same? A force cannot exist alone. Forces are always the result of interactions between two things, and they come in balanced pairs. Now suppose you get a friend to tie a rope to the front of the car and pull on it. The rope will be pulling back on your friend with exactly the same magnitude of force that she is exerting on the rope. The other end of the rope will be pulling on the car and the car will be pulling equally back on it. There are two interaction pairs, one where your friend grasps the rope and one where the rope is attached to the car. A rope or string is a transmitter of force. If it is not moving or it is moving but has a negligible mass, the forces at its two ends will also be equal. In this activity, you will learn about balanced pairs of interaction forces and about the way a string transmits forces.

Procedure

Step 1: Suspend a 500-g load from a string that is held by a spring scale Fig. A as shown in Figure A.

1. What does the scale reading tell you about the tension in the string? Put tension on a string.

Chapter 6 Newton’s Third Law of Motion—Action and Reaction 61 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage62 i.B Fig. 62 positions alongvertical. Move springscaletodifferent Hang weightoverpulley. Laboratory ManualLaboratory 18) (Experiment i.C Fig. 4. oneachsideofthepulleyvertical. keeping thestrings 2. thehangingload. ports hang vertically, asshown inFigure B. Hold thescalesteadysothatitsup- Step 2: 5. Step 3: 3. Does thereading atthehigherpositionchange? weight of theload? What doesthescaleread, andhow doesthisforce compare withthe the forcetransmittedthroughstring. The tensiondoesnotdependonthelengthofstrings,butrather The scalereadingdoesnotchangewithdifferentpositionsofthestring. position change?Briefly explaintheseresults. Move thescaletoalower position.Doesthereading atthelower No; the readingdoesnotchange. The scalereadingisequaltothetensioninstring. How doesitcompare withthetensionin string? evidenced bythesamescalereading. The tensioninthestringisstillequaltoweightofload,as Move scalefirsttoahigher, thespring thentoalower position, Drape over thestring apulleysuchthatbothendsofthestring i.D Fig. i.E Fig. i.F Fig.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 8. Figure E. over thepulleyandattachequal massestoeachend,asshown in Step 6: 7. rod. Repeat Step 4,asshown inFigure D. Step 5: 6. asshownscale ishorizontal, inFigure C. Step 4: Name string slides over therod. partner’s. Ifthe pullisharderthanthefrictionthatdeveloped, string slippage),thenthescalereadingis greater thanthat of the by an amountequaltothe friction between the rod and string (without The scaleswillread the same if the pulls are equal.If the pullisharder What dothescalesread? friction that acts betweentherodandstring. tension inthesidethatsupportsload.Itisgreaterbyamountof make the loadrise,tensionin the hand-held side isgreater than the string held by the hand isless.Ifthepulleddown harder, to of theforceneededtosupportload,sotensiononside friction actsinadirectiontoopposeslidingofthestring.Itprovidespart so thetensionisnot In thiscasefrictiononthestringtendstopreventmovementofload, Explain. Do you find adifference between theresults ofSteps 4and5? direction of the force that is transmitted through the string. The readingdoes not change.Thepulleyservesonlytochange the in theprevious steps?Briefly explainyour result. Does thereading onthescaleeverdeviatefrom whatyou measured Attach a spring scale to each end of the string. DrapeAttach scaletoeachendofthestring. aspring thestring Remove from thepulleyanddrape thestring itover ahorizontal Move untilthe anglesto thevertical, scaletovarious thespring the sameontwo sides oftherod.Theforce of Chapter 6Newton’s Third LawofMotion—Action andReaction Period Hang weightoverrod. positions awayfromvertical. Move springscaletodifferent over pulley. Pull onbothendsofstring Date 63 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage64 64 4.9 N. All answerswillbethesame, Attach stringtowallandtug. spring scales. Have minitug-of-warwithtwo Think andExplain Laboratory ManualLaboratory 18) (Experiment 10. step. Record thefollowing observations. Stringother string, B, untilthescalereads thesameasinprevious Callto thewallorasteadysupport. thisString A.Pull onthe horizontally Step 8: observations. the sameforce asitdidwhensuspendingthemass. Record thefollowing while you ontheotherend.Pull pullhorizontally untilthescalereads 9. 11. Step 7: apparatus andcheckyour prediction. 500-g loadsare ateachendofthe strings. supported Then assemblethe Step 9: Step 8? What istheessentialdifference between thesituationsinStep 7and If thebearingsinpulleyaregood,frictionissmallanditseffects playinthefunctionofapulley? What role doesfriction transmit theforce you are orthewall? onyour partner exerting From amicroscopic pointof view, how orstring doesthespring transmitted tothewall. is transmittedthroughthescaletopartner, andinStep8theforceis There isnoessentialdifferencebetweenthesesteps.InStep7theforce are alsosmall. molecules in the stringreact to thepull. the material.Fromamicroscopicpointofview, forcesbetween The forceistransmittedundiminishedbetweenmolecules throughout Attach strings on both ends of the spring scale.Attach onbothendsofthespring strings Fasten oneend Have scalestationary holdoneendofaspring your partner Study Figure Fandpredict thereading onthe scalewhentwo force______= onyour partner thescaleexerts force______onthescale= exerts your partner force onString thewallexerts ______B= force String onthewall=______Bexerts force onString thescaleexerts B=______force String______onscale= Aexerts force you exert on String A = ______= A String on exert you force force______onthescale = you exert force onyou =______thescaleexerts predicted scalereading =______actual scale reading = ______= reading scale actual Same asinSteps7and8.

Name Period Date

Chapter 7: Momentum Two-Body Collisions

19 Go Cart

Purpose

To investigate the momentum imparted during elastic and inelastic Setup: 1 collisions. Lab Time: >1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: moderate “bouncing dart” from Arbor Scientific ring stand with ring Thanks to Evan Jones for his dynamics cart (with a mass of 1 kg or more) ideas and suggestions for this string lab. pendulum clamp C clamp meterstick brick or heavy weight

Discussion Activity

If you fell from a tree limb onto a trampoline, you’d bounce. If you fell into a large pile of leaves, you’d come to rest without bouncing. In which case, if either, is the change in your momentum greater? This activity will help you answer that question. You’ll compare the changes in momentum in the collision of a “bouncing dart” where bouncing does take place and where it doesn’t. The dart consists of a thick wooden dowel with a rubber tip on each Fig. A end. Although the tips look and feel the same, the tips are made of different kinds of rubber. One end acts somewhat like a very bouncy ball. The other end acts somewhat like a lump of clay. They have different elasticities. Bounce each end of the dart on the table and you’ll easily see which end is more elastic. In the activity, you’ll do the same against the dynamics cart using the dart as a pendulum.

Procedure

Step 1: Attach the dart to the ring stand as a pendulum, using a heavy For best results, the dart weight to secure the base of the ring stand. To prevent the dart from should be mounted in such a swinging into the weight, position the ring on the stand so that it faces way that it can’t vibrate from the opposite direction. Adjust the string so that the dart strikes the side to side as it is swinging. middle of one end of the cart when the dart is at the lowest point of its One way is to mount the dart swing. on the end of a dowel with a PVC “T” on the pivot end. Step 2: Elevate the dart so that when impact is made, the cart will roll Observe collision without bouncing. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley forward a foot or so on a level table or floor when struck by the inelastic end of the dart. Use a meterstick to measure the vertical distance Chapter 7 Momentum 65 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage66 66 bouncing. Observe collisionwith Alternate setup Alternate Laboratory ManualLaboratory (Activity 19) consistent. Record theaverage stoppingdistanceofthecart. each time. Repeat several more timestoseewhetheryour results are Makeafter ithitsthecart. sure torelease from the sameheight thedart from thesameposition dart Step 3: several times. Record theaverage stoppingdistanceofthecart. between therelease andthebottomofitsswing.Repeat pointofthedart 1. Analysis 2. Write down your observations. is lessthan2mv.) just beforehittingthecart,somagnitudeofmomentumchange elastic collision,thedartdoesnot opposite directionfromtheoriginalmomentum.(Eveninaperfectly The dart’s momentumafterthecollisionisnegativebecauseitin itive? isitsmomentumnegativeorpos- bouncesoffthecart, After thedart be positive, sothatmomentumintheoppositedirection isnegative. beforeDefine themomentumofswingingdart to ithitsthecart The dartbouncesbackafterhitting the block. in momentumhasamagnitude thatisgreaterthan (magnitude to nearlyzeroanditschangeinmomentum is approximately –mv When thedartstrikesblockwithoutbouncing,its momentum goes orwhenitdoesn’t?bounces offthecart Explain. acquireWhen doesthedart thegreater momentum—whenit Repeat Be sure usingtheelasticendofdart. torelease the stopping distance(withbouncing)=______stopping distance(nobouncing)=______mv ). Whenitbouncesbackinthe otherdirection,itschange vertical distance= ______vertical as inStep 2.Note whathappenstothedart rebound withthesamespeedithad mv.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 5. 4. 3. Name and greater impulse,givesthecartacorrespondingly The greaterchange in momentumfor bouncing, andthecorresponding How wouldyou accountforthedifference instoppingdistances? at 90°,etc. the dart,andhowaccuratelydartstrikesbacksurfaceofcart depends on themassofcartand bounces.Howmuchfarther dart The cartrollsfartherbecauseofthegreaterimpulseproduced when the How compare? dothestoppingdistancesofcart greater whenthedartbounces. the sameinmagnitudeaschange of momentumthedart.Itis Since momentumisconserved,thechange in momentum ofthecartis dart thatdoesn’tdart bounce?Explain. bywhen struck thatbouncesorby theendofdart theendof When doesthecart speed. undergo thegreater changeinmomentum— momentum Period Chapter 7Momentum Date 67 CP02_SE_LAB_Ch14-20 3/5/01 11:34 AM Page 68 CP02_SE_LAB_Ch14-20 3/5/01 11:34 AM Page 69

Name Period Date

Chapter 7: Momentum Momentum Conservation

20 Tailgated by a Dart

Purpose

To estimate the speed of an object by applying conservation of momen- Setup: 1 tum to an inelastic collision. Lab Time: 1

Learning Cycle: application Experiment Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: moderate opposite types of Velcro® hook and loop fastener tape toy car Thanks to Roy Unruh for his toy dart gun using rubber darts ideas and suggestions for stopwatch this lab. meterstick balance This lab can be simulated Optional: photogate timer or computer, light probe with interface, and nicely on the computer using light source. the program of the same name on Laboratory Simulations-II.

Discussion

If you catch a heavy ball while standing motionless on a skateboard, the momentum of the ball is transferred to you and sets you in motion. If you measure your speed and the masses of the ball, the skateboard, and yourself, then you know the momentum of everything after the ball is caught. But this is equal to the momentum of the ball just before you caught it, from the law of conservation of momentum. To find the speed of the ball just before you caught it, divide the momentum by the mass of the ball. In this experiment, you will find the speeds of a toy dart before and after it collides with a toy car.

Procedure

Step 1: Fasten one type of Velcro tape to the back end of a toy car of small mass and low wheel friction. Fasten the opposite type of Velcro to the suction-cup end of a rubber dart. When the toy car is hit, it must be free to coast in a straight line on a level table or the floor until it comes Tailgate car with dart. to a stop. A track helps constrain the Practice shooting the dart onto the back end of the car. The dart car’s motion to a straight line should stick to the car and cause it to coast. but increases the friction. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 7 Momentum 69 CP02_SE_LAB_Ch14-20 3/5/0111:34AMPage70 70 Determine speeduponimpact. Laboratory ManualLaboratory 20) (Experiment Data TableA 2. Step 4: 3. trials, andrecord inData Table A. Step 3: Repeat fortwomore trials. by untilitcomestoastop. thedart, Record your datainData Table A. 1. Step 2: Was thespeedofcarconstantasitcoasted?Explain. Enter values forthespeedofcaruponimpactinData Table A. The speedimmediatelyafterimpactistwicetheaverage speed. with theaverage speed? how doesthespeedofcarimmediatelyafterimpactcompare If theretarding force onthecarisassumedtobenearlyconstant, coasted toastop. No, thespeedwasnotconstant.Ifithadbeen,carwouldhave immediately aftertheimpact? and the impactandcombinedmomentumofdart What istherelationship before between themomentumofdart momentum ofthedart-and-car combination afterthecollision. The momentumofthedartbeforecollisionisequaltocombined Find the massesneededtocomputemomenta. Calculate theaverage speedofthecarafterimpactforthree Measure thedistanceandtimethatcarcoastsafteritishit mass of dart = ______= dart of mass mass of car = ______= car of mass car just

© Addison-Wesley Publishing Company, Inc. All rights reserved. 5. Analysis beforethe initialspeedofdart impactfrom thismeasurement. sure thespeedoftoy Calculate carjustafteritcollideswiththedart. Step 6: trials. Record your inData values fortheinitialspeedofdart Table A. Compute before theinitialspeedofdart impactforeachofthethree (mass ofdart) collision. Step 5: 4. Name friction—that causesit to loseitsmomentumandcome to astop. No, once thetailgatedcarismoving,there is an external force onit— moving? Explain. Is themomentumoftailgatedcarconstantwholetimeitis should agreefairly well with the computedvalue. The speedofthe car measuredby the lightprobe or photogate timer in Step 3? light probe orphotogatetimer, compare withthevalue you obtained How doesthespeedofcaruponimpact,asmeasured by the Write anequationshowing themomentabefore andafterthe Use aphotogatetimerorcomputerwithlightprobe tomea- initial speed of dart beforeinitial speedofdart impact=______speed ofcaruponimpact=______ (combined mass of dart andcar) (initial speedofdart) (speed ofcaruponimpact) Period Chapter 7Momentum Date 71 CP02_SE_LAB_Ch14-20 3/5/01 11:34 AM Page 72 CP02_SE_LAB_Ch21-28 3/5/01 11:37 AM Page 73

Name Period Date

Chapter 8: Energy Mechanical Energy

21 Making the Grade

Purpose

To investigate the force and the distance involved in moving an object Setup: <1 up an incline. Lab Time: 1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: easy Mathematical Level: easy board for inclined plane spring scale Adapted from PRISMS. meterstick ring stand clamp cart

Discussion

One of the simplest machines that makes doing work easier is the Activity inclined plane, or ramp. It is much easier to push a heavy load up a ramp than it is to lift it vertically to the same height. When it is lifted vertically, a greater lifting force is required but the distance moved is less. When it is pushed up a ramp, the distance moved is greater but the force required is less. This fact illustrates one of the most powerful laws of physics, the law of energy conservation. Fig. A 1. A hill has three paths up its sides to a flat summit area, D, as shown in Figure A. The three path lengths AD, BD, and CD are all different, but the vertical height is the same. Not including the energy used to overcome the internal friction of a car, which path requires the most energy (gasoline) for a car driving up it? Explain your answer.

The amount of work done is independent of the path taken. Therefore,

all the paths would require the same amount of energy (gasoline) since

Chapter 8 Energy 73 CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage74 74 Change theangle of theincline. Raise thecart. B Fig. Laboratory ManualLaboratory (Activity 21) Data TableA clamp. Record theforce anddistanceinData Table A. Measure thedistances scalekeptparallelwith aspring totheplane, tomeasure the force. angle of45°,asshown inFigure B. Pull uptheinclinedplane thecart Step 1: Procedure 2. Analysis the board. Record your force anddistancedatainData Table A. For eachofthedifferent parallel angles(anddistances),pullthecart to board upordown insidetheclamptomakeanglesof10°,30°,and60°. Step 2: move thecar up them. The longer paths havesmallerslopes,and thus lessforceisrequiredto distances? orrelationshipWhat pattern doyou findbetween theforces andthe Vary theanglewhilekeepingheighth Place a clamp on a ring stand.ClamptheboardPlace aclamp onaring inplaceatan from the bottom of the incline to the ring stand from the bottomoftheinclinetoring the sameby slidingthe

Name Period Date

Chapter 8: Energy Power

22 Muscle Up!

Purpose

To determine the power that can be produced by various muscles of the Setup: <1 human body. Lab Time: >1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: easy Mathematical Level: easy bleachers and/or stairs stopwatch meterstick weights rope

Discussion

Power is usually associated with mechanical engines or electric motors. Many other devices also consume power to make light or heat. A lighted

incandescent bulb may dissipate 100 watts of power. The human body Activity also dissipates power as it converts the energy of food to heat and work. The human body is subject to the same laws of physics that govern mechanical and electrical devices. The different muscle groups of the body are capable of producing forces that can act through distances. Work is the product of the force and the distance, provided they both act in the same direction. When a person runs up stairs, the force lifted is the person’s weight, and the distance is the vertical distance moved—not the distance along the stairs. If the time it takes to do work is measured, the power output of the body, which is the work divided by the time, can be determined in watts.

Procedure

Step 1: Select five different activities from the following list: Measure force and distance. You might suggest your stu- Possible Activities dents do each activity for 100 s Lift a mass with your wrist only, forearm only, arm only, foot only, (that is, one minute and 40 s). or leg only. Do push-ups, sit-ups, or some other exercise. Run up stairs or bleachers. Pull a weight with a rope. Jump with or without weights attached.

Perform these activities, and record in Data Table A the force in newtons Count the number of reps and that acted, the distance in meters moved against the force, the number of measure the time. repetitions (or “reps”), and the time in seconds required. Then calculate © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley the power in watts. (One hundred seconds is a convenient time interval.) Chapter 8 Energy 75 CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage76 76 analysis appliestorunning. is gettingtired)!Asimilar the person(evenif being lowereddoesworkon opposite directions).Aweight (force anddisplacementin on aweightwhentheylowerit direction) andnegativework and displacementinsame weight whentheyliftit(force they dopositiveworkona Point outtoyourstudentsthat Laboratory ManualLaboratory (Activity 22) Data TableA ties performed byties performed otherclassmembers. 4. 3. 2. 1. Analysis Step 2: explain your answer. do work? Pay careful attentiontothewording ofthisquestion,and Can apulley, winch,orleverincrease therate atwhichapersoncan for a longer time. The largest force doesnot necessarily resultinthe most power if it acts power. produced? Explain how alarge force canresult inarelatively small Did theactivitythatusedlargest force result inthelargest power muscle group. Answers willvary. Usuallythelegmusclesaremostpowerful Which musclegroups were usedinthisactivity? In whichactivitydoneby your classwasthelargest power produced? The rateatwhichworkisdonethepower. Itismeasuredinwatts. units ofthisrate? What nameisgiventotherate atwhichwork isdone? What are the in more time. decreases the required power input,sothesamework is accomplished time, thus makinga job easier. Usuallyapulley, winch,orlever work. Itcan allow the persontoworkatalower rate bylengtheningthe A pulley, winch,orlevercan’t increasetherateatwhichaperson can do Complete thetableby recording theresults offourotheractivi-

Name Period Date

Chapter 8: Energy Conservation of Energy

23 Cut Short

Purpose

To illustrate the principle of conservation of energy with a pendulum. Setup: <1 Lab Time: <1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy 3 ring stands Mathematical Level: none pendulum clamp string If time is short, you might con- steel ball sider doing this activity as a rod demonstration and have your clamp students proceed to “Conserving Your Energy.”

Discussion

A pendulum swinging to and fro illustrates the conservation of energy.

Raise the pendulum bob to give it potential energy. Release it and the Activity potential energy is converted to kinetic energy as the bob approaches its lowest point. Then, as the bob swings up on the other side, kinetic energy is converted to potential energy. Back and forth, the forms of energy change while their sum is constant. Energy is conserved. What happens if the length of the pendulum is suddenly changed? How does the resulting motion illustrate energy conservation?

Procedure

Step 1: Attach a pendulum clamp to the top of a ring stand set between Make pendulum. two other ring stands, as shown in Figure A. Attach a steel ball to a piece of string that is nearly as long as the ring stand is tall.

Fig. A

Step 2: Tie a string horizontally from one empty ring stand to the other, Set up level string.

© Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley as shown in Figure A. The string should be about two-thirds as high as the pendulum clamp. Chapter 8 Energy 77 CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage78 78 Lower rod. Raise rod. Release pendulum. Predict height. Attach crossbar. Laboratory ManualLaboratory (Activity 23) Observation: ______Observation: ______Prediction: ordenyyour Perform prediction. toconfirm the string. theexperiment Step 7: ______Observation: ______Prediction: ordenyyour Perform prediction. toconfirm the string. theexperiment Step 6: Step 5: Observation Prediction by therod. Checkone: isstopped andthependulumstring string same heightasthehorizontal Step 4: isvertical. when thestring (Figure string horizontal A). The rod shouldtouchthependulumstring Step 3: 1. Analysis 3. 2. potential energy(PE)isconserved. Explanations shouldstatethatthesumof the kineticenergy(KE)and ofenergy.and theconservation ofpotentialandkineticenergy Explain interms your observations loop. position oftheballand height ofthestring,balldoesaloop-the- Yes; ifthe rod islowerthantwo-fifthsthe distancebetween the lowest you thinkthere are limits. Is there alower limitonhow low therod canbe?If so, explainwhy pendulum clamp. No; the onlypracticallimit on the height ofthe rod is the heightof the why you thinkthere are limits. Is there anupperlimitonhow hightherod canbe?If so, explain Predict whatwouldhappeniftherod were attachedlower than Predict whatwouldhappeniftherod were attachedhigher than Release thependulum!Record a,b, whetheryou observe orc. Predict whatheighttheballwillreach iftheballisreleased atthe Attach arod tothecentral standatthesameheightas ring The ballwillgojustashighthehorizontalstring. The ballwillgojustashighthehorizontalstring. X c. The ballwillnotgoashighthehorizon- b. The ballwillgojustashighthehori- a. The ballwillgohigherthanthehorizontal tal string. string. zontal string.

Name Period Date

Chapter 8: Energy Conservation of Energy

Conserving Your 24 Energy

Purpose

To measure the potential and kinetic energies of a pendulum in order to Setup: 1 see whether energy is conserved. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate ring stand Mathematical Level: moderate pendulum clamp pendulum bob This lab makes a great follow- balance up to the previous activity, string “Cut Short.” meterstick photogate timer or computer light probe with interface light source

Discussion

In Activity 23, “Cut Short,” you saw that the height to which a pendulum swings is related to its initial height. The work done to elevate it to its initial height (the force times the distance) becomes stored as potential energy with respect to the bottom of the swing. At the top of the swing, all the energy of the pendulum is in the form of potential energy. At the bottom of the swing, all the energy of the pendulum is in the form of kinetic energy. The total energy of a system is the sum of its kinetic and potential energies. If energy is conserved, the sum of the kinetic energy and potential energy at one moment will equal their sum at any other moment. For a pendulum, the kinetic energy is zero at the top, and the potential energy is minimum at the bottom. Thus, if the energy of a pendulum is conserved, the extra potential energy at the top must equal the kinetic energy at the bottom. For convenience, potential energy at the bottom can be defined to be zero. In this experiment, you will measure kinetic and potential energy and see if their sum is conserved. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 8 Energy 79 CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage80 80 Laboratory ManualLaboratory 24) (Experiment a table. Step 2: 1. Analysis such astheheight,potentialenergy, kineticenergy, speed,andsoon. Include adiagram ofyour pendulumandlabelitwithallthequantities, ofenergy.servation Write down your procedure inthespacefollowing. Step 1: Procedure converted tokilogramsand meterstogetjoules. the heightinmeters.Measurements ingramsandcentimetersmustbe The unitsofPEwillbejoulesifthemassismeasured in kilogramsand What unitsofpotentialenergy didyou useforthependulumbob? Perform Record your experiment. your databelow of intheform Devise an experiment withtheequipmentlistedtotestcon- Devise an experiment

© Addison-Wesley Publishing Company, Inc. All rights reserved. 4. 3. 2. Name often yield results withina3% differenceorless. Careful measurementsofthebob’s PE(mgh ) anditsKE( are nearlyequal. this swing.Either PE or KE could be usedin the denominator, sincethey downward swingandKEisthemeasuredgain of kineticenergyduring where PE is the measuredchangeofpotentialenergyduring the conserved usingtheequation You cancalculate thepercentagebywhichenergyappearsnottobe the samethroughout itsswing? Based onyour data,doesthetotalenergy ofthependulumremain full diameteroftheball. effects ofthelightbeamandwhetherornotiseclipsedbya dependmainly onthespreading the lightprobe.Theuncertainties bob dividedbytheeclipsetimeaspassesthroughbeamof probably correctlyassumethatthespeedofbobiswidth speed evenwhenusingalightprobeorphotogate.Your students string. Thesourceoflargesterrorisprobablythedetermination at thebottomofitsswing,andairresistanceonbob the elevatedpendulumbob,determinationofspeedbob Sources oferrorincludethemeasurementmassandheight is themostsignificant? List thesources oferror inyour experiment. Which onedoyou think to gettheenergyinjoules. the speedinmeterspersecond.Conversion to these units isnecessary The unitsofKEwillbejoulesifthemassismeasuredinkilograms,and What unitsofkineticenergy didyou useforthependulumbob? % difference PE –K PE E 100% 1 – 2 mv 2 ) Period Chapter 8 Energy Date 81 CP02_SE_LAB_Ch21-28 3/5/01 11:37 AM Page 82 CP02_SE_LAB_Ch21-28 3/5/01 11:37 AM Page 83

Name Period Date

Chapter 8: Energy Efficiency

How Hot Are Your 25 Hot Wheels?

Purpose

To measure the efficiency of a toy car on an inclined track. Setup: 1 Lab Time: 1

Required Equipment/Supplies Learning Cycle: application Experiment Conceptual Level: easy toy car Mathematical Level: moderate 3 m of toy car track meterstick Adapted from PRISMS. tape 2 ring stands 2 clamps

Discussion

According to the law of energy conservation, energy is neither created nor destroyed. Instead, it transforms from one kind to another, finally ending up as heat energy. The potential energy of an elevated toy car on a track transforms into kinetic energy as the car rolls to the bottom of the track, but some energy becomes heat because of friction. The kinetic energy of the car at the bottom of the track is transformed back into potential energy as the car rolls to higher elevation, although again some of the energy becomes heat. The car does not reach its initial height when it moves back up the incline, because some of its energy has been transformed into heat. Fig. A

Procedure

Step 1: Set up a toy car track as shown in Figure A. Both ends of the Set up track. track should be elevated to a height of 1 meter above the table or floor. Secure the track to the table or floor and supporting ring stands with tape to eliminate motion of the track.

Step 2: Mark starting point A with a piece of masking tape and record its Measure the initial and final height of the car. height h1. Release the car from starting point A. Record the height h2 of point B to which the car rises on the other end of the track.

h1 = ______

h2 = ______

Step 3: Efficiency is defined as the useful energy out divided by the total Compute efficiency.

© Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley energy in. It is a ratio or a percentage. In this activity, we can define the total energy in as the change in potential energy as the car rolls from its Chapter 8 Energy 83 CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage84 84 Laboratory ManualLaboratory 25) (Experiment point A(theinputenergy) isequaltotheratio ofthefinalheighth put energy) tothepotentialenergy lostby thecarinrolling down to of thepotentialenergy transferred backintothecaratpointB(theout- the initialheighth potential energy at any height the carnow possessesrelative tothelowest pointofitstravel. Since the car rolls from itslowest pointuntilitstopsatB. This isenergy that useful energy outwe cantaketobethepotentialenergy changeasthe highest toitslowest point. This isenergy suppliedby earth’s gravity. The 3. 2. 1. Analysis after itrolls upthetrack. Compute thisefficiency. the energy suppliedby gravity inrolling down thetrack thatisretained the car-and-track systemfrom pointAtoB. It shows thefraction of Answers mayvary. Iftheheightdifferenceissmall, little differencein the track isaltered? Is theefficiencyofcar-and-track systemchangediftheheightof efficiency isexpressedasapercent. is dimensionless.Whenthedecimalratiomultipliedby100%,then Since theefficiencyisaratiooftwovaluesenergy, ithasnounits—it In whatunitsisefficiencymeasured? The efficiencyof the car decreases ifthe track isnotsecure. not taped? Is theefficiencyofcar-and-track systemchangedifthetrack is speeds. efficiencies may differslightlybecausefrictional effects vary at different efficiency willbenoticed. If theheight difference islarge, thenthe 1 efficiency =————–– . This ratio ofh h PE PE above a reference level is point A point B 2 to h 1 = can becalledthe “efficiency” of h h 2 1 mgh, theratio 2 to

Name Period Date

Chapter 8: Energy Energy and Work

Wrap Your Energy 26 in a Bow

Purpose

To determine the energy transferred into an archer’s bow as the string is Setup: 1 pulled back. Lab Time: >1

Learning Cycle: application Experiment Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: moderate archer’s recurve or compound bow large-capacity spring scale Adapted from PRISMS. meterstick clamp graph paper This lab can be simulated on the computer using the program of the same name on Laboratory Simulations-III. The “Sample Calculation” feature Discussion makes an excellent class demonstration of the conserva- The kinetic energy of an arrow is obtained from the potential energy of tion principle in a very visual the drawn bow, which in turn is obtained from the work done in drawing manner. the bow. This work is equal to the average force acting on the bowstring multiplied by the distance it is drawn. In this experiment, you will measure the amounts of force required to hold the center of a bowstring at various distances from its position of rest, and plot these data on a force vs. distance graph. The force is relatively small for small deflections, and becomes progressively larger as the bow is bent further. The area under the force vs. distance curve out to some final deflection is equal to the average force multiplied by the total distance. This equals the work done in drawing the bow to that distance. Therefore, your graph will show not only the relationship of the force to the distance stretched, but also the potential energy possessed by the fully drawn bow. Fig. A The effect of a constant force of 10 N acting over a distance of 2 m is represented in the graph of Figure A. The work done equals the area of the rectangle.

work = F × d = (20 N) × (2 m) = 40 N•m = 40 J

When the force is not constant, as in Figure B, the work done on the system still equals the area under the graph (between the graph and the horizontal axis). In this case, the total area under the graph equals the area of the triangle plus the area of the rectangle.

work = total area = area of triangle + area of rectangle = [(12) (base) × (height)] + [(base) × (height)] = [(12) (2 m) × (20 N)] + [(3 m) × (20 N)]

© Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley = (20 N•m) + (60 N•m) = 80 N•m = 80 J Chapter 8 Energy 85 CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage86 86 Compute area. Make agraph. measure forces. Stretch bowstringand bow, andvibration. air onthearrow, heatingofthe energy goesintofrictionofthe means asignificantamountof 75% arenotunusual.This height. Values between50and predicted heightandtheactual large discrepancybetweenthe Don’t bediscouragedbythe i.C Fig. Laboratory ManualLaboratory 26) (Experiment potential energy. the bow. When thebow isdrawn, ofelastic thisenergy isintheform meters, N Step 4: axis). Use theunitsnewtonsandmeters. Step 3: in metersandtheequivalent force values innewtons. ments, andrecord your datainthetable. Compute thestretch distances and force reading. Continue tostretch thebowstring in1.0-cmincre- Step 2: ues in newtons in a fourth column.Leave10rowsues innewtonsafourth fordatainyour table. third column.If theyare not in newtons, show theequivalent force val- values in metersinthesecondcolumn.Show theforce readings inthe stretch distancesincentimetersthefirstcolumn,andtheirequivalent that farout.Prepare atableinwhichtorecord your data.Show the positionandtheforcefrom its original required toholdthebowstring scale.spring You willmeasure thedistancebowstring isstretched as shown inFigure C. You onthebowstring willpullhorizontally witha Step 1: Procedure Estimate thearea underthegraph inunitsofnewtonstimes Plot agraph oftheforce axis)vs. (vertical distance(horizontal Stretch thebowstring by 1.0cm,andrecord thestretch distance Fasten thebow position, atitshandlewithaclampinvertical i.B Fig. • m. Since 1N area = ______= area • m =1J,thisarea isthetotalenergy transferred to

© Addison-Wesley Publishing Company, Inc. All rights reserved. 4. 3. 2. 1. Analysis Name bands, bentwood,anythingflexible. Answers willvaryamongdevicesusingstretchyobjects: springs,rubber an object. List three other devicesthattransform potential energy into work on with theKEoffiredarrowandsolving this equation for The speedofthe arrow is found by equatingthePEof drawn bow At whatspeedwouldthe50-garrow leavethebow? goes onlytwo-thirdsashigh. Question 1exceptuse0.075kgforthemassofarrow. Thearrow To calculate theheightofarrow, usethesamecomputationasin How highwoulda75-garrow go? drawn bowistheworkdonedrawingitback,ascalculatedinStep4. the weightmg The height gravitational PEatthetopofitsflight. the KEoffired arrow. Thenequatethe KE of the firedarrow to the To find theheightarrowwillgo,equate PE of the drawnbowto the answer inmeters, express 50gas0.05kg.) maximum displacementofyour data,how highwoulditgo?(To find If a50-g arrow were shot straight upwiththebow stretched tothe h of thearrowisequaltoPEindrawnbowdividedby of thearrow, orPE/[(0.50kg) PE bow PE PE v = KE bow = bow √2PE/m arrow PE = = mgh arrow = PE arrow (9.8 m/s 2 )]. ThePE of the v. Period Chapter 8 Energy Date 87 CP02_SE_LAB_Ch21-28 3/5/01 11:37 AM Page 88 CP02_SE_LAB_Ch21-28 3/5/01 11:37 AM Page 89

Name Period Date

Chapter 8: Energy Friction and Energy

27 On a Roll

Purpose

To investigate the relationship between the stopping distance and the Setup: <1 height from which a ball rolls down an incline. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate 6-ft length of 5/8-inch aluminum channel Mathematical Level: moderate support about 30 cm high marble Thanks to John Hubisz for his wood ball ideas and suggestions for steel ball this lab. tennis ball meterstick piece of carpet (10 to 20 feet long and a few feet wide) graph paper or overhead transparency

Optional Equipment/Supplies

computer light probe with interface light source data plotting software

Discussion

When a moving object encounters friction, its speed decreases unless a force is applied to overcome the friction. The greater the initial speed, the more work by the friction force is necessary to reduce the speed to zero. The work done by friction is the force of friction multiplied by the distance the object moves. The friction force remains more or less constant for different speeds as long as the object and the surface stay the same. In this experiment, you will investigate the relationship between the initial height of a rolling ball and the distance it takes to roll to a stop.

Procedure

Step 1: Assemble the apparatus shown in Figure A. Elevate the ramp to a Assemble apparatus. height that keeps the marble on the carpet when started at the top of the ramp. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 8 Energy 89 CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage90 90 Graph data. Repeat usingdifferentballs. Roll marbleontocarpet. Laboratory ManualLaboratory 27) (Experiment i.A Fig. 1. each ofthefourballs. of average axis)vs. stopping distance(vertical axis)for height(horizontal Step 4: Record theheightsand distancesinData Table A. 2. Step 3: times from eachheightandrecord thestoppingdistancesinData Table A. marble toroll toacompletestoponthecarpet.Roll themarblethree release pointontheramp. Alsomeasure thedistancerequired forthe in Figure A.Measure heightfrom thefloorortableto thevertical Step 2: 3. s Describe theshapesoffourgraphsDescribe you made. from thesameheight,duetodifferentamounts of rollingfriction releases The differentkindsofballshavestoppingdistances for compare? How didthestoppingdistancesofdifferent typesofballs to theheightofreleasepoint. They areallstraightlines.Thestoppingdistanceisdirectlyproportional more or less the samedistance nomatterwhat the mass. The samekindsof balls releasedfromthe same heightroll toa stop in mass oftheballaffectstoppingdistance? Compare your results withthoseoftherest oftheclass. Doesthe that actonthem. Release of10cmalongtheramp asshown themarbleatintervals On thegraph paperprovided by your teacher, agraph construct Repeat Step 2usingawoodball,steelandtennisball.

© Addison-Wesley Publishing Company, Inc. All rights reserved. Data TableA Name Period Chapter 8Energy Date 91 CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage92 92 physics. that canbeusedtolearnmore drudge workandsavestime the graphsgreatlyreduces Using acomputertogenerate height. Graph squareofspeedvs. Repeat usingdifferentballs. Graph speedvs.height. Laboratory ManualLaboratory 27) (Experiment 6. tennis ball. vs. axis)forthemarble, height(horizontal steelball,woodand use dataplottingsoftware toplotthesquare axis) ofthespeed(vertical 5. Step 6: axis) ongraph paper. Data Table A.Make agraph axis)vs. ofspeed(vertical height(horizontal the diameterofmarbleby themeasured times. Record thespeedsin Repeat foreachoftherelease heights. Compute thespeedsby dividing 4. Step 7: Step 5: Going Further(Optional) Describe theshapeoffourgraphsDescribe you made. theshapeoffourgraphsDescribe you made. Some factors are theinitialspeedandforceof friction. ping distanceofautomobiles? Based thestop- onyour data,what factorswouldseemtodetermine height ofthereleasepoint. kinetic energyatthebottom( The graphsofthesquarespeedvs.heightarestraightlines. The graphsofspeedvs.heightarecurves. Compute thesquare ofthespeedandrecord inData Table Aor Repeat Step 5forthesteelball,woodandtennisball. Use alightprobe totimethemarbleatbottomofincline. 1 – 2 mv 2 ) is directly proportional to the ) isdirectlyproportional

© Addison-Wesley Publishing Company, Inc. All rights reserved. h Step 1: Procedure table. long itremains intheairdependsonhow highitisabove theflooror remains in theair. How fastitislauncheddependson from thecrossbar dependsonhow fast keeps going. swing, acrossbar stopsthependulum,butballleavesholderand (see Figure A)raised height.At to acertain thebottomofpendulum’s downward from rest. In pendulum you willusearigid thisexperiment, depend ontheirmass, distancetheyhavemoved butonlyonthevertical pendulums. The speedstheyachieveinfallingorswingingdonot rately ofthesamelength andtheywillswingtogetheras totwostrings Drop twoballsofdifferent massandtheyfalltogether. Tie themsepa- Discussion light source light probe withinterface computer Optional Equipment/Supplies meterstick graph paperoroverhead transparencies 2 steelballsofdifferent mass pendulum apparatus asinFigure A Required Equipment/Supplies potential energy. To findrelationships amongtheheight,speed,mass, kineticenergy, and Purpose hpe :Energy Chapter 8: Name the pendulumballfalls. Record your method inthefollowing space. 28 How fardownrange doestheballtravel? distance The horizontal Devise an appropriate method for measuring the vertical height thevertical Devise method formeasuring anappropriate Potential Releasing Your the ballisgoingandhow long . How the launcher. Period it Scientific Co. go kitisavailablefromArbor apparatus yourself,aready-to- Although youcanmakethis this lab. ideas andsuggestionsfor Thanks toRexRiceforhis Mathematical Level:difficult Conceptual Level:difficult Learning Cycle:exploratory Lab Time: >1 Setup: <1 Measure verticalheight. i.A Fig. Conservation ofEnergy Chapter 8 Energy Date 93

Experiment CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage94 94 Measure therange. Launch ballwithpendulum. speed. Calculate minimumlaunch Laboratory ManualLaboratory 28) (Experiment Data TableA – potential energy thatitlostinswingingdown, soKE of theballasitislaunchedfrom thelow pointofitsswingisequaltothe horizontally. From ofenergy, thelawofconservation thekineticenergy thecrossbar, tobecutasitstrikes cause thestring projecting theball in Figure A.If theballisreleased will from asufficientheight,itsinertia arazorsimple pendulum)thatstruck mounted onthecrossbar asshown Step 4: for asimplependulum,v treat thiscomplication here, and acknowledge thatthespeedcalculated if allitsmasswere concentrated atitsbottom.For simplicity, we won’t Chapter 11thatithasless “rotational inertia” andswingsabitfasterthan speakingitisn’tlength, sostrictly asimple 1 Data TableB. height from whichthependulumwasreleased, inthesecondcolumnof speed. Record your computationoftheminimumlaunchspeedforeach Record eachaverage distanceandheightinData Table A. Repeatdistance foreachtrial. forsixdifferent theexperiment heights. times from thesameheight.Use ametersticktomeasure thedownrange Step 3: the balldownrange. the crossbar. Practice your techniqueuntilyou getconsistentlandingsof dulum swingdown together, andtheballislauncheduponimpactwith that you donotpushthependulumupordown. Both the ball andpen- finger toholdtheballinplace. Take your fingerawayinsuchamanner Step 2: 2 mv The launcherpictured inFigure alongits Ahasitsmassdistributed 2 = mgh. Suppose theballwere (asina attachedtoalightweight string When your results havebecomeconsistent,release theballthree Raise thependulumtodesired height,usingyour vertical = √2 — gh — , isalower limit—the pendulum. We’ll seein gained minimum = PE = lost or launch

© Addison-Wesley Publishing Company, Inc. All rights reserved. Data TableB distances inData Table C. and release itfrom thesamesixheightsasbefore. Record thedownrange mass oftheballanditslaunchspeed.Use aballwithdifferent mass, Step 6: 1. umn ofData Table B. of theballateachsixheights. Record your results inthethird col- Step 5: Name on theparticularlauncher. Figure A,disagreementmayvaryanywherefrom5to25%—depending pendulum isused,suchastheonefromArborScientificCo.depictedin calculated andmeasuredspeedsshouldcompare.Ifaphysical The closerthelauncherapproximatesasimplependulum, How dotheminimumandmeasured speedsoftheballcompare? In thisstep, you willinvestigatetherelationship between the (Optional) Use asinglelightprobe tomeasure thelaunchspeed Data TableC Period Use ballsofdifferentmass. make theirgraphs. dents canusethemto Plotter If acomputerandData Chapter 8 Energy Date are available,stu- 95 CP02_SE_LAB_Ch21-28 3/5/0111:37AMPage96 96 Graph data. line. until thegraph is a straight power of the x Plotter, havethemvarythe If studentsareusing Laboratory ManualLaboratory 28) (Experiment and y Data values (c) Mass axis)vs. (vertical axis)forthesameheight. distance(horizontal axis)vs.(b) Launch speed(vertical release axis)forthe height(horizontal (a) Distance orrange axis)vs. (vertical heightfrom whichthependulum Suggested graphs them tomakeyour graphs. your results. If acomputeranddataplottingsoftware are available, use member ofyour teamshouldmakeonegraph, thenallofyou canpool quantities instead.Use overhead transparencies orgraph paper. Each Graph suggested. thepairsofvariables You maywanttograph other What isthepattern? You by canoftenvisualize apattern makingagraph. Step 7: released inorder toscore abull’s-eye. orheight atwhichthependulummustbe dict theanglefrom thevertical Have your teacher assignyou aspecifieddistancedownrange. Try topre- Going Further 4. 3. 2. Analysis values until thegraph isastraight line. If you are usingdataplottingsoftware, thepowers vary ofthex is released axis) forthesamemass. (horizontal same mass. gravity. Someofitcomesfromthepushlauncher. from done ontheballtoincreaseitskineticenergycomesonly partly The totalenergy, KE+PE,increases!Thisisbecausetheworkbeing from therelease heighttothelaunchposition. whathappenstothetotalenergyDescribe oftheballasitswings The potentialenergydecreases. swings from therelease heighttothelaunchposition. whathappenstothepotentialenergyDescribe oftheballasit The kineticenergyincreases. from therelease heighttothelaunchposition. whathappenstothekineticenergyDescribe oftheballasitswings You now haveatremendous amountofdata. What doesitmean? and y

Name Period Date

Chapter 8: Energy Coefficients of Friction

29 Slip-Stick

Purpose

To investigate three types of friction and to measure the coefficient of Setup: <1 friction for each type. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate friction block (foot-long 2 × 4 with an eye hook) Mathematical Level: moderate spring scale with maximum capacity greater than the weight of the friction block This lab avoids referencing that set of slotted masses µ = tan at the angle of repose. flat board You may wish to augment the meterstick Discussion of the lab by doing shoe so, depending on the mathematical level of your students.

Discussion

The force that presses an object against a surface is the entire weight of the object only when the supporting surface is horizontal. When the object is on an incline, the component of gravitational force pressing the object against the surface is less than the object’s weight. This component that is perpendicular (normal) to the surface is the normal force. For a block on an incline, the normal force varies with the angle. Although an object presses with its full weight against a horizontal surface, it presses with only half its weight against a 60° incline. So the normal force is half the weight at this angle. The normal force is zero when the incline is vertical because then the surfaces do not press against each other at all.

The normal force can be greater than the object’s weight if you press down on the object. In general, the coefficient of friction is defined by replacing weight in the formula above by the normal force, whatever the © Addison-Wesley Publishing Company, Inc. All rights reserved. All rights Inc. Company, Publishing © Addison-Wesley

Chapter 8 Energy 97 CP02_SE_LAB_Ch29-48 3/5/0112:02PMPage98 98 Drag frictionblock. Laboratory ManualLaboratory 29) (Experiment source oftheforce. So, ingeneral, theforce offriction coefficient of friction µ coefficient offriction tion isshown inFigure A. force.normal listofcoefficientsbothslidingandstaticfric- Apartial the greatest force friction thancanactwithoutmotiondividedby the tion holdsanobjectatrest, we definethecoefficientofstaticfriction coefficient ofslidingfriction slightly less. forslidingobjectsiscalledthe The coefficientoffriction time tosinkintoeachotherandare meshed.)Onceslidingbegins, µ andvalleys havehad theridges rest, justbefore motionstarts. (Then µ,equals so thatthecoefficientoffriction, always oppositetothedirection ofmotion. force thefriction totheright, istotheleft.Frictiona surface forces are moves downward, force thefriction isupward. For ablockslidingalong ing upward intheair, force thefriction isdownward. When theball incontact. between twosolidsurfaces onlywiththefriction concerned falling totheground isquitecomplicated!In you willbe thisexperiment, forsolids. slidingfriction ern Airisafluid,andthemotionofleaf known asfluidfriction,doesnotfollow lawsassimplethosethatgov- force scale.spring Be sure toholdthescalehorizontally. The staticfriction byand slidingfriction dragging witha blockhorizontally thefriction Record theweight inData Table thecoefficientsofstatic A. Determine Step 1: Procedure Static andSlidingFriction ComputingtheCoefficients of Part A: ing. forceThe slidingfriction moving atconstantvelocity The coefficient of friction The coefficientoffriction Friction alwaysactsinadirection toopposemotion.For aballmov- Friction alsooccursforobjectsmoving through fluids. This friction, F f Weigh blockby thefriction scale. suspendingitfrom thespring is themaximumforce thatactsjustbefore mov- theblock starts i.A Fig. F µ f = —————— = = friction forcefriction µN and the normal forceand thenormal N: weight . Your scalewillvibrate around someaverage (or coefficient of kinetic friction). (or coefficientofkineticfriction). When fric- F µ f' is greatest are whenthetwosurfaces at is theforce ittakestokeeptheblock F f depends onthe as is

© Addison-Wesley Publishing Company, Inc. All rights reserved. 2. Analysis Table A. foratleastsixdifferentcients offriction weights andrecord inData the addedmassesinData Table A.Find forces bothfriction andcoeffi- block.Recordted massestothefriction theweight ofboththeblockand Step 3: 1. force.ing friction Step 2: forces.sliding friction Record your datainData Table A. value; make thebestjudgmentyou canofthevalues ofthestaticand Name force isrequired.Thusµ friction thantokeeptheobjectmoving.Onceitismoving, asmaller It requiresappreciablygreater force to overcome theforce of static At eachweight, how doesµ sliding friction. The draggingspeedshouldhave very littleeffectonthecoefficientof friction, Does thedragging speedhaveanyeffectonthecoefficientofsliding Increase theforce pressing togetherby thesurfaces addingslot- Drag theblockatdifferent speeds. Note anychangesintheslid- µ sliding ? Explain. static static is greaterthanµ compare with µ sliding sliding . ? Period Change draggingspeed. Add weightstoblock. Data TableA Chapter 8 Energy Date 99 CP02_SE_LAB_Ch29-48 3/5/01 12:02 PMPage100 100 Drag frictionblock. Laboratory ManualLaboratory 29) (Experiment Data TableB 3. Procedure Friction TheEffect ofSurface Area on Part B: 6. 5. 4. weight oftheblockinData Table B. scale. spring means ofahorizontal Record force thefriction andthe Step 4: No, Does forces. The coefficientoffrictionhasnounits because itis the ratio of two Why are there nounits forµ? ratio of the two doesnotchangeappreciably. You increase the normalforce as wellthe force offriction,andthe but If you press down uponaslidingblock,theforce increases offriction precise, reproducibleresults. ofthesamematerialtoprevent There issufficientvariationinsurfaces than twosignificantfigures notlisted? than twosignificantfigures. From your experience, whyare more Tables inphysicsbooksrarely withmore listcoefficients offriction the and weight increases,thefrictionforceincreasesindirectproportion, ratio µ µ Drag blockofknown afriction weight atconstantspeed by sliding µ does not.Explain. sliding of forces doesnotchangesignificantly. should notdependappreciablyontheweight.As depend on the weight of the friction block?Explain.depend ontheweight ofthefriction

© Addison-Wesley Publishing Company, Inc. All rights reserved. 7. The coefficient of static friction istheratioThe coefficientofstaticfriction ofthosesides. forcenormal equalstheratio oftheheight aretwo triangles isthattheratiostance ofsimilartriangles A. versionoftriangle Bisashrunken angles—and triangle The impor- and BinFigure Care tion force F points downward, tendstoproduce sliding.Before slidingstarts, thefric- the shoetosurface. The componentparallel totheincline, which forceponent perpendiculartotheinclineisnormal N;itactstopress Triangle Bshows thevectorcomponentsofshoe’s weight. The com- clearer,etry acubecanrepresent the shoe ontheincline, asinFigure C. toslip?Studywill ashoeonaninclinestart Figure B. To makethegeom- the objectjustbeginstoslide. tion isenoughtoholditstill,thentiptheinclineatasteeperangleuntil Place an objectonaninclinedplaneanditmayornotslide. If fric- FrictiononanIncline Going Further: Step 6: ent area). Record force thefriction inData Table B. Step 5: tion force ontheshoe. ponent. By tiltingtheincline, force thenormal we canvary andthefric- of repose, forcefriction force tothenormal givesthecoefficientofstaticfriction. forcecomponent andthefriction are attheirmaximum. The ratio ofthis andtheshoebreakscome friction free. At thatangle, theparallel weight the componentofweight parallel isjustenoughtoover- tothesurface i.B Fig. Name Does thearea makeadifference inthecoefficientoffriction? At toslip(theangleofrepose theangleatwhichshoestarts toitsfunction. ofashoeiscritical The coefficientoffriction When No, the area does notaffectthecoefficientoffriction. In Figures Band C,theangleofinclinehasbeensettobe Compute Repeat Step 4,butuseadifferent sideoftheblock(withadiffer- θ f r . With thehelp ofgeometry, itcanbeproven A thattriangles is equalinmagnitudebutoppositedirection tothiscom- equal. Thus, theratio oftheparallel component tothe µ µ sliding static similar triangles—thatis, theyhavethesame = for bothstepsandlistinData Table B. — Nx F f = — y of corresponding ofthe parts i.C Fig. y to the horizontal distancex. to thehorizontal Period ) θ r , Compute µ. block. Use differentsideoffriction Chapter 8 Energy Date 101 CP02_SE_LAB_Ch29-48 3/5/01 12:02 PMPage102 Drag shoeonlevel. Tap theincline. 102 Tilt incline untilshoe slips. Laboratory ManualLaboratory 29) (Experiment angle. 8. 9. tion tance shoe justbeginstoslip. Using ameterstick, measure dis- thehorizontal Step 7: Procedure 10. is level.Compute µ Step 9: 12. 11. ing) by theweight oftheshoe. Compare your result withthatofStep 8. (kinetic) friction, µ (kinetic) friction, shoe slidesatconstantspeed.Compute thecoefficientofsliding you approach theangleofrepose. Adjust theboard anglesothatthe Step 8: Did you measure anydifference between Are your values forµ differences. Yes, theforce offrictionisgreaterwhenthesurfacehorizontal. isinclinedorhorizontal? surface whether thesupporting Does theforce dependon between twosurfaces ofslidingfriction measurements. They shouldbethesame,withinuncertaintiesof Yes, of forces. Question 10asksaboutaforce, whereasQuestion11asksaboutaratio Explain whyQuestions 10and11are different from eachother. No, the coefficient of frictionis the same. isinclinedorhorizontal? surface on whetherthesupporting depend between twosurfaces Does thecoefficientofslidingfriction µ static x and the vertical distancey.Computeand thevertical thecoefficientofstaticfric- With scale, aspring drag your shoealongthesameboard whenit Put your shoeontheboard, andslowly tilttheboard upuntilthe Repeat Step 7,except taptheboard haveapartner constantlyas µ static from the equationinthepreceding paragraph. should be greater thanµ µ µ µ sliding sliding sliding static sliding , whichequalstheratio ofy = ______= sliding by dividingtheforce (thescaleread- offriction = ______= = ______= from Steps 8and9equal?Explain any sliding . µ static and to x µ at thatboard sliding ?

Name Period Date

Chapter 9: Circular Motion Centripetal Acceleration

30 Going in Circles

Purpose

To determine the relative magnitude and direction of acceleration of an Setup: <1 object at different positions on a rotating turntable. Lab Time: 1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: difficult Mathematical Level: none dynamics cart accelerometer Adapted from PRISMS. mass pulley string support for pulley and mass phonograph turntable masking tape

Discussion Activity

How can a passenger in a smooth-riding train tell when the train undergoes an acceleration? The answer is easy: He or she can simply watch to see whether the surface of the liquid in a container is disturbed, or look for motion at the bottom of the hanging curtains. These are two simple accelerometers.

Procedure

Step 1: Attach the accelerometer securely to a cart, and place the cart on Observe accelerometer moving a smooth surface such as a table. in straight line.

Step 2: Attach the cart to the mass with a string. Attach a pulley to the edge of the table and place the string on the pulley.

Step 3: Allow the liquid in the accelerometer to settle down (level) while holding it in position ready to release. Allow the mass to fall and cause the cart to accelerate. Observe and sketch the surface of the liquid in the accelerometer. Label the direction of the acceleration of the cart. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 9 Circular Motion 103 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage104 104 turntable. Observe accelerometeron Laboratory ManualLaboratory (Activity 30) 3. the surface oftheliquideachtime.the surface turntable, speeds. atvarious andsketch androtate theturntable Observe Step 5: not flyoff. accelerometer totheturntable. Make sure thattheaccelerometer will 1. Step 4: 2. Repeat several theexperiment times. acceleration ontherotating turntable? What doyou concludeaboutthemagnitudeanddirection ofthe center oftheturntable. slope oftheliquid.Thedirection oftheaccelerationistoward the centerandatgreaterrotational speeds,asevidencedbythesteeper The magnitudeoftheaccelerationisgreaterat distancesfrom The liquid surface remains tipped atthesameanglefor constant The liquid surface continuestoaccelerate? asthecart What happenstothesurface falling mass,theangleis greater.) mass is used each time.(Atgreateracceleration,producedbya Yes, theangleofsurfaceshouldbesameiffalling behavethesamewayeachtime? Does thesurface acceleration. Place thecenterofaccelerometer atthecenterof Remove theaccelerometer andsecurely from thecart, attachthe

© Addison-Wesley Publishing Company, Inc. All rights reserved. 5. 4. Analysis Name i.C Fig. A Fig. are greaterclosertotheedge. Figure Bismostcorrect,astheaccelerationsaretoward thecenterand Which figure ismostcorrect? Explain thereason(s) foryour choice. magnitude anddirection oftheacceleration atdifferent points. The fourfigures show fourpossiblesetsofarrows representing the center ofarotatingsystemsuchasturntable. The situationshowninthefiguresisthatofanaccelerometer matches thesefigures? situation. mostclosely What situationoftheonesyou observed Figures A,B, C,andDshow oftheliquidforaparticular thesurface i.D Fig. B Fig. Period Chapter 9Circular Motion Date 105 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PM Page 106 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PM Page 107

Name Period Date

Chapter 10: Center of Gravity Center of Gravity

31 Where’s Your CG?

Purpose

To locate your center of gravity. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: difficult 2 bathroom scales Mathematical Level: none 8' × 2" × 12" “reaction” board meterstick bricks or old books 2 large triangular supports (such as 1-inch angle iron or machine-shop files)

Discussion

For a symmetrical object such as a ball or donut, the center of gravity, or CG, is located in the geometric center of the object. For asymmetrical Activity objects, such as a baseball bat or a person, the CG is located closer to the heavier end. When your arms are at your side, your center of gravity is near your navel, where your umbilical cord was attached. This is no coincidence—unborns sometimes rotate about their CG. Your CG is a point that moves when you move. When you raise your hands above your head, your CG is a little higher than when your hands are by your sides. In this activity, you will locate your CG when your hands are by your sides.

Procedure

Step 1: Using a bathroom scale, weigh yourself and then a reaction Weigh yourself. board. Record these weights.

weight of self = ______weight of board = ______

Step 2: Measure your height in centimeters. Measure your height.

height = ______

Step 3: Place one triangular support on each bathroom scale. You may Position reaction board. need to add bricks or books between the scale and the support if the bubble on the scale causes the support to rock. Position the scales so that the tops of the triangular supports are separated by a distance equal to your height. Place the reaction board on the two supports. The over-

Chapter 10 Center of Gravity 107 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage108 108 Determine yourCG. appreciably. reading somewhat, but not will decreasethescale readable. Booksthatcompress the scalereadingmore or a few bookshelpmake A thickblockof wood, a brick, Adjust your position. reading the scale. small plane mirror to facilitate It maybenecessary to utilizea board. Position yourself on reaction height. board lengthandthestudent‘s the differencebetween Each overhangshouldbehalf Laboratory ManualLaboratory (Activity 31) 1. from thebottomofyour feettoyour navel. Place your fingeronyour navelandhavesomeonemeasure thedistance your feet. Step 6: 2. support nearyour feet. support Have someonemeasure how farthebottomsofyour feetare from the tion alongthelengthofboard untilthetworeadings becomeequal. Step 5: sides. Have someonerecord thereading oneachbathroom scale. asinFigureport, A.Remain flatontheboard withyour handsby your over andthebottomsofyour feetare onesupport over theothersup- Step 4: the readings are equalorrecord thereadings forfuture calculations. any). If they are not,eitheradjustthecalibration knobononescaleuntil each behalftheweight ofthereaction board (plusthebooksorbricks, if Read theweight reading oneachbathroom scale. These readings should i.A Fig. Did you havetomove toward thefootendortoward the headend? CG ismidwaybetweenthetwosupports. When thetwoweightreadingsofstudentareequal,student’s tion tothesupports? When thereadings onthescalesare equal,where isyour CG inrela- between aperson’s CG and thefeet is about 0.6 ofthetotalheight.) Students will have to move towardthe foot end.(Typically, the distance Determine the locationofyourDetermine CG, inrelation tothebottomsof After you are of theweight readings, informed adjustyour posi- Lie down onthereaction board sothatthetipofyour headis location ofnavel=______cmfrom thefeet location ofCG =______cmfrom thefeet distance from support tofeet=______distance from support weight atfeet=______weight at head=______

© Addison-Wesley Publishing Company, Inc. All rights reserved. 5. 4. 3. Analysis Name Astronauts spinabouttheircenterofgravity(mass). space vehicle, whatpointdoesthebodyspinabout? When anastronaut spinswhendoingacrobatics aboard anorbiting two supportsasassumed. the centerofgravity of the board would notbe midway betweenthe If theweightofboard were notevenly distributed on each support, equal? What wouldhappenifthetwoweight readings oftheboard were not centimeters of the navel. The CG,asdeterminedbythisactivity, shouldbe within a few How closeisyour CG toyour navel? Period Chapter 10 Center of Gravity Date 109 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PM Page 110 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PM Page 111

Name Period Date

Chapter 11: Rotational Mechanics Torque

32 Torque Feeler

Purpose

To illustrate the qualitative differences between torque and force. Setup: <1 Lab Time: <1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy meterstick Mathematical Level: none meterstick clamp 1-kg mass Like many of the activities in mass hanger this manual, Torque Feeler should not be skipped because it is so short and simple. Proceeding to concept devel- Discussion opment after students wrestle with these concepts for them- selves will increase your Torque and force are sometimes confused because of their similarities. effectiveness dramatically. Their differences should be evident in this activity.

Procedure Activity

Step 1: Hold the end of a meterstick in your hand so that your index Rotate meterstick. finger is at the 5-cm mark. With the stick held horizontally, position the mass hanger at the 10-cm mark, and suspend the 1-kg mass from it. Rotate the stick to raise and lower the free end of the stick. Note how hard or easy it is to raise and lower the free end.

Step 2: Move the mass hanger to the 20-cm mark. Rotate the stick up Move mass farther from and down about the pivot point (your index finger) as before. Repeat this pivot point. procedure with the mass at the 40-cm, 60-cm, 80-cm, and 95-cm marks.

1. Does it get easier or harder to rotate the stick as the mass gets farther from the pivot point?

It gets harder to rotate the stick the farther away the mass gets from

Chapter 11 Rotational Mechanics 111 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage112 112 Laboratory ManualLaboratory (Activity 32) 2. Analysis 3. from the pivotpoint(your indexfinger)? Does theweight ofthemassincrease asyou move themassaway point aswellon the force. torque a The pulloftheearthonlarger the mass at the larger distance exerts difficulty inrotating thestickincrease inStep 2? If theweight ofthemassisnotgettinganylarger, whydoesthe the pivotpoint. The weightofthemassdoesnotincreaseasyoumoveitawayfrom on the meterstick.Torque dependsondistancefromthepivot

Name Period Date

Chapter 11: Rotational Mechanics Balanced Torques

33 Weighing an Elephant

Purpose

To determine the relationship between masses and distances from the Setup: <1 fulcrum for a balanced seesaw. Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate meterstick Mathematical Level: moderate wedge or knife-edge 2 50-g mass hangers Thanks to Art Farmer for his slotted masses or set of hook masses ideas and suggestions for this knife-edge level clamps lab.

Discussion

An object at rest is in equilibrium (review Section 4.7 of the text). The sum of the forces exerted on it is zero. The resting object also shows another aspect of equilibrium. Because the object has no rotation, the sum of the torques exerted on it is zero. When a force causes an object to start turning or rotating (or changes its rotation), a nonzero net torque is present. The seesaw is a simple mechanical device that rotates about a pivot or fulcrum. It is a type of lever. Although the work done by a device can never be more than the work or energy invested in it, levers make work easier to accomplish for a variety of tasks. Suppose you are an animal trainer at the circus. You have a very strong, very light, wooden plank. You want to balance a 600-kg baby elephant on a seesaw using only your own body weight. Suppose your body has a mass of 50 kg. The elephant is to stand 2 m from the fulcrum. How far from the fulcrum must you stand on the other side in order for you to balance the elephant? Laboratories do not have elephants or masses of that size. They do have a variety of smaller masses, metersticks, and fulcrums that enable you to discover how levers work, describe their forces and torques math- ematically, and finally solve the elephant problem.

Procedure

Step 1: Carefully balance a meterstick horizontally on a wedge or knife- edge. Suspend a 200-g mass 10 cm from the fulcrum. Suspend a 100-g mass on the opposite side of the fulcrum at the point that balances the meterstick. Record the masses and distances from the fulcrum in Data

Chapter 11 Rotational Mechanics 113 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage114 114 Analyze dataforpattern. (see answertoStep4). of forceanddistance that torque is theproduct Remind yourstudents Laboratory ManualLaboratory 33) (Experiment Data TableA pair ofvariables. You ratios forming or products. canalsotry thesmallmassvs.the fulcrum, oranother itsdistance from the fulcrum, of Data Table A. You graphing the large mass vs. cantry its distancefrom Step 3: 1. Table A.Be sure totakeintoaccountthemassofanyhangerorclamp. lighter mass. Record inData themassesanddistancesfrom thefulcrum heavier masswithanotherandrebalance theleverby moving the rebalance the meterstick with the lighter mass. move away, theheaviermasstoanewlocation5 cmfarther andthen the massesofStep 1andchangingtheirpositions. For instance, you can Step 2: Yes. Itcanbebalancedifitisclosertothefulcrumthanlighter Can aheaviermassbebalancedby alighterone?Explain how. You canalsochangethemagnitudesofmasses. Replace the mass. Make more tofillinData trials Table A. You candothisby using Use anymethodyou candevisetodiscover inthedata a pattern

© Addison-Wesley Publishing Company, Inc. All rights reserved. (2310 kg) × Solving ford the fulcrum,m Equivalently, 2. Analysis If board).mass ofthesupporting in order tobalancethe600-kgelephant.Show your work (neglectthe tion tofindthedistancea50-kgpersonshouldstandfrom thefulcrum Step 6: One equationis Be sure toexplainwhateachsymbolstandsfor. Step 5: statement. that you havediscovered intoaword thispattern convert apattern, Step 4: Name d is theperson’s distancefromthefulcrum, then masses do. These itemsexertforcesand torquesonthemeterstickjustas account inthisexperiment? Why mustthemassofhangersandclampsbetaken into are equal. statement isequivalenttosayingthatthetorquesontwomasses toitsmass,thisword force oneachmass(itsweight)isproportional distance.) Sincetorqueistheproductofforce by the secondmass equals the seconddistancedividedbyfirst may statethis in terms of the equivalent ratios:the first massdivided product of the othermassandits distance from thefulcrum.(Students The product of onemass and its distance fromthefulcrumequals With oryour thehelpofyour teacher, partners useyour equa- Now thisword convert statementintoamathematicalequation. After you haveconvincedyourself partners andyour laboratory (2 m)=(50kg)× m gives avalueof92m.You would need averylongplank! 2 1 is theothermass,andd /m m 1 2 d d 1 = = ______m m ______= = d 2 m /d 2 d 1 . 2 (d , wherem ) 1 2 is onemass,d is itsdistancefromthefulcrum. and distance,the 1 is itsdistancefrom Period Chapter 11Rotational Mechanics Solve forunknowndistance. equation. Convert statementinto Express patternasstatement. Date 115 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage116 116 Laboratory ManualLaboratory 33) (Experiment 3. 4. Mention atleasttwothings. much lessthanyou), whatcanyou dotobalancetheseesaw? If you are playingseesawwithyour younger sister(whoweighs provided bytheboard. Closer, sincesomeofthetorqueneededtobalanceelephantis thancalculatedinStepthe fulcrum 6? would theactualpositionoftrainer from orcloserto befarther and thetrainer (seesketchintheDiscussion section)hasweight, Taking accountofthefactthatboard holdinguptheelephant closer toyou. from thefulcrum.Iffulcrumis not fixed,youcan You canmoveclosertothefulcrumand/orshefartheraway move the fulcrum

Name Period Date

Chapter 11: Rotational Mechanics Balanced Torques

34 Keeping in Balance

Purpose

To use the principle of balanced torques to find the value of an unknown Setup: <1 mass. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate meterstick fulcrum Mathematical Level: moderate standard mass with hook fulcrum holder rock or unknown mass string triple-beam balance masking tape

Discussion

Gravity pulls on every part of an object. It pulls more strongly on the more massive parts of objects and more weakly on the less massive parts. The sum of all these pulls is the weight of the object. The average position of the weight of an object is its center of gravity, or CG. The whole weight of the object is effectively concentrated at its center of gravity. The CG of a uniform meterstick is at the 50-cm mark. In this experiment, you will balance a meterstick with a known and an unknown mass, and compute the mass of the unknown. Then you will simulate a “solitary seesaw.”

Procedure

Step 1: Balance the meterstick horizontally with nothing hanging from Balance the meterstick. it. Record the position of the CG of the meterstick.

position of meterstick CG = ______

Using a string, attach an object of unknown mass, such as a rock, at the 90-cm mark of the meterstick, as shown in Figure A. Place a known mass on the other side to balance the meterstick. Record the mass used and its position. mass = ______position = ______

Chapter 11 Rotational Mechanics 117 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage118 118 Set up“solitaryseesaw.” Calculate percenterror. Measure massofunknown. Compute unknownmass. Laboratory ManualLaboratory 34) (Experiment i.B Fig. 2, andcalculatethepercentage difference. Step 4: Step 3: in words andthenwiththeknown values. Compute theunknown mass. distance from to the place where the fulcrum the force acts. Step 2: marks, asinFigure B. Record themassused anditsposition. meterstick usingasinglemasshungbetween the85-cmand100-cm Step 5: (unknown mass) In thefollowing space, anequationforbalancedtorques, write first These twodistancesare known asleverarms. isthe The leverarm mass = ______position = ______= position ______= mass Compare themeasured masstothevalue you computed inStep Measure theunknown mass, balance. usingatriple-beam Compute toeachobject. thedistancesfrom thefulcrum Place the fulcrum exactlyonthe85-cmmark.Place Balance thefulcrum the mass distance from fulcrum toknowndistance from fulcrum mass=______tounknowndistance from fulcrum mass=______mass ro ————————————— = error % measured computed ______= (its distancetofulcrum)= |mass (known mass) = ______= = ______= computed mass – mass measured (its distancetofulcrum) measured | × 100%

© Addison-Wesley Publishing Company, Inc. All rights reserved. meterstick. Step 8: balance. Step 7: tion of the center of gravity for an asymmetrical rigid object. tion ofthecenter ofgravity rigid foranasymmetrical end. In how you willlearn oftheexperiment, thispart tofindtheloca- objectsuchasabaseball bat,theCG isnearerasymmetrical theheavier center. meterstickisatthe50-cmmark.The CG But ofauniform foran For objectthe CG islocated atitsgeometrical symmetrical auniform, Going Further (meterstick mass) space. Compute themassofmeterstick.Show your work inthefollowing 1. foreachmass. andtheleverarm to torques oneachsideofthefulcrum, space. Be sure themasseswhoseweights giverise tolabelthefulcrum, Step 6: Name mark). The massofthemeterstickiseffectivelyatitsCG(near50-cm Where isthemassofmeterstickeffectivelylocated? Find thepercent error forthecomputedvalue ofthemass Remove themeterstickandmeasure itsmassonatriple-beam Draw aleverdiagram ofyour metersticksysteminthefollowing mass mass ro —————————————— = error % measured computed × ______= (distance fromCGtofulcrum)= |mass (hung mass)× = ______= = ______= computed mass – mass measured (its distance) measured | × 100% Period Chapter 11Rotational Mechanics Calculate percenterror. Measure massofmeterstick. Draw leverdiagram. Date 119 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage120 120 “growth” onthemeterstick. to thinkoftherockasa triple-beam balance.Tell them meterstick whenusingthe remove therockfrom Caution yourstudentsnotto Balance meterstick. Laboratory ManualLaboratory 34) (Experiment i.C Fig. first inwords andthenwithknown values. for balancedtorques. In thefollowing space, down write theequation balance.triple-beam Step 10: 3. 2. atthepredictedmass andplacingthefulcrum CG point. Step 11: (mass ofcombination) balance themeterstick.Record themassusedanditsposition. Figure C.Hang aknown massbetween the60-cmand100-cmmark to and 50-cmmark. Move tothe60-cmmark, asshown thefulcrum in Use maskingtapetoattachtherock tothemeterstickbetween the0-cm the newCG ofthecombined Step 9: Find theCG ofthemeterstick/rock combinationusinganequation They shouldagreewithinafewpercent. location? How farwasyour predicted locationoftheCG from itsactual Answers willvary. Does themeterstickbalance? If arock isattachedtoyour meterstickawayfrom themidpoint, Verify thelocationofCG by removing theaddedknown Find themassofmeterstick/rock combinationwitha mass ofmeterstick/rock combination=______computed positionofCG =______distance from =______CG tofulcrum mass = ______position = ______= position ______= mass × (known mass)× = (distance fromCGofcombinationtofulcrum) meterstick plusrock isnot (its distancefromfulcrum) in thecenter.

Name Period Date

Chapter 11: Rotational Mechanics Rotational Inertia

35 Rotational Derby

Purpose

To observe how round objects of various shapes and masses roll down Setup: <1 an incline and how their rotational inertias affect their rate of rotation. Lab Time: >1 Learning Cycle: concept Required Equipment/Supplies development Conceptual Level: moderate smooth, flat board, 1 m in length Mathematical Level: moderate ring stand or metal support with clamp and rod balance Thanks to John Davis for ideas meterstick and suggestions for this lab. 3 solid steel balls of different diameter (3/4” minimum) 3 empty cans of different diameter, with both the top and the bottom removed 3 unopened cans of different diameter, filled with nonsloshing contents (such as chili or ravioli) 2 unopened soup cans filled with different kinds of soup, one liquid (sloshing) and one solid (nonsloshing) Activity

Discussion

Why is most of the mass of a flywheel, a gyroscope, or a Frisbee concentrated at its outer edge? Does this mass configuration give these objects a greater tendency to resist changes in rotation? How does their “rotational inertia” differ from the inertia you studied when you investigated linear motion? Keep these questions in mind as you do this activity. The rotational speed of a rotating object is a measure of how fast the rotation is taking place. It is the angle turned per unit of time and may be measured in degrees per second or in radians per second. (A radian is a unit similar to a degree, only bigger; it is slightly larger than 57 degrees.) The rotational acceleration, on the other hand, is a measure of how quickly the rotational speed changes. (It is measured in degrees per second squared or in radians per second squared.) The rotational speed and the rotational acceleration are to rotational motion what speed and acceleration are to linear motion.

Procedure

Step 1: Make a ramp with the board and support. Place the board at an Set up ramp. angle of about 10°. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 11 Rotational Mechanics 121 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage122 122 Roll hollowcylinders. Roll ballsdownramp. Roll solidcylinders. Laboratory ManualLaboratory (Activity 35) 3. Repeat the race fortheotherpairsofsolidcylinders. sloshing contents).Record your predictions andresults. 2. Repeat therace fortheotherpairsofhollow cylinders. your predictions andresults. 1. Repeat therace fortheotherpairofballs. Record your results. stick. Quickly remove thesticktoallow theballstoroll down theramp. Place ameterstick across theramp nearthetop, andrest theballson ramp time. intheshorter Step 2: Step 4: Step 3: of different diametertoroll down the sameincline? What doyou concludeaboutthetimeittakesfortwosolidcylinders ders ofdifferent diametertoroll down thesameincline? What doyou concludeaboutthetimeittakesfortwohollow cylin- of different diametertoroll down thesameincline? What doyou concludeaboutthetimeittakesfortwosolidsteelballs incline, regardlessofdiameter(andmass). Hollow cylindersalltakeaboutthesametimetorolldown incline, regardlessofdiameter(andmass). Solid steelballsalltakeaboutthesametimetorolldown incline, regardlessofdiameter (andmass). Solid cylindersalltakeabout thesametimetorolldown Repeat the race fortwosolidcylinders(filledcanswithnon- Repeat therace fortwohollow cylinders(emptycans).Record Select twoballs. Predict whichballwillreach thebottomof actual winner: ______winner: actual ______winner: predicted ______winner: actual ______winner: predicted ______winner: actual ______winner: predicted

© Addison-Wesley Publishing Company, Inc. All rights reserved. your prediction andresult. Step 7: 6. prediction andresult. Step 6: 5. 4. Repeat forotherpairsofhollow vs. solidcylinders. Now it,andrecord try your results. ing it,predict whichcylinderwillreach thebottomoframp first. Step 5: Name Theoretically, theballwillbeatcylinder. A solidsteelballandacylindermaybetooclose tocall. solid cylindertoroll down thesameincline? What doyou concludeaboutthetimeittakesforasolidball anda cylinder, muchofthemass is closetotheturningaxis. concentrated at thegreatestdistancefromturning axis. Inthesolid distribution of mass does. In thehollow cylinder, themassisall Although neithermassnordiameteraffectstherollingtime, the solid cylinders? How doyou explaintheresults forthehollow you observed and regardless ofdiameter(andmass). A solidcylinderbeatsahollowdownthesameincline, solid cylindertoroll down thesameincline? What canyou concludeaboutthetimeittakesforahollow anda Repeat the race forasolidballandhollow cylinder. Record Repeat therace forasolidballandcylinder. Record your Repeat therace forahollow cylinderandasolidone. Before try- actual winner: ______winner: actual ______winner: predicted ______winner: actual ______winner: predicted ______winner: actual ______winner: predicted Period Chapter 11Rotational Mechanics Roll hollow and solidcylinders. Roll balls andsolidcylinders. Roll ballsandhollowcylinders. Date 123 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage124 124 soup. Roll cansofdifferentkinds Laboratory ManualLaboratory (Activity 35) 8. prediction andresults. contents andtheotherwithsolid(nonsloshing)contents. Record your 7. 9. Analysis Step 8: 10. nonsloshing kindsofsoup? How canyou explaintheresults forthesloshingvs. you observed Students shouldbeabletopredictcorrectlythatthesteelballwillbeat hollow cylindertoroll down thesameincline? What canyou concludeaboutthetimeittakesforasolidballand The ballsreachedthebottominshortesttime. the incline? Of alltheobjectsyou tested,whichtooktheleasttimetoroll down different. AcanofBeanwithBaconbeatsaBeefBouillon. them. Thus,thedistributionof whereas theliquidy(sloshing)soupsallowcantoslidearound thicker, moreviscous(nonsloshing)kindsofsouprollwiththecan, Soup cansdonottakethesametimetoreachbottombecause the hollowcylinder, regardlessofdiameter(andmass). and diameter). The hollowcylindershadthe greatestrotationalinertia(fortheirmass resistance objects had the greatest rotationalis, inertia—that the greatest rotational acceleration. Of the objects you tested, what shape of Gravity fasterandfaster—thatis, causedtheobjectstoturn theyhad Repeat therace fortwosoupcans, onewithliquid(sloshing) to rotational acceleration? culwne: ______winner: actual ______winner: predicted rolling mass canbemarkedly

Name Period Date

Chapter 13: Gravitational Interactions Acceleration of Gravity

Acceleration of 36 Free Fall

Purpose

To measure the acceleration of an object during free fall with the help of Setup: >1 a pendulum. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate Free Fall apparatus from Arbor Scientific Co. or Mathematical Level: difficult meterstick with 2 eye hooks in one end 3-inch-long, 3/4-inch-diameter wooden dowel with 2 nails in it Thanks to Herb Gottlieb for ring stand ideas and suggestions for condenser clamp this lab. C clamp stopwatch drilled steel or brass ball string masking tape carbon paper white paper

Discussion

Measuring the acceleration g of free fall is not a simple thing to do. Galileo had great difficulty in his attempts to measure g because he lacked good timing devices and the motion was too fast. His measurements were done on inclined planes, to slow the motion down. Galileo would have appreciated the technique you will use in this lab. He was the first to note that the time it takes a pendulum to swing to and fro depends only on the length of the pendulum (provided the angle of swinging is not too great). The time it takes for a pendulum to make a complete to-and-fro swing is called its period. How long does a pendulum take to swing from its lowest position to an angle of maximum deflection? The answer is one fourth of its period. If the period is known, it can be used as a unit of time. If a freely falling object and a pendulum are released from elevated positions at the same time, their times can be compared.

Fig. A Procedure

Step 1: Assemble the meterstick pendulum shown in Figure A, attaching Assemble pendulum. the dowel to the ring stand with a condenser clamp. Suspend the meterstick from the lower of the two nails in the wooden dowel. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 13 Gravitational Interactions 125 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage126 126 B Fig. Make trial run. Check alignment. Attach ball. Measure period. Laboratory ManualLaboratory 36) (Experiment i.C Fig. with themeterstick. This provides amore exactmeasurement. repeated, theballwillleaveamark onthewhitepaperwhere itcollides taping the carbon side white papertothemeterstickandcover ofcarbonpaper, itwithastrip between theballandmeterstick.At of thislocation,tapeastrip measured from thetopofmetersticktopointcollision ofthemeterstick. theperiod fourth The distancethattheballfalls is between thetimeofrelease andthetimeofcollisionisexactlyone- tion, theballandmeterstickwillcollide(Figure D). The interval stick swinging. The instantthatthemeterstickreaches posi- itsvertical release tosimultaneouslyrelease thestring themeter- theballandstart (seeFigurethe vertical C). With theapparatus inthisposition,you will the meterstickandbottomofdisplaced20cmfrom Step 5: stick allthewaydown. slowly lowering theballalongmeterstick. It shouldjustgraze the meterstick (seeFigure C).Checkthealignment oftheapparatus by Step 4: brass over ball.Loopthestring theuppernailindowel, asinFigure B. steelor bottom ofthemeterstickandattachotherendtoadrilled Step 3: record theperiod. Compute ofthemeterstick.Show theperiod your computationand 10times.stick toswingbackandforth With a stopwatch, measure and record the time it takes for the meter- Step 2: Make a trial run to determine theapproximate todetermine Make run atrial pointofthecollision Hold withthecenterofballat0-cmmark of thestring Pull theballupsothatitbarely touchesthe0-cmmark onthe Using tothe 210cmlong,connectoneendofthestring astring Displace thebottomofmeterstick20cmfrom thevertical. period = ______= period time for10completeswings=______against thewhitepaper i.D Fig. . is When theexperiment

© Addison-Wesley Publishing Company, Inc. All rights reserved. Data TableA 2. Analysis Table A.Record your average value for Compute theacceleration ofgravity forthree andrecord trials inData from rest andundergoes theacceleration Step 7: 1. the distancesinData Table A. 0-cm mark onthemetersticktomarks onthewhitepaper. Record trials. Remove thecarbonpaperandmeasure thedistancesfrom the Step 6: When thisequationissolvedfor Name value of g.Thedirect effect is todecrease thedistance ball falls. It providesaforce that acts opposite togravityandthus decreases your have onyour value ofg? ofthecordWhat effectdoesthefriction againsttheuppersupport Measure tothetopbecausethatiswhereitfirsthits. the top, themiddle, orthebottomofthisline? In thedistancethatballfell,shouldyou measure measuring to lineapproximatelypaper isavertical 0.5cmlong,rather thanadot. When theballandmeterstickcollide, themark leftonthewhite With thecarbonpaperinpositiononmeterstick,makethree The equationforthedistanced d g —— = — = 2d 1 2 t 2 gt 2 g, itbecomes g. traveled by anobjectthatstarts g of gravity fortimet is Period Chapter 13 Gravitational Interactions Compute g. Measure distance. Date 127 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage128 128 Laboratory ManualLaboratory 36) (Experiment 3. The airresistancewasalreadytakenintoaccountwhentheperiod of Why doesn’t theairresistance onthemeterstickaffectyour value measured. Therefore,yourvalueof g? g is unaffected by airresistance.

Name Period Date

Chapter 13: Gravitational Interactions Acceleration of Gravity

Computerized 37 Gravity

Purpose

To measure the acceleration due to gravity using the computer. Setup: >1 Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development computer Conceptual Level: moderate light probe with interface Mathematical Level: difficult light source 2 ring stands Thanks to Dewey Dykstra and 2 clamps Marvin De Jong for their ideas cardboard or metal letter “g” and suggestions for this lab. Plexiglas® acrylic plastic strip with black electrical tape on it printer

Part A: The Letter “g” Method Discussion

If you know the initial and final speeds of a falling object, and the time interval between them, you can compute the object’s acceleration. In this experiment, you will exploit the computer’s ability to time events accurately using its game port. The falling object is a square letter “g” cut out of stiff cardboard or sheet metal (see Figure A). The computer has been programmed to clock the time t1 it takes for the figure to fall the first distance, d1, and the time t2 it takes to fall the second distance, d2. The measurement of how long it takes to fall each distance past a light probe enables you to compute the average speed for each interval. The average acceleration is then easily computed. From the definition of acceleration as the change in velocity per second, the acceleration g of a Fig. A freely falling object is

(v – v ) g = a = —————2av 1av t av You might wonder if these equations are exact, since they d1 use finite distances, average where v1av = — speeds, and average times. In t1 fact, they are exact so long as

the distances d1 and d2 are d2 adjacent. v2av = — t2

(t1 + t2)

Chapter 13 Gravitational Interactions 129 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage130 130 Measure d Set uplightprobe. i.B Fig. Laboratory ManualLaboratory 37) (Experiment 1 and d 2 . not within2%oftheacceptedvalue, repeat theexperiment. through the lightbeam,asinFigure B. If your computedvalues forg Step 2: stick tothenearest thousandthofameter(millimeter). Step 1: Procedure 4. 3. 2. 1. Analysis be affected? beam, how wouldthecalculationofacceleration duetogravity andthendropped andhorizontal, throughlonger vertical thelight If theletter “g” were heldatonecorner, sothattheedgeswere no of thepositioninlightbeam(providedletterisnottilted). For asquareletter“g”thedistancesd round one? What are theadvantages ofusingasquare letter “g” insteadofa The effectdueto air resistancewouldbelessforthesheetmetal. one madeofcardboard? Why wouldaletter “g” madeofsheetmetalprobably bebetterthan of the letter “g.” and (2)inaccuracy in timingdue to spreadingoflightaroundtheedges Sources oferrorare(1)uncertaintiesinthemeasurements computer hasbeenprogrammed with100%accuracy! List thepossiblesources Assumethatthe oferror inthisexperiment. and known, onecouldeliminatetheerrorbyusinglargervalues for gravity wouldbelessthantheactualvalue.(Ifangle oftheletteris The timeswouldbelonger, andthecomputed accelerationdueto Set upthecomputerwithalightprobe. Drop theletter “g” Measure thedistancesd d 2 .) 1 and d 2 1 of theletter “g” withameter- and d 2 are thesameregardless d 1 d and 1 are d 2

© Addison-Wesley Publishing Company, Inc. All rights reserved. report. Save ofyour your graph; dataandmakeaprintout include itwithyour 6. Step 6: Save ofyour your graph. dataandmakeaprintout 5. software. axis)vs.distance (vertical axis)usingdataplotting time(horizontal Step 5: it. ble tothelightprobe withouttriggering possible. For bestresults, holdthebottomoffenceasclosepossi- the topoffenceandrelease as itsothatfallsasnearlyvertically Step 4: of foamunderthelightprobe tocushionthestopofdropped fence. in metersintotheprogram. Position somethingsquishysuchasapiece Step 3: Procedure through the lightprobe! (Wouldn’t Galileo haveloved toseeyou dothis!) steel balldown anincline. In thisone, you simplydrop thepicketfence 4, Experiment “Merrily We Roll Along.” In you rolled thatexperiment, a becomesthe (equidistant), thisexperiment “undiluted” inclineof next. If the spacesbetween oftapeare thedark strips allthesame (“fence”) tofallfrom (“picket”) thetopofonedark strip tothetopof probe arrangement asinPart Aisusedhere. fence”) fallspastthelightprobe. asthePlexiglas strip The samelight of tapecreate opaqueandtransparent alternating regions (“picket spaced 5cmfrom oneedgetothenext,asshown inFigure C. The strips probe instead ofaletter “g”. haseightdarkThe Plexiglas strips strip Part plasticisdropped pastthelight ofPlexiglas acrylic A.Alongstrip g This methodofmeasuring Discussion ThePicketFenceMethod Part B: Name The velocityvs.timegraphisastraightline. yourDescribe graph. The distancevs.timegraphisaparabola. yourDescribe graph. The computermeasures thetimeittakesforPlexiglas strip Plot velocity (vertical axis)vs.Plot velocity(vertical axis). time(horizontal After you successfullyacquire data,saveitandthenplot Drop thepicketfencethrough thelightprobe. Be sure topinch Measure thedistancefrom pickettopicket.Enterthisdistance is anextensionofthemethodusedin Period Chapter 13 Gravitational Interactions plot dvs.t Use dataplottingsoftwareto i.C Fig. 2 . Date 131 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage132 132 Laboratory ManualLaboratory 37) (Experiment 7. Analysis of your graph? measure theslopeofgraph. What isthesignificanceofslope Are eitherofyour graphs straight lines?If so, askyour teacherhow to the accelerationofgravity. The slopeofthestraightlineinvelocityvs.timegraphisequalto

Name Period Date

Chapter 13: Gravitational Interactions Free Fall

Apparent 38 Weightlessness

Purpose

To observe the effects of gravity on objects in free fall. Setup: 1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy 2 plastic foam or paper cups masking tape Mathematical Level: none 2 long rubber bands large paper clip 2 washers or other small masses water Thanks to Tim Cooney for his ideas and suggestions for this lab. Discussion

Some people believe that because astronauts aboard an orbiting space vehicle appear weightless, the pull of gravity upon them is zero. This condition is commonly referred to as “zero-g .” While it is true that they feel weightless, gravity is acting upon them. It acts with almost the same magnitude as on the earth’s surface. Activity The key to understanding this condition is realizing that both the astronauts and the space vehicle are in free fall. It is very similar to how you would feel inside an elevator with a snapped cable! The primary difference between the runaway elevator and the space vehicle is that the runaway elevator has no horizontal velocity (relative to the earth’s surface) as it falls toward the earth, so it eventually hits the earth. The horizontal velocity of the space vehicle ensures that as it falls toward the earth, it also moves around the earth. It falls without getting closer to the earth’s surface. Both cases involve free fall. Fig. A Procedure

Step 1: Knot together two rubber bands to make one long rubber band. Attach washers. Knot each end around a washer, and tape the washers to the ends. Bore a small hole about the diameter of a pencil through the bottom of a Styrofoam or paper cup. Fit the rubber bands through the hole from the inside. Use a paper clip to hold the rubber bands in place under the bottom of the cup (see Figure A). Hang the washers over the lip of the cup. The rubber bands should be taut.

Step 2: Drop the cup from a height of about 2 m. Drop cup.

1. What happens to the washers?

Chapter 13 Gravitational Interactions 133 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage134 134 Fill cupwithwater. i.B Fig. Laboratory ManualLaboratory (Activity 38) 3. masking tapeover theholeonbottomofcup. holes pokedthrough itssides 2. directly over asink.Drop thecupintosink. with water, usingyour fingerasastopperover thehole. Hold thecup Step 3: 6. 5. 4. Analysis Step 4: What happenstothewaterascupfalls? What happenstothewaterascupfalls? Your weightreadingwoulddecrease. b. Your weight readingwouldincrease. a. happen toyour weight reading whentheelevator: Based inthisactivity, onyour observations predict whatwould Suppose you were standingonabathroom scaleinsideanelevator. There is(nearly)nodrainingbecausethecupandwaterfalltogether. Explain whythedraining wateractedasitdidinSteps 3and4. length. washers intothecup as therubberbandsreturnto their unstretched In free fall the tensioninrubberbandspulls “weightless” Explain whythewashersactedastheydidinStep 2. Hardly anywatercomesoutoftheholewhilecupisfalling. Hardly anywatercomesoutoftheholewhilecupisfalling. accelerating downward faster thanfreefall. The readingofthescale would betheforceneededto keep thescale e. Your weightreadingwouldbethesameasnormal. d. Your weightreadingwouldbethesameasnormal. c. accelerated upward. moved upward ataconstantspeed. accelerated downward atanacceleration greater than accelerated downward atanacceleration lessthan moved downward ataconstantspeed. Repeat Step 3forasecondcuphalf-filledwithwatertwo Remove bandsfrom thecupandfillhalf-full therubber (Figure B). You maywishtoplaceapieceof g. g.

Name Period Date

Chapter 14: Satellite Motion Elliptical Orbits

39 Getting Eccentric

Purpose

To get a feeling for the shapes of ellipses and the locations of their foci Setup: <1 by drawing a few. Lab Time: 1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: easy Mathematical Level: none 20 cm of string 2 thumbtacks or small pieces of masking tape To save time, you might have pencil students do this lab at home. graph paper

Discussion

The path of a planet around the sun is an ellipse, the shadow of a sphere cast on a flat table is an ellipse, and the trajectory of Halley’s comet around the sun is an ellipse. Activity An ellipse is an oval-shaped curve for which the distances from any point on the curve to two fixed points (the foci) in the interior have a constant sum. One way to draw an ellipse is to place a loop of string around two thumbtacks and pull the string taut with a pencil. Then slide the pencil along the string, keeping it taut.

Procedure

Step 1: Using graph paper, a loop of string, and two thumbtacks (you may wish to use a small piece of masking tape instead), draw an ellipse. Label the two foci of your ellipse.

Step 2: Repeat twice, using different separation distances for the foci.

Step 3: A circle is a special case of an ellipse. Determine the positions of the foci that would give you a circle, and construct a circle.

Step 4: A straight line is a special case of an ellipse. Determine the positions of the foci that would give you a straight line, and construct a straight line. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 14 Satellite Motion 135 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage136 136 Laboratory ManualLaboratory (Activity 39) 1. Analysis 2. around the sun? Which ofyour drawings isclosesttotheearth’s nearlycircular orbit foci areveryfarapart. The orbitofHalley’s comet is very eccentric (elongated) because the around the sun? Which ofyour drawings isclosesttotheorbitofHalley’s comet compared with the distanceacross ellipse. The earth’s orbitisnearlycircular. Thetwofociareveryclosetogether

Name Period Date

Chapter 14: Satellite Motion Kepler’s Third Law

40 Trial and Error

Purpose

To discover Kepler’s third law of planetary motion through a procedure Setup: <1 of trial and error using the computer. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: difficult computer Mathematical Level: difficult data plotting software Thanks to Jay Obernolte for developing the software Data Plotter, which makes this activ- Discussion ity possible.

Pretend you are a budding astronomer. In order to earn your Ph.D. degree, you are doing research on planetary motion. You are looking for a relationship between the time it takes a planet to orbit the sun (the period ) and the average radius of the planet’s orbit around the sun. Using a telescope, you have accumulated the planetary data shown in Table A. You have access to a program that allows you to plot data easily on a computer. It can also plot many different relations between the variables. You can plot the period T vs. the radius R. You can also plot T vs. R2, T vs. R3, and so on. You can even plot R vs. T, R vs. T 2, and R vs. T 3, and so on, just as easily.

Procedure

Step 1: Using data plotting software, try to make a graph involving T and R that is a straight line. A linear (straight-line) relationship shows that the two plotted variables are directly proportional to each other. Try plotting T vs. R, T vs. R2, T vs. R3, R vs. T, R vs. T 2, and R vs. T 3 to see whether any of these relationships form a straight line when graphed. Table A

Step 2: If the relationship between T and R cannot be discovered by An astronomical unit (AU) is modifying the power of only one variable at a time, try modifying the the average distance between power of both variables at the same time. the sun and the earth. If you find the exact relationship between T and R during this lab Stress the importance of period, feel good. It took Johannes Kepler (1571–1630) ten years of discovering functional relation- painstaking effort to discover the relationship. Computers were not ships rather than Kepler’s around in the seventeenth century! third law. This is such a powerful data reduction technique that you may wish to kick off your course with this activity. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 14 Satellite Motion 137 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage138 138 Laboratory ManualLaboratory 40) (Experiment 1. 2. as astraight line? some power ofR Did you discover alinearrelationship between somepower of with your report. Make ofthegraph aprintout closesttoastraight lineandincludeit years. toR proportional Using Data Plotter,yourstudentscandiscoverinminutesthat 3 using theprogram? What powers ofT —an amazingfeatconsideringthatittookKepler and R T graph 2 T is and

Name Period Date

Chapter 17: The Atomic Nature of Matter Diameter of a BB

41 Flat as a Pancake

Purpose

To estimate the diameter of a BB. Setup: ≤1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy 75 mL of BB shot Mathematical Level: moderate 100-mL graduated cylinder tray The computer simulation by rulers the same name on Laboratory micrometer Simulations-II complements this lab nicely.

Discussion

Consider 512 cubes, each with sides one centimeter long. If all the cubes are packed closely with no spaces between them to make a large cube with sides 8 cubes long, the volume of the large cube is (8 cm) × (8 cm) × Activity (8 cm), or 512 cm3. If the cubes are stacked to make a block 4 cm by 16 cm by 8 cm, the volume remains the same but the outside surface area becomes greater. In a block 2 cm by 16 cm by 16 cm, the area of the surface is greater still. If the cubes are spread out so that the stack is only one cube high, the area of the surface is the greatest it can be. The different configurations have different surface areas, but the volume remains constant. The volume of pancake batter is also the same whether it is in the mixing bowl or spread out on a surface (except that on a hot griddle the volume increases because of the expanding bubbles that form as the batter cooks). The volume of a pancake equals the surface area of one flat side multiplied by the thickness. If both the volume and the surface area are known, then the thickness can be calculated from the following equations. volume volume = area × thickness thickness = ———– area

Instead of cubical blocks or pancake batter, consider a shoe box full of marbles. The total volume of the marbles equals the volume of the box (length times width times height). Suppose you computed the volume and then poured the marbles onto a large tray. Can you think of a way to estimate the diameter (or thickness) of a single marble without measuring the marble itself? Would the same procedure work for smaller size balls such as BB’s? Try it in this activity and see. It will be simply another step smaller to consider the size of molecules. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 17 The Atomic Nature of Matter 139 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage140 140 turn teach the otherstudents. “experts” andhave them in eter is to make severalstudent students howtousea microm- An effective waytoteachyour Laboratory ManualLaboratory (Activity 41) Describe yourDescribe procedure andshow your computations. shape onyour labtable. thearea Determine covered by theBB’s. tray. If trays are notavailable, tapingthree togetherinaU- try rulers Step 2: diameter ofaBB. Step 4: a BB. Show your computations. (Note that1mL=cm Step 1: Procedure 2. 1. Analysis Step 3: 3. How dothemeasured andestimateddiametersoftheBBcompare? increases the volume they occupy. are atleastseverallayersdeep,sospreading them intoasinglelayer than cubesofthe same width.This compaction appliesonlywhenthey change. SincetheBB’s arespheres,theypack together more compactly It is assumed thatthetotalvolumeoccupiedbyBB’s didnot the BB? What assumptionsdidyou makewhenestimatingthediameterof the nextexperiment. covers. Dividethevolumeby the areatoestimate thickness. See Drop aknownvolumeofoleicacidonwaterand measure thearea it method toestimatethesize ofanoleicacidmolecule. water surface, creating alayer a onemolecule thick.Describe drop ofoleicacidisplacedonwater, itusually spreads outover the Oleic acidisanorganic substancethatisinsolubleinwater. When a Answers willvary. Spread theBB’s tomakeacompactlayer onepelletthickonthe Check your estimateby usingamicrometer tomeasure the Using thearea andvolumeoftheBB’s, estimate thediameterof Use agraduated cylindertomeasure thevolumeofBB’s. ra=______cm ______= area ______= volume measured diameter=______cm estimated diameter=______cm 3 .) 2

Name Period Date

Chapter 17: The Atomic Nature of Matter The Size of a Molecule 42 Extra Small

Purpose

To estimate the size of a molecule of oleic acid. Setup: <1 Lab Time: 1

Required Equipment/Supplies Learning Cycle: application Experiment Conceptual Level: moderate chalk dust or lycopodium powder tray Mathematical Level: difficult oleic acid solution water 10-mL graduated cylinder eyedropper Thanks to Dave Olsen for his ideas and suggestions for this lab. Discussion

An oleic acid molecule is not spherical but elongated like a hot dog. One end is attracted to water, and the other end points away from the water surface. During this investigation, you will estimate the length of a single molecule of oleic acid, to determine for yourself the extreme smallness of a molecule. The length can be calculated by dividing the volume of oleic acid used by the area of the monolayer, or layer one molecule thick. The length of the molecule is the depth of the monolayer.

volume = area × depth

volume depth = ———– area

Procedure

Step 1: Pour water into the tray to a depth of about 1 cm. Spread chalk Set up tray. dust or lycopodium powder very lightly over the surface of the water; too much will hem in the oleic acid.

Step 2: Using the eyedropper, gently add a single drop of the oleic acid Compute area of film. solution to the surface of the water. When the drop touches the water, the alcohol in it will dissolve in the water, but the oleic acid will not. The oleic acid spreads out to make a circle on the water. Measure the diameter of the oleic acid circle in three places, and compute the average diameter of the circle. Also, compute the area of the circle.

average diameter = ______cm

Chapter 17 The Atomic Nature of Matter 141 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage142 142 are conceptuallyidentical. Pancake” and“ExtraSmall” remind themthat“Flatas a down inthecalculations, tations. Ifstudentsgetbogged help studentswiththecompu- The computersimulationwill Compute lengthofmolecule. Laboratory ManualLaboratory 42) (Experiment of asingledrop. ume ofoleicacidby thearea ofthecircle. (or 3cm Step 3: 3. 2. 1. Analysis Step 5: of oleicacidinthesolutionis5cm less thanthevolumeofasingledrop ofthesolution. The concentration Step 4: 4. Divide 3 cm average numberofdrops in3cm cubic centimeterofthesolutionthuscontainsonly5/1000cm the drop. This isthevolumeoflayer ofoleicacidinthetray. Multiply thevolumeofadrop by 0.005tofindthevolume of oleicacidin acid. The ratio ofoleicacidtototalsolutionis0.005foranyvolume. alcohol? themonolayer film—theoleicacidorthe Which substanceforms swimming pool). At fullstrength,asingledropwouldcoverhugearea(suchas todilutetheoleicacid? Why isitnecessary A monolayerisalayeronemoleculethick. What ismeantby amonolayer? one-tenth the lengthtimesone-tenththe length. The volume of onerectangular moleculewouldbe the lengthtimes of oneoleicacidmolecule? is 10timesaslongitwide, how wouldyou computethevolume heavy leadweight atoneend.If eachoftheserectangular molecules water sothatthemoleculeactually “floats” likealogwith vertically hot dogthanacubeormarble. Furthermore, oneendisattracted to The shapeofoleicacidmoleculesismore likethatofarectangular The oleicacidmoleculesformthemonolayer. The volumeoftheoleicacidaloneincircular filmismuch Estimate thelengthofanoleicacidmoleculeby dividingthevol- Count thenumberofdrops ofsolutionneededtooccupy 3mL 3 ) inthegraduated cylinder. Dothisthree times, andfindthe 3 by thenumberofdrops in3cm volume ofdrop = ______cm length ofmolecule=______number ofdrops in3cm volume ofoleicacid= ______cm 3 of solution. 3 per 1000cm 3 = ______= 3 to determine thevolume to determine 3 of solution.Every 3 3 3 of oleic

Name Period Date

Chapter 18: Solids Elasticity and Hooke’s Law

43 Stretch

Purpose

To verify Hooke’s law and determine the spring constants for a spring Setup: <1 and a rubber band. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate ring stand or other support with rod and clamp Mathematical Level: moderate 3 springs paper clip masking tape meterstick set of slotted masses large rubber band graph paper computer, printer, and data plotting software (optional)

Discussion

When a force is applied, an object may be stretched, compressed, bent, or twisted. The internal forces between atoms in the object resist these changes. These forces become greater as the atoms are moved farther from their original positions. When the outside force is removed, these forces return the object to its original shape. Too large a force may overcome these resisting forces and cause the object to deform permanently. The minimum amount of stretch, compression, or torsion needed to do this is called the elastic limit. Hooke’s law applies to changes below the elastic limit. It states that the amount of stretch or compression is directly proportional to the applied force. The proportionality constant is called the spring constant, k. Hooke’s law is written F = kx, where x is the displacement (stretch or compression). A stiff spring has a high spring constant and a weak spring has a small spring constant.

Procedure

Step 1: Hang a spring from a support. Attach a paper clip to the free end Set up apparatus. of the spring with masking tape. Clamp a meterstick in a vertical position next to the spring. Note the position of the bottom of the paper clip relative to the meterstick. Place a piece of masking tape on the meterstick with its lower edge at this position. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 18 Solids 143 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage144 144 Repeat usingdifferentsprings. Attach massestospring. Laboratory ManualLaboratory 43) (Experiment Data TableA and strains inthenexttwosectionsofData Table A. Step 3: stretch inthefirstsectionofData ofeachtrial Table A. careful nottoexceed Record theelasticlimitofspring. themassand Be andwhennoloadisonthe spring. clip whenaloadisonthespring stretch in each case is the difference between the positions of the paper level withthebottomofpaperclip, noteitspositioneachtime. The Step 2: Repeat Steps 1and 2fortwomore springs. Record themasses Attach different massestotheendofspring. With your eye

© Addison-Wesley Publishing Company, Inc. All rights reserved. 3. combination. Step 8: end). Record themassesandstretches inthelastsectionofData Table A. Step 7: Going Further 2. 1. your values inData Table A. your graphs, constantk the spring determine graph constant.By isequaltothespring findingtheslopeofeach angle dividedby side. thehorizontal The slopeofaforce vs. stretch have atriangle. The slopeofthegraph sideofthetri- equalsthevertical linethrough oneofthehighestpointsongraph.a vertical Now you linethroughhorizontal oneofthelowest pointsonthegraph. Then draw Step 6: ware outyour toplotyour graph. dataandprint band.If available, andtherubber for eachspring usedataplottingsoft- paper, makeagraph offorce axis)vs. (vertical stretch axis) (horizontal Step 5: Table A. masses andthecorresponding stretches sectionofData inthefourth Step 4: Name spring byitself.) spring byitself.(Fortwoidentical springs,itishalfthevalueforone The springconstantfortwospringsinseriesislessthan thatforeither compare with thatofasinglespring? How connectedinaseries constantoftwosprings doesthespring of metals. molecular structure,incontrasttotherelativelysimplelatticestructure bands deviatefromastraight-linegraphprincipallybecauseoftheir The pointsforthespringsshouldlieonnearlystraightlines.Rubber reason why? Are allyour graphs straight lines? If they are not,canyou thinkofa The springconstantk How isthevalue of Repeat Steps constantfor the thespring 5and6todetermine Repeat Steps (endto connectedinseries 1and2fortwosprings For eachgraph thatisanupward slopingstraight line, draw a Calculate theforces, andrecord theminData Table A.Ongraph Repeat Steps band.Record 1and2usingalarge rubber the k related tothestiffnessofsprings? should be larger forstiffersprings. for each spring, andrecordfor eachspring, Period Measure slopeofgraphs. Graph data. Repeat usingrubber band. spring constant. Graphically determine the series. Connect severalspringsin Chapter 18Solids Date 145 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PM Page 146 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PM Page 147

Name Period Date

Chapter 18: Solids Scaling 44 Geometric Physics

Purpose

To investigate ratios of surface area to volume. Setup: 1 Lab Time: >1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: difficult Styrofoam (plastic foam) balls of water Mathematical Level: easy diameter 1", 2", 4", 8" 10 g granulated salt 4 sheets of paper 10 g rock salt stopwatch or clock with 2 stirrers second hand thermometer or 50-mL beaker computer hot plate 2 temperature probes with 2 200-mL beakers interface 400-mL beaker printer 800-mL beaker

Discussion Activity

Why do elephants have big ears? Why does a chunk of coal burn, while coal dust explodes? Why are ants not the size of horses? This activity will give you insights into some secrets of nature that may at first appear to have no direct connection to physics.

Part A Procedure

Step 1: Drop pairs of different-size Styrofoam balls from a height of Drop Styrofoam balls. about 3 m. Drop the balls at the same moment with no push or retarda- tion. Compare their falling times by observing when one ball strikes the ground relative to another. Summarize your observations in Data Table A. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley Data Table A Chapter 18 Solids 147 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage148 148 Laboratory ManualLaboratory (Activity 44) 1. 6. 5. 4. 3. 2. Analysis 7. Larger Styrofoam balls reach thegroundsooner. anyregularityDescribe you observe. and thevolumedependsoncube( volume. (Sincesurfaceareadependsonthesquare(r The smallestStyrofoamballhasthegreatestratioofsurfaceareato volume? Which size Styrofoam ballhasthegreatest ratio area ofsurface to The largest Styrofoam ball hasthegreatestvolume. Which size Styrofoam ballhasthegreatest volume? area. The largest Styrofoam ball hasthegreatestsurface Which size Styrofoam ballhasthegreatest area? surface The smallestStyrofoamballhadtheleastaveragespeed. dropped? Which size Styrofoam ballhadtheleastaverage speedwhen The largest Styrofoam ball hadthegreatestaveragespeed. dropped? Which size Styrofoam ballhadthegreatest average speedwhen volume (since the ratio is inversely proportional totheradius). volume (sincetheratioisinversely proportional The largestStyrofoamball has thesmallestratioofsurfaceareato volume? Which size Styrofoam ballhasthesmallestratio area ofsurface to to, the radius.) proportional to( face areatovolumeisproportional r r 3 2 ) oftheradius,ratiosur- /r 3 ) = 1/r, or inversely 2 ) oftheradiusr,

© Addison-Wesley Publishing Company, Inc. All rights reserved. 9. 8. Name its weight. smaller ratioofarea to weight and thuslessupward drag compared to The heavier (and larger)raindrop willfallfasterbecause it hasthe one. Why? lighter Predict whichwillfalltothe ground faster—aheavierraindrop ora greatest acceleration.) mass, theballwithgreatestnetforceperunitmass hasthe tonetforceperunit acceleration. (Sinceaccelerationisproportional Yes; theball withthegreatestaveragespeedhas d. which decreasesasr tor constant. Thedrag force perunitmassis proportional downward forceperunitmass. The gravitationalforceperunitmass is The largest Styrofoam ball shouldhaveexperienced the greatest net net c. upward force due to drag. The largest Styrofoam ball shouldhaveexperienced the greatest upward force duetodrag? b. area. to the surface The upwardforceduetodragisproportional a. area tothesurface portional oftheball. force ofairresistance—drag—which opposesthefall.Drag ispro- toitsvolume.the ballisproportional The otherforce istheupward One isthedownward force duetogravity—its weight. The weight of A Styrofoam ballfallingthrough theairhastwoforces actingonit. which shouldshow thegreatest acceleration? Which size Styrofoam thegreatest ballshouldhaveexperienced To whatistheupward force duetodrag proportional? Which size Styrofoam thegreatest ballshouldhaveexperienced Does your answer to(c)agree withyour observations? downward force perunitmass(duetogravity and gets larger. drag)—that is, 2 /r 3 = 1/r, Period Chapter 18Solids Date 149 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage150 150 Dissolve saltinwater. Laboratory ManualLaboratory (Activity 44) sheets ofpaper. Record whichonefliesthefarthest. vigorously. Repeat, substituting10gofrock saltforthegranulated salt. lated saltin100mLofwateratroom temperature thatisbeingstirred Procedure Part B Step 3: Procedure Part C 11. 10. Analysis Step 2: 12. Analysis volume. granules—a smallergranuleofsalthasalargerratiosurfaceareato to the sizeof The dissolvingtimeisinverselyproportional ules ofdifferent size, suchas rock salt andtablesalt. Suggest arelationship forpredicting dissolvingtimesfor saltgran- more surfaceareapergram. The granulatedsaltdissolvesfasterthantherockbecauseithas salt? Why? Which saltdissolvedmore quickly—thegranulated saltortherock proportional to the inverse ofitslinear dimension.) proportional being decelerated.Themagnitude ofitsaccelerationisapproximately per unitmass.(Duringmost of atypicalflight, the paperairplaneis as forthelargerStyrofoamballs,theyexperienceless retarding force volume (orsurface-to-mass)ratioislessthanforsmaller planes,so,just Larger paperairplaneswillgenerallytravelfarther. Theirsurface-to- Which paperairplanegenerally traveled farthest? Why? Make similarpaperairplanesfrom whole, half,andquarter Record thenumberofsecondsittakestodissolve10ggranu- airplane that flies farthest: ______airplane thatfliesfarthest: time forrock salt=______time forgranulated salt=______

© Addison-Wesley Publishing Company, Inc. All rights reserved. 14. 13. Analysis your lab report.) Record your findingsinData Table B. water. Save acopy your data,andprint ofyour graph; include itwith perature probes tomonitorthetemperatures ofthetwobeakers connected toacomputer. (If you are usingthecomputer, usetwotem- 30seconds, ortemperature usingeitherathermometer every probes down by themselvesonthelabtable. Measure thetemperature ofboth beaker and400mLintoa400-mLbeaker. Allow thebeakerstocool Step 4: Procedure Part D Name The larger beaker has more surface area. The largerbeakerhasmoresurface Which beakerhasmore area? surface The smallerbeakershouldcoolfaster. watercooledfaster? Which beakerofwarm Heat 500 mL of water to 40°C. HeatThen pour50mLintoa50-mL 500mLofwaterto40°C. Data TableB Period first. water tothe400-mLbeaker beaker; itisbesttoaddthe compared withthe400-mL 50-mL beakerisquitedramatic The temperaturedropin the Monitor coolingwater. Chapter 18Solids Date 151 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage152 152 Laboratory ManualLaboratory (Activity 44) 15. 19. 18. 17. 16. The largerbeakerhasthegreatervolume. Which beakerhasthegreater volume? surface area(heatingsurface)tovolume(waterbeheated). The smallerpoolwillheatupfaster because ithasalargerratio of Predict theday. whichpoolwillheatupfasterduring Why? Suppose thatasmallwadingpoolisnexttoswimmingpool. The rateofcoolingdependsontheratiosurfaceareatovolume. the rate ofcooling(thetemperature drop withtime)depend? temperature dependsonthevolume. Therefore, onwhatratio does total amountofheatthatmustleavethewaterforittocoolroom watertakesplaceatthesurface.The coolingofabeakerwarm The The largerbeakerhasthesmallerratioofsurfaceareatovolume. Which beakerhasthesmallerratio area ofsurface tovolume? The smallerbeakerhasthelargerratioofsurfaceareatovolume. Which beakerhasthelarger ratio area ofsurface tovolume?

Name Period Date

Chapter 19: Liquids Displacement and Density 45 Eureka!

Purpose

To explore the displacement method of finding volumes of irregularly Setup: <1 shaped objects and to relate their masses to their volumes. Lab Time: >1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: moderate two 35-mm film canisters (prepared by the teacher): one of which is filled with lead shot, and the other with a bolt just large enough to Thanks to Rog Lucido for his cause the canister to sink when placed in water ideas and suggestions for triple-beam balance this lab. string graduated cylinder water masking tape 5 steel bolts of different size irregularly shaped piece of scrap iron 1000-mL beaker Activity

Discussion

The volume of a block is easy to compute. Simply measure its length, width, and height. Then, multiply length times width times height. But how would you go about computing the volume of an irregularly shaped object such as a bolt or rock? One way is by the displacement method. Submerge the object in water, and measure the volume of water displaced, or moved elsewhere. This volume is also the volume of the object. Go two steps further and (1) measure the mass of the object; (2) divide the mass by the volume. The result is an important property of the object—its density.

Part A Fig. A Procedure

Step 1: Your teacher has prepared two film canisters for you. Each Find the mass of each canister. canister should have a piece of string attached to it. Use a triple-beam balance to find the mass of each one.

mass of lighter canister = ______

Chapter 19 Liquids 153 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage154 154 bolts. Measure massandvolumeof Observe riseinwaterlevel. Predict riseinwaterlevel. Observe riseinwaterlevel. Laboratory ManualLaboratory (Activity 45) Data TableA Data TableA. sure theirvolumes usingthedisplacementmethod.Record your datain down your findings. Step 4: canister? the sameas, orgreater inwaterlevelforthelighter thantherise canister willbewhenitissubmerged. Doyou thinkitwillbelessthan, Step 3: Remove the canister. inwaterlevel.Mark therise thenewwaterlevelon thetape.Observe tape. Submerge thelightercanisterinwater, asshown inFigure A. graduated cylinderabout2/3fullofwater. Mark thewaterlevelon Step 2: Step 5: Procedure Part B 2. 1. Analysis volume butnotitsmass. The amountofwaterdisplacedbyasubmergedcanisterdependsonits depend onthemassofcanister?Onvolume Does theamountofwaterdisplacedby asubmerged canister each displacethesameamountofwater. Since theriseinwaterlevelissameforeachcanister, theymust How dotheamountsofwaterdisplacedby eachcanistercompare? Test your prediction by submerging theheaviercanister. Write Measure themassesoffivedifferent-sized boltsandthenmea- Predict inthewater levelfortheheavier whatyou thinktherise atthewaterlevelofa ofmaskingtapevertically Place astrip findings: ______findings: ______prediction:

© Addison-Wesley Publishing Company, Inc. All rights reserved. the crown. crown forthisactivity. Alessvaluable pieceofscrap iron willsimulate cheated ornot. devise awaytotell,withoutdamagingthecrown, whetherthekingwas by replacing someofthegoldwithlessprecious metals. You are askedto pure gold. thatthegoldsmithmayhavecheatedhim The kingisworried Archimedes. The kinghascommissionedanewcrown tobemadeof Pretend thatyou are livinginancientGreece thetimeof during Going Further Part C 5. 4. 3. Analysis in thelastcolumnofData Table A. Step 6: Name and displacement) toget the density. Ifthecrownhas the same mass Measure themassof the crown and dividebythevolume (via Write down your procedure andanymeasurements you make. Unfortunately, your schoolcannotsupplyyou withanactualgold The ratioofmasstovolumeisthedensity. at thetopoflastcolumninData Table A.) What nameisgiventotheratio ofmasstovolume?(Fill this name in Bolts of differentmetalswouldhave different ratios of masstovolume. bolts ofdifferent metals? Would you expecttheratio ofmasstovolumebethesamefor All theboltsshouldhaveaboutsameratioofmasstovolume. How dotheratios ofmasstovolumecompare foreachofthebolts? For eachbolt,divideitsmassby itsvolumeandentertheresults density astheoriginalgold,goldsmithisvindicated. Period Chapter 19Liquids Date 155 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PM Page 156 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PM Page 157

Name Period Date

Chapter 19: Liquids Archimedes’ Principle and Flotation

46 Sink or Swim

Purpose

To introduce Archimedes’ principle and the principle of flotation. Setup: <1 Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development spring scale water Conceptual Level: difficult triple-beam balance masking tape Mathematical Level: moderate string chunk of wood rock or hook mass modeling clay Thanks to Art Farmer for his 600-mL beaker toy boat ideas and suggestions for 500-mL graduated cylinder 50-g mass this lab. clear container 2 100-g masses

Discussion

An object submerged in water takes up space and pushes water out of the way. The water is said to be displaced. Interestingly enough, the water that is pushed out of the way, in effect, pushes back on the submerged object. For example, if the object pushes a volume of water with a weight of 10 N out of its way, then the water reacts by pushing back on the object with a force of 10 N. We say that the object is buoyed upward with a force of 10 N. In this experiment, you will investigate what determines whether an object sinks or floats in water. Procedure

Step 1: Use a spring scale to determine the weight of an object (rock or Weigh an object in air and sub- hook mass) first in air and then underwater. The difference in weights is merged in water. the buoyant force. Record the weights and the buoyant force.

weight of object in air = ______

apparent weight of object in water = ______

buoyant force on object = ______

Step 2: Devise an experimental setup to find the volume of water dis- Measure the water displaced. placed by the object. Record the volume of water displaced. Compute the mass and weight of this water. (Remember, 1 mL of water has a mass of 1 g and a weight of 0.01 N.)

volume of water displaced = ______

weight of water displaced = ______Chapter 19 Liquids 157 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage158 158 Float apieceofwood. Laboratory ManualLaboratory 46) (Experiment Data TableA of abuoyant force. This force isduetothe equivalent weights. Keep inmind,however, thatanobjectfloatsbecause ment, you willmeasure masses, anddetermine withoutfindingthe and record themassinData Table A. 1. Step 3: Record thevolumeandmassofwaterdisplacedinData Table A. 4. 3. 2. NOTE: To keepthecalculationssimple, from here oninthisexperi- The buoyantforce should equal theweightofwaterdisplaced(or the weight ofthewaterdisplaced? How doesthebuoyant force onthesubmerged objectcompare with nearly so). Measure thevolumeofwaterdisplacedwhenwoodfloats. equals theweightofwater displaced,sincethemassesareequal. The buoyantforce on the wood, equal to the weightof wood, also of waterdisplaced? How doesthebuoyant force on thewoodcompare withtheweight displaced. The massofthefloatingobjectshouldequal ofwater water displaced? How doesthemassoffloatingwoodcompare tothemassof would risehigher.) object. (If it wereless,the object wouldsink;if it were more, theobject The buoyantforce on anyfloatingobjectequalstheweightof the object andtheweight oftheobject? What istherelation between thebuoyant force onanyfloating Find balance, themassofapiecewoodwithtriple-beam weight of thewaterdisplaced.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 8. Calculate themassofwater, andrecord inData Table A. allows ittofloat.Sketch thisshape. ordescribe Step 6: 7. 6. water displaced,andrecord allvolumesandmassesinData Table A. water itdisplaceswhensinkstothebottom.Calculate themassof Step 5: 5. them inData Table A. Measure thevolumeofwaterdisplacedandcalculateitsmass, recording water Step 4: Name The claydisplacesmorewater whenitfloats. it floatsasdidwhensank? Does theclaydisplacemore, less, orthesameamountofwaterwhen Measure thevolumeofwaterdisplacedby thefloating clay. the clay couldnot remain submerged. Otherwise, The buoyantforce on the submerged clay is less than itsweight in air. less thanitsweight inair?Explain. Is thebuoyant force onthesubmerged claygreater than,equalto, or The massofwaterdisplacedislessthantheclay. mass oftheclay? How doesthemassofwaterdisplacedby theclaycompare tothe equals theweightofwaterdisplaced,sincemassesareequal. The combinedbuoyantforce,equaltotheweight,also mass compare withtheweight ofwaterdisplaced? How doesthecombinedbuoyant force onthewoodand50-g but stillfloats. The 50-gmassneedstofloatontopofthewood. Retrieve theclayfrom thebottom,andmolditintoashapethat Find themassofaballmodelingclay. Measure thevolumeof Add a50-gmasstothewoodsothatdisplacesmore Period Measure dipslacement of clay. Mold theclaysothatitfloats. Float woodplus50-gmass. Chapter 19Liquids Date 159 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage160 as cargo. masses suchasleadweights For bestresults,usedense 160 canal lock. Predict newwaterlevelin Laboratory ManualLaboratory 46) (Experiment 11. and puttheminthewater. Mark andlabelthenewwaterlevels. container andonthesidesofboat.Remove themassesfrom theboat masses. Mark andlabelthewaterlevelsonmaskingtapeplaced masses) inacontainerfilledwithwaterdeeperthantheheightof Step 8: ceed toStep 8. go up, down, orstaythesame? Write down your answer before overboardbricks intothecanallock,willwaterlevelinlock 9. 12. Step 7: 10. 14. 13. place the cargo in the water? What happenstothewaterlevelonsideofboatwhenyou The buoyantforce on the floating clayequalsitsweight in air. less thanitsweight inair? Is thebuoyant force onthe floatingclaygreater than,equalto, or A freighterridinghighis carrying a relativelylightcargo. light orheavyloadofcargo? If alarge freighter highinthewater, isriding arelatively isitcarrying higher inthewater. The waterlevelonthesideofboatgoesdown;rides in airoftheobject. The weightofwaterdisplacedbyanyfloatingobjectequalsthe floating objectcompared withtheweight inairoftheobject? What canyou concludeabouttheweight ofwaterdisplacedby a The waterlevelinthecanal lockwilldrop. are thrown overboard? What willhappentothewater levelinthecanallockwhenbricks is floating. It drops,sincethe cargo displaceslesswater when itsinks thanwhenit cargo in the water? Explain why it happens. What happenstothewaterlevelincontainerwhen you place the Float atoy boatloadedwith “cargo” (suchasoneortwo100-g Suppose you are onashipincanallock.If you throw atonof prediction forwaterlevelincanallock: ______you pro-

Name Period Date

Chapter 20: Gases Weight of Air

47 Weighty Stuff

Purpose

To recognize that air has weight. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: moderate centigram balance Mathematical Level: moderate sheet of paper basketball hand pump needle valve tire pressure gauge (preferably scaled in 1-lb increments)

Discussion

If you hold up an empty bottle and ask your friends what’s in it, they will probably say that nothing is in the bottle. But strictly speaking, there is Activity something in the “empty” bottle: air. Perhaps a fish would say similarly that there is nothing in an “empty” bottle at the bottom of the ocean. We don’t ordinarily notice the presence of air unless it is moving. And we don’t notice that air has mass and weight, like all matter on earth. In this activity, you will focus attention on the mass and weight of air.

Procedure

Step 1: Flatten out a basketball so that there is no air in it. Place a sheet Find mass of deflated of paper on a centigram balance. (In Step 3, you will crumple the paper basketball. and use it to keep the basketball from rolling off the balance.) Carefully measure the mass of the flattened basketball and paper.

mass of flattened basketball and paper = ______

Step 2: Remove the basketball from the balance. Inflate it with air to a Inflate basketball. pressure of 7.5 lb/in.2, as measured by the pressure gauge.

Step 3: Crumple the piece of paper so that it will keep the inflated bas- Find mass of inflated ketball from rolling off the balance. Measure the mass of the inflated basketball. basketball and paper.

mass of inflated basketball and paper = ______

Step 4: Compute the mass of the air pumped into the basketball. Compute mass of air in basketball. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley mass of air = ______Chapter 20 Gases 161 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage162 Compute volumeof extra air. 162 read zero. The gaugepressureshould basketball. Measure pressureofdeflated Laboratory ManualLaboratory (Activity 47) ball to a gauge pressure of about 7.5 lb/in. at zero finalgaugepressure. However, you actuallyinflatedthebasket- been justenoughtoinflateasecondflattenedbasketballfullvolume extra the pressure exceeds pressure—to atmospheric 14.7lb/in. thesecondstage.added during further. The reading onthebalanceincreased by themassofair displace anyadditionalair, sothebuoyant force didnotincrease any ketball withoutappreciably changingitsvolume. The basketballdidnot escaping. Then, measure the final pressure inside the basketball. to escape without flattening the ball. Wait until you no longer hear air Step 5: 2. The volumeshouldberoughlyhalftheofbasketball. above airpressure normal (14.7lb/in. flattened basketball.In the secondstage, you increased thepressure added. The reading onthebalancewouldhavebeensameasfor Therefore, shape, thebasketballdisplacedanamountofairequal shape.you inflated itouttoitsfullspherical When itreached aspherical Step 6: 1. 3. of 14.7lb/in. air inthebasketball. ball wouldjustbeinflatedtofullsize atzero gaugepressure by theextra If you had,hypothetically, raised thepressure—the amountby which The airneededtofilloutaflattenedbasketballitsfull spherical sure above zero? measure onlythemassofextra When airisaddedtoaflattenedbasketball,whydoesbalance Yes, thereis still air in the basketball. Itisatnormalairpressure. two endsofthegauge. Is there stillairinthebasketball? A pressure gaugemeasures thedifference with mass. Yes; theearth’s gravitypulls onallair, justasitpullsonanythingelse Does theairinyour classroom haveweight aswell asmass? atmospheric pressure. the massofextra on thebalancethanwhenitisflattened.The will detectonly equals theadditionalweight.Thebasketballpressesdown noharder shape weighsthesameasairitdisplaces,sobuoyant force CAUTION: air pumped into the basketball during thesecondstagewouldhave air pumpedintothebasketballduring You really inflatedtheflattenedbasketballintwostages. First Insert aneedlevalve intheinflatedbasketball,andallow theair the buoyant force ontheballequaledweightofair pressure after air escapes = ______lb/in. basketball atzero gaugepressure______= volume ofextra airpumpedinto 2 ! It mayburstviolently. Do NOTDo attempttoinflateabasketballgaugepressure air thatincreasesthepressureabove 2 ) by forcing extra air thatincreases thegaugepres- 2 . Compute whatsize flattened between pressures atthe to theairadded. air intothebas- 2 2 , thenthe surrounding

Name Period Date

Chapter 20: Gases Pressure and Force

48 Inflation

Purpose

To distinguish between pressure and force, and to compare the pressure Setup: <1 that a tire exerts on the road with the air pressure in the tire. Lab Time: 1 Learning Cycle: application Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: moderate automobile owner’s manual for vehicle (optional) Thanks to Evan Jones and Ken graph paper Ford for their ideas and sug- tire pressure gauge (preferably scaled in 1-lb increments) gestions for this lab.

Discussion

People commonly confuse the two words force and pressure. Tire manufacturers add to this confusion by saying “inflate to 45 pounds” when they really mean “inflate to 45 pounds per square inch.” The amount of Activity pressure depends on how a force is distributed over a certain area. It decreases as the area increases.

force pressure = ——– area

In this activity, you will determine the pressure that an automobile tire exerts on the road. Then you’ll find out how that compares with the pressure of the air in the tire. If it weren’t for the support given by the sidewalls of the tire, the two pressures would be the same. You can directly measure the air pressure in the tire with a pressure gauge. You can measure and calculate the pressure of the tire against the road by dividing the weight of the car by the area of contact for the four tires (the tires’ “footprints”). Although there are gaps between the treads that don’t support the car, their role is small compared with that of the sidewalls, so will be neglected.

Procedure

Step 1: Position a piece of graph paper directly in front of the right front tire. Roll the automobile onto the paper.

Step 2: Trace the outline of the tire where it makes contact with the graph paper. Roll the vehicle off the paper. Compute the area inside the

Chapter 20 Gases 163 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage164 164 Compare pressures. Measure tirepressure. Compute thepressures. Determine theforce. Repeat foreachtire. Laboratory ManualLaboratory (Activity 48) Data TableA ______, ______, ______, ______, ______, ______, pressure onground forthefour tires: accounted forby theairpressure? Airpressure asapercentage oftire in thetire. What percentage ofthepressure by exerted thetire is Step 7: per square inch.Record thepressures ofthetires inData Table A. Step 6: the tire. Record inData Table A. print” area ofthetire togettheactualpressure ontheground by exerted Step 5: oftheweight. Entertheforcefourth by exerted eachtire inData Table A. bysupported eachtire. Otherwise, assumethateachtire one supports tion between front andrear tires isavailable, useittofindtheweight front door jamonthedriver’s side. ontheweight If distribu- information the dealer. Oftentimestheweight ofthevehicleisstampedonto Step 4: Table A. 1. Analysis Step 3: were amembrane withnostrength ofitsown? pressure inthetire. Doyou thinkthiswouldbethecaseiftire The pressure by exerted the tire ontheroad isgreater than theair An actualautomobiletirefalls betweenthesetwoextremes.) pressure on the road would not be related to any internal air pressure. tire were a strong, rigid structure that required little or no air, its tire pressure on the road would be the same as the air pressure. If the weight. (If the tire were a membrane with no strength of its own, the The structureofthetire,especiallysidewalls,supports someofthe Compare thepressure by exerted eachtire withtheairpressure Use atire gaugetomeasure thepressure ineachtire inpounds For eachtire, dividetheforce by exerted thetire by the “foot- theweight ofthevehiclefromAscertain theowner’s manualor Repeat Steps 1and2fortheothertires. Record your datainData

© Addison-Wesley Publishing Company, Inc. All rights reserved. 6. 5. 4. 3. 2. Name exists init). What isthetotalpressure inside butatmosphericpressure reads zero onthegauge, a perfectly “flat tire” of pressure the weightofcar. Whenyouhaveaflattire,thereisstill14.7lb/in. not netforce.Atmospheric pressure doesnot contribute to supporting There isasmuchatmosphericpressureinsideoutside. Theresultis pressureWhy wastheatmospheric (14.7lb/in. the atmosphericpressure. The totalpressureequalsthe measured pressure(gaugepressure)plus pressureand atmospheric (14.7lb/in. A tire gaugemeasures thedifference into thetreadchannelswhere it can escape. pressure ontheroadsurface.Asaresult,tiresquisheswater tread (smallerareaofcontactthanwhenthetireisbald)exertsalarger Good treadprovides better contactwiththeroadbecause sharp weather. Why? ignore therole oftire treads inpractice—particularly inrainy We ignored thetire tread incomputingpressures. Oneshouldnot may maketheactualweightgreater. A loadinthetrunk,afulltankofgas,andextrainstalledequipment the actualweight ofthecar? How mighttheweight givenintheowner’s manualbedifferent from air” thatmaybeinthesteeltire)dividedbytires’footprints. against theroad.Pressureisonlyweightofcar(andthat“extra Air pressureinasteeltirewouldhavenobearingonthetire’s pressure correspond tothepressure thetire againsttheroad? Explain. exerts structure thatrequired littleornoair. Would airpressure inthetire Consider theotherextreme. Suppose thetire were astrong rigid were compared? pressure ofthetire gaugewhen thetire pressure andairpressures inside the tire(aswellasoutside between thepressure inthetire 2 ) outsidethetire (forexample, the tire). the front tire? 2 ) notaddedtothe Period 2 Chapter 20Gases Date 165 CP02_SE_LAB_Ch29-48 3/5/01 12:03 PMPage166 166 Laboratory ManualLaboratory (Activity 48) sure ontheground. sure accountsforagreater orlesserpercentage oftheactualtire pres- pressure. You’ll islarger. noteitsfootprint Find outifthelower airpres- Repeat theabove withoneofthetires air deflated,saytohalfitsnormal Going Further

Name Period Date

Chapter 21: Temperature, Heat, and Expansion Specific Heat of Water 49 Heat Mixes: Part I

Purpose

To predict the final temperature of a mixture of cups of water at different Setup: <1 temperatures. Lab Time: 1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: easy Mathematical Level: easy 3 Styrofoam (plastic foam) cups liter container thermometer (Celsius) Thanks to Verne Rockcastle for his ideas and suggestions for pail of cold water this lab. pail of hot water

Discussion

If you mix a pail of cold water with a pail of hot water, the temperature of the mixture will be between the two initial temperatures. What information would you need to predict the final temperature? This lab inves- Activity tigates what factors are involved in changes of temperature. Your goal is to find out what happens when you mix equal masses of water at different temperatures. Before actually doing this, imagine a cup of hot water at 60°C and a pail of room-temperature water at 20°C.

(circle one)

1. Which do you think is hotter—the cup or the pail? cup pail

2. Which do you think has more thermal energy? cup pail

3. Which would take longer to change its temperature by 10°C if the cup and pail were set outside on a winter day? cup pail

4. If you put the same amount of red-hot iron into the cup and the pail, which one would change temperature more? cup pail

Procedure

Step 1: Two pails filled with water are in your room, one with cold water Mark cups. and one with hot water. Fill one cup 3/4 full with water from the cold- Marking the inside of the cup water pail. Mark the water level along the inside of the cup. Pour the eliminates guessing where the cup’s water into a second cup. Mark it as you did the first one. Pour the actual water level is.

© Addison-Wesley Publishing Company, Inc. All rights reserved. All rights Inc. Company, Publishing © Addison-Wesley cup’s water into a third cup, and mark it as before. Now all three cups have marks that show nearly equal measures. Chapter 21 Temperature, Heat, and Expansion 167 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage168 168 mixture. Measure temperatureof tures. average ofthethreetempera- The correct prediction isan Predict temperature of mixture. cups. Measure temperatureofthree mixture. Measure temperatureof tures. average of the two tempera- The correct prediction isthe Predict temperature of mixture. cups. Measure temperatureoftwo Laboratory ManualLaboratory (Activity 49) 5. mixture, andmeasure andrecord itstemperature. Step 7: mixed inonecontainer?Record your prediction. Step 6: water pail.Measure andrecord theirtemperatures. Fill theothertwocupstotheirmarks withhotwaterfrom thehot- Step 5: the pailofeithercoldorhotwater! Pour themixture intothesinkorwastepail.Donotpouritback 6. mixture, andmeasure andrecord itstemperature. Step 4: in thelitercontainer?Record your prediction. Step 3: pail. Measure andrecord thetemperature ofbothcupswater. Step 2: Some watermightbelostorspilled. Why don’t themarks show exactlyequalmeasures? reached ormaynothavemeasuredthetemperaturescarefully. Students mayhavewaitedtoolongafterthermalequilibriumwas vation, whatmighthavecausedit? If there wasadifference between your prediction andyour obser- What willbethetemperature whenallthree cupsof waterare What willbethetemperature ifyou mixthetwocupsofwater Pour thethree cupsofwaterintothelitercontainer, stirthe Fill onecuptoitsmark withwaterfrom thecold-waterpail. Pour thetwocupsofwaterintolitercontainer, stirthe Fill thefirstcuptomark withwaterfrom thehot-water actual temperature ofmixture______°C = predicted temperature ofmixture______°C = temperature ofhotwater(cup2)=_____°C temperature ofhotwater(cup1)=_____°C temperature ofcoldwater=______°C actual temperature ofmixture______°C = predicted temperature ofmixture______°C = temperature______°C ofhotwater= temperature ofcoldwater=______°C

© Addison-Wesley Publishing Company, Inc. All rights reserved. 10. 9. mixture, andmeasure andrecord itstemperature. Step 10: cups ofwaterare mixedinonecontainer. Step 9: their marks withcold Step 8: pail ofeithercoldorhotwater! Pour themixture intothesinkorwastepail.Donot 8. 7. Name mixture wasclosertothatofthecoldwater. gives offheattobothcupsofcoldwater. The temperatureofthe The hotwaterchangesmorebecausetherewaslessof it,andit ofthemixture?became part Why doyou thinkthishappened? Which ofthewatersamples(coldorhot)changedmore whenit Answers willvary. How compare didthisobservation withyour prediction? mixture wasclosertothatofthehotwater. absorbs heatfrombothcupsofhotwater. Thetemperatureofthe The coldwaterchangesmorebecausetherewaslessofit,andit ofthemixture?became part Why doyou thinkthishappened? Which ofthewatersamples(coldorhot)changedmore whenit Answers willvary. How compare didyour observation withyour prediction? Record your prediction ofthetemperature whenthesethree Fill onecuptoitsmark withhot Pour thethree cupsofwaterintothelitercontainer, stirthe temperature ofcoldwater(cup2)=______°C temperature ofcoldwater(cup1)=______°C temperature______°C ofhotwater= actual temperature ofmixture______°C = predicted temperature ofmixture______°C = water. Measure andrecord theirtemperatures. water. Fill theothertwocupsto pour itbackintothe Chapter 21 Temperature, Heat, andExpansion Period water. the greater initial amount of age nearer thetemperatureof cold waterwillhaveanaver- Differing amounts of hot and equal amounts of water. is trueonly temperatures ofthecups.This is anaverageoftheindividual nize thatthefinaltemperature students willprobablyrecog- divided by3.Ingeneral,the sum ofthethreetemperatures The correctpredictionisthe Predict temperatureofmixture. Reverse Step5. Date if thecupshave 169 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PM Page 170 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PM Page 171

Name Period Date

Chapter 21: Temperature, Heat, and Expansion Specific Heat of Nails 50 Heat Mixes: Part II

Purpose

To predict the final temperature of water and nails when mixed. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: moderate Harvard trip balance Mathematical Level: moderate 2 large insulated cups bundle of short, stubby nails tied with string thermometer (Celsius) Thanks to Verne Rockcastle for hot and cold water his ideas and suggestions for this lab. paper towels

Discussion

If you throw a hot rock into a pail of cool water, you know that the temperature of the rock will go down. You also know that the temperature of the water will go up—but will its rise in temperature be more than, less Activity than, or the same as the temperature drop of the rock? Will the temperature of the water go up as much as the temperature of the rock goes down? Will the changes of temperature instead depend on how much rock and how much water are present and how much energy is needed to change the temperature of water and rock by the same amount? You are going to study what happens to the temperature of water when hot nails are added to it. Before doing this activity, think about the following questions.

1. Suppose that equal masses of water and iron are at the same temperature. Suppose you then add the same amount of heat to each of them. Would one change temperature more than the other?

(circle one) yes no

If you circled “yes,” which one would warm more?

(circle one) water iron

2. Again, suppose that equal masses of water and iron are at the same temperature. Suppose you then take the same amount of heat away from each of them. Would one cool more than the other?

(circle one) yes no

If you circled “yes,” which one would cool more?

Chapter 21 Temperature, Heat, and Expansion 171 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage172 172 and hot water. Measure temperatureofcold Balance nailswith hot water. mixture. Measure temperatureof mixture. Predict temperatureof Warm nailsinhotwater. Balance nailswithcoldwater. Laboratory ManualLaboratory (Activity 50) 4. cold water. When thetemperature ofthemixture record stopsrising, it. Step 6: nails are addedtothecoldwater. 3. temperature ofthehotwateraround thenails. Step 4: nails to come to the temperature of the hot water. nails intothehotwaterandleaveitthere fortwominutestoallow the Step 3: nails outofitscupandplaceitbesidethecoldwater. Step 2: other. is ineachcup—amassofnailsone, andanequalmassofwaterinthe ances thecupofnails. When thetwocups are balanced,thesamemass nails intooneofthecups. Add coldwatertotheothercupuntilitbal- Step 1: Procedure the nails,moststudentswillprobablygiveaveragetemperature. the initialtemperatureofcoldwaterthanto Although somemayrecognizethatthefinaltemperaturewillbecloserto Step 5: cup with the dry bundleofnailswithacup ofhot cup withthe dry nails. thebundleofnailswithapaper towel. First, dry Then, balancea Step 7: How closeisyour prediction value? totheobserved to heatthenailsaknown temperature? nails? Why doyou thinkitisornot?Can you thinkofabetterway Is thetemperature ofthehotwaterequaltotemperature ofthe to heatthenailsaknowntemperature. the nails.(Theyshouldbeinthermalequilibrium.)Thisisbestway Yes, thetemperature of the hotwatershouldequaltemperature of water thanto the initialtemperature ofthenails. value should be closertotheinitialtemperatureof the The observed Lift thenailsfrom thehotwaterandputthemquicklyinto Predict whatthetemperature ofthemixture willbewhenthehot Measure andrecord thetemperature ofthecoldwaterand Fill theemptycup3/4fullwithhotwater. Lower thebundleof Set thecupofcoldwateronyour work table. Liftthebundleof Place alarge cuponeachpanofthebalance. Drop thebundleof Now you will repeat Steps 1through 6forhotwaterandcold actual temperature ofmixture______°C = predicted temperature ofmixture______°C = temperature______°C ofhotwater= temperature ofcoldwater=______°C water.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 6. Analysis 5. record it. the hotwater. When thetemperature ofthemixture stopschanging, Step 11: cold nailsare addedtothehotwater. Step 10: nails. minute (why?),andthenrecord thetemperature ofthewateraround the Step 9: the temperature ofthehotwaterinfirst cup. Step 8: Name (or releasing)heatwithoutchangingitstemperatureas greatly. easily thanthewater. Thewaterhasagreater capacityforabsorbing equal massesofdifferentmaterials.Thenailschangetemperature more equal amountsofheatdonotcausethesametemperature changein equals theamountofheatabsorbedbycoolermaterial.However, In eachcase,theamountofheatgivenoffbywarmermaterial explanation forwhathappened. Discuss withtherest your observations an ofyour team,andwrite the water than to the initial temperature of the nails. Again, theobservedvalueshouldbeclosertoinitialtemperatureof How closeisyour prediction value? totheobserved Lower thebundleofnailsintocupcoldwater, waitone Remove thenailsandfillcup3/4fullwith Lift thenailsfrom thecoldwaterandputthemquicklyinto Predict whatthetemperature ofthemixture willbewhenthe actual temperature ofmixture______°C = predicted temperature ofmixture______°C = temperature ofcoldwater=______°C temperature______°C ofhotwater= cold water. Record Chapter 21 Temperature, Heat, andExpansion Period mixture. Measure temperatureof mixture. Predict temperature of Cool nails in cold water. Record temperature. Date 173 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage174 174 Laboratory ManualLaboratory (Activity 50) 8. 7. 9. at thesametemperature asthewater?Explain. bottle filledwithhotwater, oronefilledwithanequalmassofnails your feet. something towarm Would you prefer tohaveahot-water Suppose you havecoldfeetwhenyou gotobed,andyou want (circle one) higher temperature? If your answer tothequestion is “yes,” whichonewouldreach a (circle one) other? Would changetemperature oneofthematerials more thanthe under eachofthemasses, forequaltimes. lettingthecandlesburn perature. Suppose you thenlightsimilarcandles andplaceacandle Suppose you haveequalmassesofwaterand nailsatthesametem- one seasontoanother. island, thissameeffectwilloccurduringdayandnightaswellfrom the soilinwinterandcoolitduringsummer. Foramid-ocean substances, includingsoilandair. Thismeansthattheoceanswarm Water hasamuchlarger specificheatcapacitythanmostother cold? hotnorvery getting neithervery Why doestheclimateofamid-oceanislandstaynearlyconstant, change intemperature. is, watergivesoffmoreheatthananequalmassofnailsforthesame take longertocooldowndueitshigherspecificheatcapacity. That It wouldbebettertohavethebottlefilledwithwaterbecauseit ae nails water e no yes

Name Period Date

Chapter 21: Temperature, Heat, and Expansion Specific Heat and Boiling Point

Antifreeze in the 51 Summer?

Purpose

To investigate what effect antifreeze (ethylene glycol) has on the cooling Setup: <1 of a car radiator during the summer. Lab Time: >1

Learning Cycle: application Experiment Required Equipment/Supplies Conceptual Level: difficult Mathematical Level: difficult 400 mL (400 g) water timer Adapted from PRISMS. 380 mL (400 g) 50% mixture of antifreeze and water 500-mL graduated cylinder 2 600-mL beakers single-element electric immersion heater thermometer (Celsius) or computer temperature probe with interface

Part A Discussion

Put an iron frying pan on a hot stove, and very quickly it will be too hot to touch. But put a pan of water on the same hot stove, and the time for a comparable rise in temperature is considerably longer, even if the pan contains a relatively small amount of water. Water has a very high capacity for storing internal energy. We say that water has a high specific heat capacity. The specific heat capacity c of a substance is the quantity of heat required to increase the temperature of one gram of the substance by one degree Celsius. This means that the amount of heat Q needed to increase the temperature of a mass m of material by a temperature difference ∆T is

Q = mc∆T

Turning this formula around, the specific heat capacity is related to the quantity of heat absorbed, the mass of the material, and the temperature change by

Chapter 21 Temperature, Heat, and Expansion 175 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage176 176 them. heaters regarding theimmersion Point outthecautionarynote Heat water. before Laboratory ManualLaboratory 51) (Experiment students use temperature. Record theinitialandfinaltemperatures, andcomputethechangein immediately. Operating itin airdestroys it heater elementissubmerged inliquid. CAUTION: (a littleover 3minutes). Step 1: Procedure calibrate thetemperature probe. mometer. Hook upa temperature box. probe toaninterface Be sure to the liquidispure wateroramixture ofwaterandantifreeze. uid. The energy dissipatedby aheateristhesameregardless ofwhether transfers being heated,inthiscasealiq- allofitsenergy tothematerial a toaster. efficientdevice,This isavery forunlikeahotplateorflame, it used toheatsmallamountsofliquids. It heatsupmuchlikethewire in To immersionheater. supplyheat,you willuseanelectric tity ofheatthatisabsorbedandthecorresponding temperature change. water. thespecificheatcapacityofa50%mixturedetermine ofantifreeze and mixture’s specificheatcapacity?In Part you will Aofthisexperiment, 50% antifreeze. But whateffectdoesaddingtheantifreeze haveonthe lowest freezing are pointwhentheproportions about50%waterand mixture hasamuchlower freezing pointthanwater. The mixture hasits such amishap, antifreeze (ethyleneglycol) ismixedwiththewater. The crack theautomobileengineblockorfracture theradiator. To prevent and, what’s evenworse, itexpandswhenfreezes. This expansioncan ing. But disadvantage inwinter. waterhasastriking It freezes at0°C, That’s whyitisusedinanautomobiletokeeptheenginefrom overheat- The highspecificheatcapacityofwatermakesitanexcellent coolant. water, itstemperature willfallby 1°C. perature by willrise ofheatisextracted 1°C; orif1calorie from 1gram of cal/g°C. So, (cal)ofheatisabsorbedby if1calorie 1gofwater, itstem- ofthatsubstance.teristic The specificheatcapacityofpure wateris1.0 You canuseacomputer withatemperature probe insteadofather- An immersionheaterisasmallcoilofnichrome wire commonly To findthespecificheatcapacity, you willsimplymeasure thequan- Water hasahigherspecificheatcapacitythanmostothermaterials. Each substancehasitsown specificheatcapacity, whichischarac- Heat 400mL(400g)ofwaterwiththeheaterfor200seconds Plug andunplugtheimmersion heateronlywhenthe

© Addison-Wesley Publishing Company, Inc. All rights reserved. antifreeze mixture from theequation Step 4: change intemperature. ture for200seconds. Record theinitialandfinaltemperatures andthe antifreeze mixture hasamass of400g.Heat the400gofantifreeze mix- a beaker. Since antifreeze isslightlydenserthanwater, 380mLof50% Step 3: where equation Step 2: 2. 1. Analysis Name The 50%antifreezemixture heatsupmorequickly. energy input—pure waterora50%mixture ofantifreeze? from 25°CWhich wouldwarm to40°C fasterwiththesame rate of water. The 50%antifreezemixturehaslowerspecificheatcapacity thanpure 50% mixture ofantifreeze? Which liquidhasthelower specificheatcapacity—pure water ora With thesedata,computethespecificheatcapacityof50% Pour 380mLofamixture of50%antifreeze and50%waterinto Find thequantityofheattransferred tothewaterfrom the specific heatc change intemperature (∆T final temperature______°C = initial temperature______°C = ∆T c m change intemperature (∆T final temperature______°C = initial temperature______°C = A goodvalueis0.8cal/g°C. = specificheatcapacityofwater1cal/g°C = massofwater = changeintemperature Q of antifreeze mixture______cal/g°C = ______calories ______= c Q = = m∆T ——– mc∆T Q ) = ______°C = ) ) = ______°C = ) Chapter 21 Temperature, Heat, andExpansion Period Compare energydissipated. ties ofantifreezemixture. Compare specificheatcapaci- Heat antifreezemixture. Date 177 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage178 178 boiling point. Heat antifreezemixturetoits Laboratory ManualLaboratory 51) (Experiment heater, andmeasure itsboilingpoint.Record thistemperature. Discussion Part B 3. Analysis Step 5: engine isoverworked. You tofindout. willexperiment pure water?If so, thiswouldlessenthelikelihoodofboil-overs whenthe higher.) Could anantifreeze mixture haveahigherboilingpointthan pressure capontheradiator, boththepressure andtheboilingpointare pure pressure, wateratatmospheric a thistemperature is100°C. (With coolant iseffectiveonlyattemperatures below boiling.If thecoolantis engine. But ifitreaches itsboilingpoint,thesystemboilsover. So a phere. The coolantisthenrecycled backtotheengine. then circulates ittotheradiator, where itisdissipatedtotheatmos- coolant inanautomobile. Coolant draws heatfrom theengineblockand be replaced withpure water? nience, toleavingantifreeze intheradiator summer, during orshouldit antifreeze insummermonths. Is there anadvantage, otherthanconve- a poorer coolantthanpure water. Yet itisadvisabletocontinueusing antifreeze andwaterislower thanthatofpure water. This suggestsitis By now you havefoundthatthespecificheatcapacityofamixture of 4. before itboilsin a carradiator. The higher boiling point allows theliquidtoreacha higher temperature the mixture’s ability toactasacoolant? What effectdoestheboilingpointofantifreeze mixture haveon The temperature ofthecoolantincreases asitabsorbsheatfrom the To answer thisquestion,you needtounderstandtherole ofthe it boils. than purewater, sothemixturewillreach a highertemperaturebefore Yes, amixtureofethyleneglycolandwaterhashigherboilingpoint freezing? “antifreeze” inclimateswhere thetemperature nevergoesbelow Would tocallethylene glycol itbeappropriate “antiboil” insteadof Heat asampleof50%antifreeze mixture withtheimmersion boiling pointofantifreeze mixture =______°C

Name Period Date

Chapter 21: Temperature, Heat, and Expansion Convection

Gulf Stream 52 in a Flask

Purpose

To observe liquid movement due to temperature differences. Setup: 1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy safety goggles Mathematical Level: none paper towels 250-mL flask Adapted from PRISMS. food coloring stirring rod hot plate thermometer (Celsius) 2-hole rubber stopper (with glass tubing as shown in Figure A) battery jar or a large pickle jar water

Discussion Activity

The air near the floor of a room is cooler than the air next to the ceiling. The water at the bottom of a swimming pool is cooler than the water at the surface. You can feel these different temperatures that result from fluid motion, but you cannot see the fluid motion in these cases. In this activity, you will be able to see the movements of two liquids with different temperatures.

Procedure

Step 1: Read Steps 2 through 5 completely before conducting the activity, and predict what you expect to observe.

Fig. A

Step 2: Put on safety goggles. Mix some food coloring into a flask filled Heat colored water. completely with water. Stir well. Heat the colored water to a temperature of 70°C. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 21 Temperature, Heat, and Expansion 179 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage180 180 Immerse flask. Record observations. Insert stopper. Laboratory ManualLaboratory (Activity 52) Step 5: 1. be above bothpiecesoftubing. jar filledwithplainwateratroom temperature. The water level should Step 4: thestopperintoflask. flask andinsert shown inFigure A. With adamppapertowel, grasp firmly theneckof Step 3: of the container. Denser, coolerwaterpushedwarmer, less dense water towardthetop What causedthemovements ofliquidyou observed? flask throughthelower, longertube. spreading intothesurroundingwater. Clear, coolerwaterentersthe Hot, coloredwaterrisesoutofthehigher, shortertubeinthestopper, CAUTION: Record over your observations thenext10minutes. As shown inFigure B, immersethehotflask carefully intoalarge Make sure thattheglasstubinginstopperarrangement isas i.B Fig. The flask will be very hot. Be careful Be nottoburnyourself. hot. The flaskwillbevery

Name Period Date

Chapter 21: Temperature, Heat, and Expansion Linear Expansion of Solids

The Bridge 53 Connection

Purpose

To calculate the minimum length of the expansion joints for the Golden Setup: 1 Gate Bridge. Lab Time: >1

Learning Cycle: application Experiment Required Equipment/Supplies Conceptual Level: difficult Mathematical Level: difficult safety goggles micrometer hollow steel rod steam generator thermal expansion apparatus bunsen burner (roller form) rubber tubing

Discussion

Gases of the same pressure and volume expand equally when heated, and contract equally when cooled—regardless of the kinds of molecules that compose the gas. That’s because the molecules of a gas are so far apart that their size and nature have practically no effect on the amount of expansion or contraction. However, liquids and solids are individual- ists! Molecules and atoms in the solid state are close together in a variety of definite crystalline structures. Different liquids and solids expand or contract at different rates when their temperature is changed. Expansions or contractions of metal can be critical in the construc- tion of bridges and buildings. Temperatures at the Golden Gate Bridge in San Francisco can vary from –5°C in winter to 40°C in the summer. On this very long bridge, the change in length from winter to summer can be almost 2 meters! Clearly, engineers must keep thermal expansion in mind when designing bridges and other large structures. Suppose you owned an engineering firm before the Golden Gate Bridge was built and you were asked for advice on the minimum length to make expansion joints for the proposed bridge. (See a typical expansion joint in Figure 21.9 in your textbook.) Consider two expansion joints that connect the bridge to land at each end. The steel to be used is the same as that in the steel rods you will use in this experiment. You are to measure how much the steel expands per meter for each degree increase in temperature. This ratio is called the coefficient of linear expansion. Then, compute the amount that the 2740-m structure will expand as its temperature increases. Now you can advise a minimum size of the expansion joints needed, to assure the success of the bridge. You will determine the coefficient of linear expansion for steel by measuring the expansion of a steel rod when it is heated with steam at 100°C. The amount of expansion ∆L depends on the original length L, the change in temperature ∆T, and the coefficient of linear expansion α (which is characteristic of the type of material). © Addison-Wesley Publishing Company, Inc. All rights reserved. All rights Inc. Company, Publishing © Addison-Wesley ∆L = αL∆T Chapter 21 Temperature, Heat, and Expansion 181 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage182 182 Assemble apparatus. micrometer. instruction onhowtousea Some studentsmayneed Measure axlediameter. Laboratory ManualLaboratory 53) (Experiment Do pointer (sinceyou are samplingexpansionbetween thesetwopoints). tance inmillimetersfrom thegroove inthesteelrod totheaxleof tor ready to go. Make sure therod hasaplacetodrain. Measure thedis- Step 2: pointer. ∆L ture. By L measuring Step 1: Procedure Once you havecomputedthevalue of equation enablesyou tocomputethecoefficientoflinearexpansion. distance equaltoitscircumference. The circumference the pointerthrough anangle. When thesteelrod resting ontheaxleexpands, itrotates the axleand of thesteelrod isarranged tobeperpendiculartheaxleofpointer. expansion issmall.Onewaytomeasure itisshown inFigure A. The end one completerotation equalstheratio oftheangle The ratio oftheactualdistance∆L ence oftheaxle. Ratio giveyou andproportion ∆L then theincrease ∆L equals itsdiameterd mer andwinter. andtheestimatedtemperaturelength ofthebridge difference forsum- ficient oflinearexpansion,by rearranging theequation. pointer rotates through to360°. , thechangeoflengthafterheating,you cancompute not The temperature change∆T Solve thisequationfor h one un 6°(onefullrotation) whentheaxlehasrotated a 360° The pointerturns It isdifficulttomeasure how muchtherod expandsbecausethe fteepninrttstepitrtruh10 (ahalfrotation), If theexpansionrotates thepointerthrough 180° measure the lengthoftheentire rod. Assemble your apparatus asinFigure A,withthesteamgenera- Using amicrometer, measure thediameterofaxle in lengthoftherod isequaltohalfthecircumfer- , the original lengthoftherod before, theoriginal heating,and times thenumberpi. ∆L. Substituting thisvalue intothesecond L d ___ mm ______= ___ mm ______= α πd —– =—— C ∆L is simply100°C minusroom tempera- = —— = rotated tothedistanceπd πd L ∆L ∆T 360° θ α , you cancomputetheminimum for otherexpansions. θ through whichthe C of theaxle α rotated in , thecoef-

© Addison-Wesley Publishing Company, Inc. All rights reserved. your work. Step 7: sured values ofL, Step 5: Step 4: your measured values of 1. Analysis Record theangle perature ofyour atroom rod, temperature. assumingitstarted of therod. Is theincrease suddenorgradual? Record thechangeintem- Step 3: (that is, asanumbertimespower often). Step 6: sion oftherod. Name It istheaxlethatrotatesto movethepointerthoughanangleof instead ofthediameter thesteelrod? Why doyou measure thediameterofaxle ofthepointerinStep 1 Compute theminimumlengthofexpansionjoint(s).Show Compute thecoefficientoflinearexpansionusingyour mea- Compute theincrease ∆L Connect thesteamgenerator, thechangeinlength andobserve Express thecoefficientoflinearexpansioninscientificnotation θ ∆T through which the pointer turned duetotheexpan- through which thepointerturned , and∆L. ∆L θ α and —=____ mm ______= —— = = —— = ______= —— = angle ∆T L 360° π ∆L ∆L ∆T θ α d = ______°C = d = ______= into thefollowing equation. θ = ______= in lengthoftherod by substituting = ______° = Chapter 21 Temperature, Heat, andExpansion Period θ . joint. Compute lengthofexpansion expansion. Compute coefficientoflinear rod. Compute increase in length of and angle pointer turns. Record temperaturechange i.A Fig. Date 183 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage184 184 Laboratory ManualLaboratory 53) (Experiment 2. 6. 5. 4. 3. 7. the rod? to thepointofcontactwithaxleinsteadentire lengthof Why doyou measure thedistanceL Usually asafetyfactorof2ormoreisadvised,butcutting itclose account forsafety? would you recommend themtobe, takingyour margin oferror into the expansionjointshadtobeaminimumof2mlong.How large In that your determined consultation,supposeyou experimentally (d) the diameterd (c) (b) thechangein (a) The sourcesoferrorincludeinaccuratemeasurements with anestimateofthepercent ofeach. contribution What are thesources oferror Listthemalong inyour experiment? The unitsof What are theunitsof the The valuewouldbethesame—forinstance,halfchangein less, orthesame? Why? Would thecoefficientoflinearexpansionforsteelrod belarger, Suppose you placedthepointerdevicein themiddleofrod. groove and the axle expands. are measuringonlyhowmuchtheportionofrodbetween The rodis held fixedat the grooveandexpandsonbothsidesof it. We that interlock.) Answers willvary. (Thedesigninthetextistwowide-teethedcombs What doyou thinkwouldbeagooddesignforanexpansion joint? 2.2 mlong. would beplusorminus10%sotheexpansionjointsshould beatleast ∆T L L. (error of1mmin600mm,orunder1%) (error of 1°Cin80°C,orabout1%) are inversetemperature,or“per°C.” L of theaxle(errorabout2%) (error of 1 degree in20degrees,or5%) α ? from the groove inthesteelrod L for half

Name Period Date

Chapter 22: Heat Transfer Comparing Cooling Curves

54 Cooling Off

Purpose

To compare the rates of cooling of objects of different colors and surface Setup: 1 reflectances. Lab Time: >1 Learning Cycle: application Required Equipment/Supplies Conceptual Level: difficult Mathematical Level: difficult 4 empty soup cans of the same size (one covered with aluminum foil, one painted black, one white, and one any other color) Thanks to John Layman for 100-watt lightbulb and receptacle his ideas and suggestions for 4 thermometers (Celsius) or this lab. computer temperature probes with interface printer large test tube one-hole rubber stopper, with thermometer or temperature probe mounted in it, to fit test tube 600-mL beaker graduated cylinder

Styrofoam (plastic foam) cups with covers Activity hot water crushed ice and water mixture variety of different size, color, and shape containers made of various materials meterstick graph paper computer and data plotting software (optional)

Discussion

When you are confronted with a plate of food too hot to eat, you may have noticed that some things cool faster than others. Mashed potatoes can be comfortably eaten when boiled onions are still too hot. And blue- berries in a blueberry muffin are still hot when the rest of the muffin has cooled enough to eat. Different materials cool at different rates. Explore and see.

Procedure

Step 1: Place the four cans 20 cm from an unshielded lightbulb. Place a Data Table A thermometer in each can, and turn on the light. Record the temperature of each can after 1 minute, 2 minutes, and 3 minutes in Data Table A. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 22 Heat Transfer 185 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage186 186 Styrofoam cup. Monitor coolingofwaterin test tube. Monitor coolingofwaterin Laboratory ManualLaboratory (Activity 54) Data TableB Make agraph oftemperature axis)vs. (vertical axis). time(horizontal the temperature ortemperature drop with eitherathermometer probe. Step 3: 5. axis). eter.) Draw agraph oftemperature axis)vs. (vertical time(horizontal you haveacomputer, useatemperature probe insteadofathermom- 30secondsinData the next5minutesevery Table B. (Onceagain,if iceandwater.beaker filledwithcrushed Record thetemperatures over stopper. mountedintherubber thermometer Place thetesttubeina 1. of eachcan.Save your dataandmakeaprintout. read your data.Calibrate your probes, andmonitorthetemperature rise As analternative, ifacomputerisavailable, useatemperature probe to Step 2: 4. 3. 2. quickly atfirstandthenlevels off. Temperature dropsexponentiallywithtime.Thecurve drops most yourDescribe graph. For whichcanwasthetemperature thefastest? rise radiated andconvectedaway. The amountofradiantenergyabsorbedequalsthe the can? amount ofradiant energy beingradiated andconvectedawayfrom the amountofradiant energy beingabsorbedby thecanand For acanatconstanttemperature, whatistherelationship between energy, withno When thetemperaturelevelsoff,eachcanisabsorbingandemitting ant energy from thelightbulb? remain constant.Doesthismeanthatthecansstopabsorbingradi- After several minutesthetemperatures ofallthecansleveloffand The slowestcantoheatupwillprobablybethefoil-coveredcan. For whichcanwasthetemperature theslowest? rise The blackcanshouldheatupthefastest. Fill a Styrofoam (plasticfoam)cupwithhottap water. Monitor Place 25mLofhotwaterfrom thetapinatesttube. Insert the net absorption ofenergy.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 8. mometers. Record whichcooledthefastestandmostslowly. Step 6: cool mostslowly. used. You maywanttowrap materials. themwithvarious Listthecontainers Step 5: Going Further 7. 6. the temperature. doesn’t already theprobe inthewatertomonitor haveone),andinsert Step 4: Name thickness ofcontainer. (4) container coveredornot;(5)typeofinsulationmaterial;(6)wall area ofwater;(2)darkvs.lightcolor;(3)shinydull surface; Factors thatdeterminetherateofcoolinginclude:(1) exposed surface Step 6? therateWhat factorsdetermine ofcooling,basedonyour datafrom Predict whichcontainerwillcoolfastestand the lid. Convection isprimarilyresponsibleforthedifference.Itimpededby responsibleWhat coolingprocess isprimarily forthedifference? The cupwiththelidcoolsatamuchslowerrate. How compare? dothetwocoolingcurves Monitor thecoolingwitheithertemperature probes orther- Place ofcontainers. 200mLofhottapwaterineachavariety Repeat, butcover thecupwithaplasticlid.Poke ahole(ifit Observed slowest: Observed ______fastest:______Observed Predicted slowest: ______Predicted fastest:______Period to cool most slowly. A container with alidis likely ing material have lessereffect. while color and type of insulat- usually has the greatesteffect, exposed to the air. Convection greatest surfacearea of water fastest islikelytohave the The container thatcools the variety ofcontainers Predict coolingratesof a Chapter 22Heat Transfer Date 187 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage188 188 Plot temperaturevs.time. Laboratory ManualLaboratory (Activity 54) variable (vertical axis),where (vertical variable and, forconvenience, sett your samples. axis), (horizontal Lettimebetheindependentvariable Step 7: Extra forExperts 9. perature difference), suchasitssquare oritssquare root oritslogarithm. straight line?Hint: is room temperature. Can you thinkofawaytomakeyour graph a temperature difference that therateoftemperaturechange follows mathematicallyfromNewton’s lawofcooling,whichstates is thenastraightlinewithnegativeslope.(Thisexponentialcooling its finalvalueof0.Thelogarithm difference (T to thefinaltemperature The temperatureofasamplecoolingfromaninitial The graphoflog( this one!) tion requires someheavy-duty math—askyour teacherforhelpon answer tothisques- exists between thecoolingrate andtime?(The What doesyour graph looklike? What mathematicalrelationship 1 – Using dataplottingsoftware, plotdatafrom Step 6foreachof T 2 )e –kt T , wherek – T 2 Try (tem- variable usingsomefunctionofthevertical declines exponentially from itsinitialvalueof T – is aconstant.Inotherwords,thetemperature T 2 T ) vs.timeisastraightlineslopingdownward. = 0 at the origin. LetT = 0attheorigin. T –T 2 T of its surroundingsisgivenby 2 is thetemperature ofthesampleandT between thesampleanditssurroundings.) T dT/dt –T 2 , whenplottedagainsttime, is proportional tothe is proportional – T 2 be thedependent T = T T 2 1 + T 1 T 2 2 to

Name Period Date

Chapter 22: Heat Transfer Solar Energy

55 Solar Equality

Purpose

To measure the sun’s power output and compare it with the power out- Setup: 1 put of a 100-watt lightbulb. Lab Time: >1

Learning Cycle: application Experiment Required Equipment/Supplies Conceptual Level: difficult Mathematical Level: difficult 2-cm by 6-cm piece of aluminum foil with one side thinly coated with flat black paint clear tape meterstick two wood blocks glass jar with a hole in the metal lid one-hole stopper to fit the hole in the jar lid thermometer (Celsius, range –10°C to 110°C) glycerin 100-watt lightbulb with receptacle

Discussion

If you told some friends that you had measured the power output of a lightbulb, they would not be too excited. However, if you told them that Wind or convective cooling can you had computed the power output of the whole sun using only house- affect your results significantly. hold equipment, they would probably be quite impressed (or not believe you). In this experiment, you will estimate the power output of the sun. You will need a sunny day to do this experiment.

Procedure

Step 1: With the blackened side facing out, fold the middle of the foil Assemble apparatus. strip around the thermometer bulb, as shown in Figure A. The ends of the metal strip should line up evenly.

Chapter 22 Heat Transfer 189 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage190 190 with lightbulb. Match outdoortemperature lightbulb. Set upapparatususing room temperature. Allow apparatusto cool to reached. Record maximumtemperature sun. Place apparatusoutdoorsin Measure distancetolightbulb. Laboratory ManualLaboratory 55) (Experiment tained fortwominutes. Turn thelightbulboff. ratus 0.1cmatatimeuntilthetemperature obtainedinStep 5ismain- move theapparatus only 1cmatatime. Adjust thedistanceofappa- bilize eachtime. Asthetemperature approaches thatreached inStep 5, lightbulb, 5cmatatime, allowing temperature thethermometer tosta- Step 8: put somebooksunderthejarapparatus. exactly perpendiculartothelightrays from thebulb. You mayneedto jar apparatus atthe95-cmmark withtheblackenedsideoffoilstrip ment locatedatthe0-cmmark ofthemeterstick(Figure D).Center the Step 7: mometer tocoolroom temperature. Step 6: maximum temperature isreached. Record thistemperature. Step 5: sun. isexactlyperpendicularto the raysblackened sideofthefoilstrip ofthe Step 4: located inthemiddleofjar. Place thelidonjar. the lidfrom thebottomside. Slide is untilthefoilstrip thethermometer one-hole stopper. Remove thelidfrom thejar, andplacethestopperin Step 3: unpainted sidetoholdthefoilonthermometer. stick tomakeaflat,evensurface. Use apieceofcleartapeonthe Figure B. outward Bend eachendofthefoilstrip (Figure C).Use ameter- Step 2: Record thisvalue. oftheapparatusthe absorberstrip andthefilamentoflightbulb. Step 9: i.D Fig. Turn thelightbulbon.Slowly move the apparatus toward the Take your apparatus outdoors. Prop itatananglesothatthe Set themeterstickontable. Place thelightbulbwithitsfila- Return theapparatus totheclassroom, andallow thether- Leave theapparatus inthispositionthesunlightuntil Use thefree toinsert glycerin into the endofthethermometer thefoilsothatitcompletelysurroundsCrimp thebulb, asin Measure asexactlypossiblethedistanceinmeters between maximum temperature______= distance from light filament to foil strip = ______distance from lightfilamenttofoil strip m

© Addison-Wesley Publishing Company, Inc. All rights reserved. Show your work. 100-watt lightbulbsneededtoequalthesun’s power. Show your work. Step 11: 2. 1. Analysis The numberof100-wattbulbsequalsthesun’s wattagedividedby100W. pute thewattageofsun. The sun’s distanceinmetersis1.5 Step 10: Name fraction oftheenergyradiated bythesun. diverted towardjustlightingbulbs,theywouldstillproduce onlyatiny No—even ifalltheoperatingelectricalgeneratorsin worldwere you computedinStep 11atonce?Explain. Would onthenumberof100-wattlightbulbs itbepossibletoturn the wattagesisratioofsquares the distances.) (Accept equivalentequations,especiallyonestatingthatthe ratio of the ratioof the bulb’s wattagetothesquareofbulb’s distance. The ratioofthesun’s wattagetothesquareofsun’s distanceequals (sun’s distance) ratio of..” ratios. Express thenewequationasasentencethatbegins, “The Re-express theequation inStep 10asarelationship between two ———————— = u’ atg bulb’s wattage sun’s wattage Use thevalue ofthesun’s wattagetocomputethenumberof For thedistanceobtained,usefollowing equationtocom- sun’s wattage=(bulb’s wattage)× number of100-wattlightbulbs=______W ______= sun’s wattage 2 (bulb’s distance) 2 ———————— (bulb’s distance) (sun’s distance) 2 2 × 10 Period 11 m. Chapter 22Heat Transfer lightbulbs. Compute numberof Compute wattageofthesun. Date 191 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PM Page 192

3. The accepted value for the sun’s wattage is 3.83 × 1026 W. List at least three factors that might account for the difference between your experimental value and the accepted value.

Possible errors include: (a) Bulb’s wattage is not exactly 100 watts.

(b) Distance to bulb is not measured accurately. (c) Not all of the sun’s

energy gets through—atmospheric absorption. (d) Distance to the sun

is not always 1.5 × 1011 m; the sun is closer in January than in July.

(e) Did not get radiation perpendicular to black vanes in either

measurement. (f) Energy radiating from the lightbulb is not the same in

192 Laboratory Manual (Experiment 55) CP02_SE_LAB_Ch49-56 3/5/01 12:07 PM Page 193

Name Period Date

Chapter 22: Heat Transfer Solar Energy

56 Solar Energy

Purpose

To find the daily amount of solar energy reaching the earth’s surface and Setup: 1 relate it to the daily amount of solar energy falling on an average house. Lab Time: >1 Learning Cycle: application Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: moderate 2 Styrofoam (plastic foam) cups plastic wrap graduated cylinder rubber band Adapted from PRISMS. water thermometer (Celsius) blue and green food coloring meterstick

Discussion

How do we know how much total energy the sun emits? First, we assume that it emits energy equally in all directions. Imagine a heat detector so big that it completely surrounds the sun—like an enormous basketball Activity with the sun at its center. Then, the amount of heat reaching the detector would be the same as the total solar output. Or if our detector were half a basketball and caught half the sun’s energy, then we would multiply the detector reading by 2 to compute the total solar output. If our detector encompassed a quarter of the sun and caught one-fourth its energy, then the sun’s total output would be four times the detector reading. Now that you have the concept, suppose that our detector is the water surface area of a full Styrofoam cup here on earth facing the sun. Then it comprises only a tiny fraction of the area that surrounds the sun at this distance. If you figure what that fraction is and also measure the amount of energy captured by your cup, you can tell how much total energy the sun emits. That’s how it’s done! In this activity, however, you will measure the amount of solar energy that reaches a Styrofoam cup and relate it to the amount of solar energy that falls on a housetop. You will need a sunny day to do this activity.

Procedure

Step 1: Fill a Styrofoam cup, adding small equal amounts of blue and Add food coloring. green food coloring to the water until it is dark (and a better absorber of solar energy). Then measure and record the amount of “water” in your cup.

volume of water = ______

mass of water = ______© Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley Nest the cup in a second Styrofoam cup (for better insulation). Chapter 22 Heat Transfer 193 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PMPage194 194 Compute solarenergyflux. Measure surfaceareaofcup. Measure temperature. Laboratory ManualLaboratory (Activity 56) centimeter perminute. Show your work. Step 8: specific heatofwater. Show your work. You mayassumethat thespecificheatofmixture isthesameas centimeters. of thecup. Compute area thesurface ofthetopcupinsquare Step 6: after itwassetinthesun. Step 5: the thermometer, andrecord thefinalwatertemperature. Step 4: Step 3: plastic wrap band. sealedwitharubber Step 2: A typicalvalueobtainedforthesolarenergyfluxis1.1 cal/cm Step 7: Compute thesolarenergy flux,theenergy collectedpersquare Compute thatwascollectedinthecup. theenergy incalories Measure andrecord thediameterincentimetersoftop Find thedifference inthetemperature ofthewaterbefore and Remove theplasticwrap. Stir thewaterincupgentlywith Put thecupinsunlightfor10minutes. Measure thewatertemperature andrecord it.Cover thecupwith nry=______cal ______= energy areasurface cm ofwater=______cm ______= diameter temperature difference______= final watertemperature______= initial watertemperature______= solar energy______flux= cal/cm 2 2 •min 2 •min.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 11 000cal/m consumed withinthehouse. cal valueis45000W, or45kW, whichislargerthanthepowerlikelytobe this ismultipliedby4.18J/caltogivethepowerinJ/s,orwatts(W).Atypi- surface anddecreasesurface thefluxofsolarenergy thatyou measure? What factorscouldaffecttheamountofsunlightreaching theearth’s minute reaches theearth’s afterpassingthrough theatmosphere. surface persquarecalled thesolarconstant.Only1.5calories centimeterper area perpendiculartothedirection ofthesun’s rays. This energy fluxis atmosphere persquare tobe2calories centimeterperminuteonan Scientists havemeasured theamountofsolarenergy fluxoutsideour Analysis 1. The areaofa6-mby12-m roof is72m Since thereare10000cm (Hint: perminuteatyour presentthe earth timeandlocation.Show your work. Step 9: tity is thendividedby60s/min.Atypical value is1.1 ber ofcaloriesper square meterperminuteobtained in Step9.Thatquan- Step 8shouldbemultipliedby10 000 cm then inwatts. Show your work. made your measurement. persecond, Obtaintheanswer firstincalories on aflat6-mby 12-mroof locatedinyour area atthetimewhenyou Step 10: Name also bereducedby that factor. to thedirectionof the radiation, themeasuredenergyper unit area will obstructions. Ifthesurfaceareabeingilluminatedisnot perpendicular pollution; (d) time of day; (e) season of year; (f) latitude; (g) nearby location on the earth’s are: (a) cloudcover;(b) humidity; (c) air surface The factors that mightaffecttheamountofsolar energy reaching a within thehouse? How doesthissolarpower compare withtypicalpower consumption There are 10000cm Compute how muchsolarenergy reaches eachsquare meterof Use your datatocomputetherate atwhichsolarenergy falls solar power received by roof______= W solar power received by roof______= cal/s solar energy______flux= cal/cm 2 •min. 2 in 1m 2 in 1m 2 , thesolarenergyfluxobtainedin 2 .) 2 . Thisisthenmultiplied by the num- 2 /m 2 . Atypicalvaluewouldbe 2 •min 10 4 cal/s. Finally, Period Chapter 22Heat Transfer by roof. Compute solarenergyreceived Date 195 CP02_SE_LAB_Ch49-56 3/5/01 12:07 PM Page 196 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PM Page 197

Name Period Date

Chapter 23: Change of Phase Boiling of Water

Boiling Is a Cooling 57 Process

Purpose

To observe water changing its phase as it boils and then cools. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy safety goggles paper towels Mathematical Level: none ring stand wire gauze 2 plastic-coated test-tube clamps 1000-mL Florence flask (flat-bottomed) or Franklin’s flask (crater- bottomed) one-hole rubber stopper to fit flask, fitted with short (15-cm) thermometer or temperature probe water crushed ice or beaker of cool tap water Bunsen burner thermometer (Celsius), regular length (30 cm), or computer temperature probe with interface Activity printer pan or tub computer and data plotting software (optional) graph paper (if computer is not used)

Discussion

When water evaporates, the more energetic molecules leave the liquid. This results in a lowering of the average energy of the molecules left behind. The liquid is cooled by the process of evaporation. Is this also true of boiling? Try it and see.

Procedure

Step 1: Attach an empty flask to the ring stand with a test-tube clamp. Adjust height of flask. Insert the teacher-prepared stopper with the thermometer or temperature probe into the neck of the flask. Loosen the wing nut on the clamp so that when the flask is rotated upside down, the end of the thermometer clears the table top by about 3 cm.

Step 2: Before filling the flask with water, you need to practice the pro- Prepare setup for dry run. cedure you will be performing later. Remove the stopper from the flask. Attach a ring and gauze below the flask, and place an unlit Bunsen © Addison-Wesley Publishing Company, Inc. All rights reserved. All rights Inc. Company, Publishing © Addison-Wesley

Chapter 23 Change of Phase 197 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage198 198 Insert rubberstopper. Monitor water temperature. Practice invertingflask. Laboratory ManualLaboratory (Activity 57) in Figure A. position,asshownnut ontheclamptokeepflaskininverted paper towel, itby andinvert rotating itintheclamp. Tighten thewing the wingnutonclamp. Carefully into theflask.Atmospheric pressure willmakeitfitsnugly. Loosen damp papertowel. Insert orprobe the stopperwiththethermometer mometer. Drop Firmly grasp thering. theclampandneckwitha Step 5: ware tomakeagraph oftemperature vs. time. Print outyour graph. probe before heatingthewater. If available, usedataplottingsoft- standinplaceofthethermometer.probe tothering Calibrate your water, andrecord your data. until 3minutesafterthewaterbeginsboilingvigorously. Heat the a datatablesothatyou canrecord thetemperature 30seconds every stand sothatitsbulbisinthewaterbutnottouchingflask.Make safety. stand. attach ittothering andgauze shouldbebelowThe ring itfor Step 4: with boiling-hotwater. able manipulatingtheapparatus inthiswaywhentheflaskisfilled this position. the clampuntilitisupsidedown. Tighten thewingnuttokeepitin clamp. Holding withadamppapertowel, theflaskfirmly rotate itin towel. Insert thestopperintoneck.Loosenwingnuton Firmly grasp theclampandneckof “hot” flaskwithadamppaper the screw andlower onthering, itandthegauze tothetabletop. or probesecond thermometer and its clamp from the stand. Loosen offtheburner.have justturned Move aside. theburner Remove the Step 3: stand,andsuspenditinsidetheflask. ring belowburner Attach orprobe thering. tothe asecondthermometer Alternatively, ifyou are usingacomputer, attachatemperature If you are tothering usingthermometers, attachathermometer Place the stopperasideforuseinStep 5. Practice thisprocedure afewtimessothatyou willbecomfort- When you stopheatingtheflask,remove thesecondther- Put onsafetygoggles. Fill theflaskhalffullofwater, and Imagine thatyou havebeenboilingwaterintheflask,and i.A Fig. hold theflask,usingadamp

© Addison-Wesley Publishing Company, Inc. All rights reserved. 5. 4. 3. Analysis the computer. tal axis),eitherplottingdatafrom from your tableormakingaprintout Step 7: 2. 1. water intheflask. eral times. If you are usingacomputer, monitorthetemperature ofthe iceonit.Repeattop halfoftheflask,orplacecrushed sev- thepouring Step 6: Name They arethesame. the waterby boiling? boiling onastove compare withtheamountofenergy removed from How doestheamountofheatenergy absorbed by apotofwater water withthenewlyformedvapor(steam). absorbed fromtheflameisexactlyequaltoenergythatleaves The watertemperaturedoesnotincreasebecausetheheatenergy tinues toboil. Explain ofthetemperature your observations ofthewaterasitcon- atmospheric pressure). The waterremainsatconstanttemperature (100°C at standard to beapplied? Does thetemperature ofboilingwaterincrease whenheatcontinues The temperatureofthewaterdropsdramaticallywhenitboils. What happenstothetemperature ofthewater intheflask? water orice. The waterintheinvertedflaskboilswheniscooledwith happeninginsidetheflask? What doyou observe Prepare agraph oftemperature axis)vs. (vertical time(horizon- Place apan ortubundertheflask.Pour cooltapwaterover the Period Chapter 23Change ofPhase Make graph. Cool flask. Date 199 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage200 200 Laboratory ManualLaboratory (Activity 57) 6. The waterboilsbecausetheairpressureinflaskisreducedwhen cool wateroricewasputonit. flask after Explain oftheinsideinverted your observations is heat isbeingsuppliedbyanoutsidesourceasthewaterboils,sothere water, soitstemperaturedrops.(Unlikethefirstpartofthisactivity, no altitude). The boiling process removes energy from the remaining 100°C whentheairpressureisreduced(thiscanbe observed at high the airissuddenlycooled.Water boilsatatemperaturelowerthan a temperature drop duringboiling.)Boilingisa cooling process!

Name Period Date

Chapter 23: Change of Phase Heat of Fusion

58 Melting Away

Purpose

To measure the heat of fusion of water. Setup: 1 Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development 250-mL graduated cylinder Conceptual Level: difficult 8-oz. Styrofoam (plastic foam) cup Mathematical Level: moderate water ice cube (about 25 g) Thanks to Lisa Kappler for her paper towel ideas and suggestions for this thermometer (Celsius) or lab. computer temperature probe with interface computer and data plotting software (optional) printer graph paper (if computer is not used)

Discussion

If you put heat into an object, will its temperature increase? Don’t automatically say yes, for there are exceptions. If you put heat into water at 100°C, its temperature will not increase until all the water has become steam. The energy per gram that goes into changing the phase from liquid to gas is called the heat of vaporization. And when you put heat into melting ice, its temperature will not increase until all the ice has melted. The energy per gram that goes into changing the state from solid to liquid is called the heat of fusion. That’s what this experiment is about.

Procedure

Step 1: Use a graduated cylinder to measure 200 mL of water, and pour it into a Styrofoam cup. The water should be about 5°C warmer than Monitor temperature of water. room temperature. If you are using a thermometer, make a data table for temperature and time. With the thermometer or temperature probe, measure and record the temperature of the water every 10 seconds for 3 minutes.

Step 2: Dry an ice cube by patting it with a paper towel. Add it to the water. Continue monitoring the temperature of the water every 10 seconds while gently stirring it until 3 minutes after the ice cube has melted. Record the data in a table or with the computer. Note the time at

Chapter 23 Change of Phase 201 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage202 202 absorbed duringwarming. Compute heatenergy water. Compute theenergylostby Make graph. water. Determine thefinalvolumeof Laboratory ManualLaboratory 58) (Experiment cal/g•°C), and∆T tial massofthewater, c the melted ice warmed from 0°Cthe meltedicewarmed toitsfinaltemperature. Step 6: perature isstabilized. from thebeginningofRegion IItotheendofRegion IIIwhere thetem- 2. melting. Region IIIcovers thetimeaftercubehasmelted. was placedinthewater. Region IIcovers thetimewhilecubewas into three distinctregions. Region Icovers thetimebefore theicecube software, acopy print foryour analysisandreport. axis)graph.(horizontal If you are usingacomputerwithdataplotting 1. Step 3: 3. Step 4: the icecubewasmelting.Use therelation Q Step 5: was melting(Region II)? What wasthetotaltemperature changeofthewaterwhilecube Study your graph. Draw dashedlinestobreak vertical your graph Explain howice cubeoriginally? thesemasses. you determined What wasthemassofwateroriginally? What wasthemassof Region I,asevidencedby the steeperdownwardslopeof the graph. In Region IIthetemperatureshould drop at a fasterratethan in water wascooling? How didplacingtheicecubeinwateraffectrate atwhich the droponthegraphfrombeginningto theendofRegionII. vertical The totaltemperaturechangewhiletheicewasmeltingequals of thefinalvolumewaterandmeltedicesubtract200g. mass ofonegram.To findthemassoficecube,startwith The massofthewaterwas200g,sinceeachmilliliterhasa Compute theamountofheatenergy absorbedasthe waterfrom Plot your datatomakeatemperature axis)vs. (vertical time thefinalvolumeofwater.Determine Compute thetotalamountofheatenergy Q is themagnitudeofwater’s temperature change etdiedrn amn __cal ____ = warming melted iceduring heat energy absorbedby cal heat energy lostby water=______original final volume = ______is thespecificheatcapacityofwater(1.00 = mc∆T, where m lost by thewateras is theini-

© Addison-Wesley Publishing Company, Inc. All rights reserved. 6. 5. Analysis 4. 7 by themassoficethatmeltedincup. Step 8: melted. compute theamountofheatenergy thatwasabsorbedby theiceasit Step 7: Name from 0°Ctothefinaltemperature ofthewater. of heatenergyto(1)meltthe ice,and(2)warmthemeltedicewater The totalamountofheatenergylostbythewaterequals theamounts amounts ofheatenergy ittooktodowhatthings? The totalamountofheatenergy lostby thewaterisequalto the solid timestheheatoffusion. The amountofheatenergyabsorbedinmeltingequals themassof the massofsolid? heat energy absorbedby thesolidrelated totheheatoffusionand solid toaliquidiscalledtheheatoffusion.How istheamountof heat energy absorbedpergram whenasubstancechangesfrom a The meltingiceabsorbsheatenergy, andthuscoolsthewater. The thenalarger(which we amounttomelt. neglectinthisexperiment), water,the warmer upto0°C firstasmallamount ofheattowarm In order fortheicecubetomelt,ithasextract heatenergy from sit atroomtemperatureforseveralminutesbeforeuse. will affecttheaccuracyofthisexperiment.Leticetakenfromafreezer directly fromafreezerismostoftensignificantlycoolerthan0°Cand is intheprocessofmeltingwhenyourexperimentbegins.Icetaken minimize orpreventthis,useicethatisquitewetontheoutside—that energy goesintowarmingtheiceuptomeltingtemperature.To ofthe value. Onesourceoferrorisusingicecolderthan0°C.Thenpart The computedvalueshouldbewithinafewpercentofthestandard percentage difference. Compare thisvalue tothestandard value, 80cal/g,andcalculatethe Compute theheatby fusionby dividingthevalue foundinStep From thedifference between thevalues foundinSteps 5and6, heat offusion=______cal/g by cal ______melting= iceduring heat energy absorbed Period Chapter 23Change ofPhase Compute heatof fusion. absorbed duringmelting. Compute heatenergy Date 203 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage204 204 Laboratory ManualLaboratory 58) (Experiment 7. Sources oferrorinclude:(a)film of water on ice cube; (b) temperature What are somesources oferror inthisexperiment? due toevaporation and radiation. final volumeofwaterplus melted icecube;(e)heatlost to surroundings mometer; (d) inaccurate measurementofinitial volume ofwaterand of ice cubebelow 0°C if taken directlyfromfreezer;(c) inaccurate ther-

Name Period Date

Chapter 23: Change of Phase Heat of Vaporization

59 Getting Steamed Up

Purpose

To determine the heat of vaporization of water. Setup: 1 Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development safety goggles Conceptual Level: moderate Bunsen burner Mathematical Level: moderate steam generator with rubber tubing and steam trap 3 large Styrofoam (plastic foam) cups water balance thermometer (Celsius)

Discussion

The condensation of steam liberates energy that warms many buildings This quantity is relatively small on cold winter days. In this lab, you will make steam by boiling water but should not be neglected. and investigate the amount of heat energy given off when steam con- denses into liquid water. You will then determine the heat energy released per gram, or heat of vaporization, for the condensation of steam.

Procedure

Step 1: Make a calorimeter by nesting 3 large Styrofoam cups. Measure Measure mass of cups. the mass of the empty cups and record it in Data Table A.

Chapter 23 Change of Phase 205 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage206 206 during cooling. Compute theenergylost Compute heatenergygained. Compute massofsteam. mass. Measure final temperature and Adjust steamgenerator. Ignite Bunsenburner. Assemble apparatus. and mass. Measure initialtemperature Laboratory ManualLaboratory 59) (Experiment Show your work. condensed steamasitcooledfrom 100°C down toitsfinaltemperature. Step 9: as itcoolsfrom 100°C tothefinaltemperature. Show your work. condensation ofsteam,andthenfrom thecondensedsteam (now water) in thetemperature ofthewater. This heatcomesintwosteps:from the water, water usingtherelation Q Step 8: from thechangeinmassofwatercalorimeter. Step 7: water, andrecord theminData Table A. Immediately the final mass and temperature determine of the warm Step 6: no higherthan50°C. Bubble untilthewaterreaches steamintothecalorimeter atemperature vigorously, butnotviolently. stirthewaterwiththermometer. Gently water out of the calorimeter. The steam should make the water bubble rate at which steam comes out of the tubing so that it does not gurgle Step 5: tor andigniteittoheatthewaterinside. Step 4: (Figure A). tubinginthewatercalorimeter Place the endoftherubber Step 3: A. Alsorecord temperature theoriginal ofthewatertonearest 0.5°C. cupandwatertothenearestthe triple 0.1gandrecord itinData Table Step 2: c Compute theamountofheatenergy lostby thewaterfrom the Compute thetotalamountofheatenergy Q Compute themassofsteamthatcondensedinyour calorimeter Shut offtheburner, andremove thetubingfrom thewater. Once thewaterinsteamgenerator boiling,adjustthe starts Put onsafetygoggles. underthesteamgenera- Place theburner Fill thesteamgenerator half-fullwithwater, andputitscapon. Fill theinnercuphalf-fullwithcoolwater. Measure themassof is thespecificheatofwater(1.00cal/g•°C), and∆T i.A Fig. fwtrfo h odne ta __ cal of waterfrom thecondensedsteam =_____ cooling heat energy lostduring heat energy______gained= cal mass ofsteam=______g = mc∆T, where m is theinitialmassof gained by thecool is thechange

© Addison-Wesley Publishing Company, Inc. All rights reserved. 4. 3. 2. Analysis 1. in Step 10by themassofsteamthatcondensedincup. Step 11: condensed. compute theamountofheatenergy thatwasreleased by thesteamasit Step 10: Name surrounding air insteadof the water. It also reduces evaporation. Keeping the cap on reduces convection, whichwouldwarmthe generator causethewatertoboil more quickly? Why doeskeepingthecaponwhenheatingwater inthesteam of it. does notsignificantlywarmit,noritcondenseand becomepart warms upthe water. Thesteamthatbubblesupand out of the water Only thesteamthatactuallycondensesandbecomespartofwater ence inthisexperiment? Does theamountofsteamthatescapesintoairmakeanydiffer- and givesoffenergythat warms the cool water. changes intosteam. In the calorimeter, thesteamcondensesintowater In the generator, the water absorbsenergyfromtheheatsourceand Where doestheenergy thesechanges? comefrom orgotoduring One happensinthegenerator, andtheotherincalorimeter. There are twomajor energy changesinvolvedinthisexperiment. fusion shouldcomeoutwithin10%of540cal/g. If studentsarecarefulandusesteamtraps,theirvaluesfortheheatof the percentage difference. Compare thisvalue tothestandard value, 540cal/g,andcalculate Compute by theheatofvaporization dividingthevalue found From thedifference between thevalues foundinSteps 8and9, eto aoiain=____cal/g =______heat ofvaporization cal heat energy released condensation=______during Period Chapter 23Change ofPhase Compute heatof vaporization. Date 207 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PM Page 208 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PM Page 209

Name Period Date

Chapter 23: Change of Phase Changes of Phase

60 Changing Phase

Purpose

To recognize, from a graph of the temperature changes of two systems, Setup: 1 that energy is transferred in changing phase even though the tempera- Lab Time: >1 ture remains constant. Learning Cycle: concept development Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: easy hot plate 2 15-mm × 125-mm test tubes Adapted from PRISMS. heat-resistant beaker paraffin wax 2 ring stands 2 test-tube clamps hot tap water 2 thermometers (Celsius) in #3 stoppers to fit test tubes or computer 2 temperature probes in slotted corks to fit test tubes printer

graph paper (if computer is not used) Activity

Discussion

When water is at its freezing point, cooling the water no longer causes its temperature to drop. The temperature remains at 0°C until all the water has frozen. After the water has frozen, continued cooling lowers the temperature of the ice. Is this behavior also true of other substances with different freezing temperatures?

Procedure

Step 1: Fill one test tube 3/4 full with wax (moth flakes). Fill another test Set up apparatus. tube with water to the same level. Fasten the test tubes in clamps fas- tened to a ring stand, and place them in hot tap water in a heat-resistant beaker. The beaker should be heated with a hot plate. Place a stopper with a thermometer or a cork with a temperature probe in each of the test tubes. Calibrate the temperature probes before using them. The thermometer or probe in wax should reach only just below the surface.

Step 2: Heat the water until all the wax has melted. Both thermometers Melt wax. or temperature probes should show nearly the same temperature. Turn the heat off, and record the temperatures. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 23 Change of Phase 209 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage210 210 Plot yourdata. and water. Monitor temperatureofwax Laboratory ManualLaboratory (Activity 60) with your labreport. puter toplotthedata.Print outthedataandgraph, andincludethem Alternatively,ferent ofeachmaterial. colorsforthecurve usethecom- axis) of(1)thewaterand(2)wax.Use dif- axis) vs. time(horizontal Step 4: temperature atwhichthewaxbeginstosolidify (freeze). 30 secondsuntil5minutesafterthewaxhasentirely solidified.Note the Step 3: 4. 3. 2. 1. Analysis The heatsourceistheportionofwaxthatchanging statefrom responsible forthis? that ofthesurrounding waterbath. What wastheheatsource When thetemperature ofthewaxwasconstant,ithigherthan The waxfroze,orsolidified. constant? What physicalchangeoccurred whilethewaxtemperature remained horizontal plateau. The watercontinuouslycoolswhilethewaxcurvehasaflat,nearly How dothetemperature ofthewaxandwaterdiffer? curves Both temperaturecurvesarefalling. How isthetemperature ofthewaxsimilartothatwater? curve liquid tosolid.Freezingisawarmingprocess! On asinglepieceofgraph paper, plotthetemperature (vertical Record thetimesandtemperatures ofthewaxandwaterevery

Name Period Date

Chapter 23: Change of Phase Energy Transfer

Work for Your Ice 61 Cream

Purpose

To measure the energy transfers occurring during the making and freez- Setup: 1 ing of homemade ice cream. Lab Time: >1 Learning Cycle: concept Required Equipment/Supplies development Conceptual Level: moderate homemade ice cream machine insulated cups Mathematical Level: easy ice ice cream mix rock salt triple-beam balance Thanks to David Vernier for thermometer spring scale with maximum his ideas and suggestions for capacity of 50 N or 10 lb this lab.

Discussion

Energy must be supplied to a home to heat it on a cold winter day. Energy must also be supplied to an air conditioner that is cooling a Activity home on a hot summer day. The air conditioner is transferring heat from the cooler indoors to the warmer outdoors. Energy input is always required to move heat from a region of lower temperature to a region of higher temperature. Energy must be taken away from a liquid to make it a solid. If the liquid is cooler than the surrounding air, additional energy must be added to move heat from the liquid to the warmer air, just as extra energy is needed to move heat from a room to the warmer outdoors in summer. When the liquid is sweet cream, the solid that results is ice cream. (Making ice cream also involves swirling in air; ice cream is actually a mixture of a solid and a gas.) The freezing of homemade ice cream involves several energy transfers.

1. Energy (work) is expended in turning the crank to overcome inertia and friction. 2. The slush of ice and rock salt takes up energy as it melts. 3. The ice cream mix cools from its original to its final temperature. 4. The metal container cools from its original to its final temperature. 5. The ice cream mix gives up energy as it freezes.

Procedure

Each group in the class should determine how it will make the measurements to determine the amount of energy transferred in one of the five

Chapter 23 Change of Phase 211 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage212 212 Laboratory ManualLaboratory (Activity 61) data toshare withtheclasstomakeaprofile ofalltheenergy transfers. of theadvances ofsciencecameonlyaftergreat Organize sacrifices! your mine theseconstantsandtheenergy transferred. Don’t forget thatmany theenergy transferred.determine fusion oficecream. outitsmethodto Eachgroup shouldalsocarry constants mightbethespecificheatoficecream mixandtheheatof thoseconstants.also shoulddoaseparate todetermine experiment The 3. 2. 1. Questions Describe yourDescribe procedure. You someoftheicecream mayhavetosacrifice you maketodeter- tice paradoxical, ordoesitmakegoodphysicssense? made icecream, saltisusedtohelppromote freezing. Is thisprac- Salt isputonicyroads topromote melting. When you makehome- being tracked. of energy isinvolvedin chemical changes here,andthisenergy isnot The energy absorbed shouldequal the energyreleased,butquiteabit salt compare withtheenergy released by theotherprocesses? How didtheenergy absorbedby themeltingslushoficeandrock Melting theslushoficeandrocksaltisbiggestabsorberenergy. Which process ofthefivelistedisgreatest absorberofenergy? melting pointisloweredby pressure. water (ice!)therebyextractingenergyfromitsenvironment; (2)the Two effects are atwork:(1) salt dissolvesinthesolid (as well asliquid)

Name Period Date

Chapter 23: Change of Phase Heat Engines

62 The Drinking Bird

Purpose

To investigate the operation of a toy drinking bird. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: application Conceptual Level: moderate toy drinking bird Mathematical Level: none cup of water Thanks to Willa Ramsey for her ideas and suggestions for this lab. Discussion

Toys often illustrate fundamental physical principles. The toy drinking bird is an example.

Procedure Activity Step 1: Set up the toy drinking bird with a cup of water as in Figure A. Position the cup to douse the bird’s beak with each dip. The fulcrum may require some adjustment to let it cycle smoothly.

Fig. A

Step 2: After the bird starts “drinking,” study its operation carefully. Your goal is to explain how it works. Answering the questions in the “Analysis” section will help you understand how it works. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 23 Change of Phase 213 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage214 214 Laboratory ManualLaboratory (Activity 62) 1. Analysis 6. 5. 4. 3. 2. 8. 7. What causes the fluid to rise upthetoyWhat causesthefluidtorise bird’s neck? Yes, asthewaterwillnotevaporatequicklyfrombeakif the dipping? Will therelative humidityofthesurrounding airaffecttherate of down motionslowsandthenstops. At firstitwillcontinueitsmotion,butasthebeakdriesout,upand Will thebird ifthecupisremoved? continuetodrink The fuzzyheadenhancesevaporation. What isthepurposeoffuzzyhead? reservoir. the liquid in the lower reservoir, allowing fluid to flow back into the When thebirddips,bottomoftubepokesabovesurface What causesthebird tomakeitselferect? The headgainsfluidandbecomesheavier. What causesthebird todip? forces theliquidupneck. pressure inthehead.Thehighervaporlowerreservoir Cooling oftheheadbyevaporationfrombeaklowersvapor water levelincuptoolow. Some conditionsare:saturated air;fulcrumnotadjustedproperly; Under whatconditionswillthebird failtooperate? It willprobablydip faster outdoors;abreezeincreasesevaporation. Will thebird dipfasterindoorsoroutdoors? Why? surrounding air is humid.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 10. Name 9. Explain how thebird works. the drinking bird.the drinking Brainstorm aboutpractical withyour labpartners applicationsof modified drinkingbirdscouldbeusedinSaudiArabiaaspumps. Student answerswillvary. Studieshavebeenmadetoseewhether repeated. Each pivotwetsthefeltsurfaceofbeakandhead,cycleis and the ether spillsbackinto the lowerreservoir.bird pivotsforward, beak andhead.Whentheweightofether in the head is sufficient, the head iscooledby the evaporation of water from theouter felt-covered up the tube.Etherin upper bodydoesnot vaporize because the creates pressureonthesurfaceofliquid,whichpushesliquid at roomtemperature.As the vaporaccumulatesaboveliquid,it head. Thelowerbodycontainsliquidether, which evaporates rapidly body andbytheevaporationofwaterfromoutersurfaceits The toydrinkingbirdoperatesby the evaporation of etherinsideits Period Chapter 23Change ofPhase Date 215 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PM Page 216 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PM Page 217

Name Period Date

Chapter 24: Thermodynamics Estimating Absolute Zero

63 The Uncommon Cold

Purpose

To use linear extrapolation to estimate the Celsius value of the tempera- Setup: 1 ture of absolute zero. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate safety goggles Mathematical Level: moderate paper towel Bunsen burner Adapted from PRISMS. wire gauze ring stand with ring 250-mL Florence flask flask clamp short, solid glass rod one-hole rubber stopper to fit flask 500-mL beaker water thermometer (Celsius) ice bucket or container (large enough to submerge a 250-mL flask) ice large graduated cylinder graph paper

Optional Equipment/Supplies

computer data plotting software

Discussion

Under most conditions of constant pressure, the volume of a gas is pro- The idea that an extrapolated portional to the absolute temperature of the gas. As the temperature of graph can give an accurate a gas under constant pressure increases or decreases, the volume answer even when the graph increases or decreases, in direct proportion to the change of absolute itself is not valid in the region temperature. If this relationship remained valid all the way to absolute where it is extrapolated is a difficult idea for the student to zero, the volume of the gas would shrink to zero there. This doesn’t hap- grasp. Point out that the impor- pen in practice because all gases liquefy when they get cold enough. tant part of the student’s graph Also, the finite size of molecules prevents liquids or solids from contract- is its slope in the region where ing to zero volume (which would imply infinite density). the measurements are made, In this experiment, you will discover that you can find out how cold and that it is this slope that absolute zero is even though you can’t get close to that temperature. You determines where absolute zero is. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley will cool a volume of air and make a graph of its temperature-volume

Chapter 24 Thermodynamics 217 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage218 218 Graph andextrapolate. Measure volumesofair. Remove flaskfrombath. Record bathtemperature. Set upicebath. i.A Fig. Laboratory ManualLaboratory 63) (Experiment the gasiszero). points andtothex-axis(where theextrapolated value forthevolumeof axis.to 250mLonthevertical Draw astraight linethrough thetwo Celsius to+100degrees Celsius axisandascaleof0mL onthehorizontal ture axis)forthetwoconditions. (horizontal Use ascale of–400degrees Step 7: both temperatures. Record thevolumes. Step 6: of thestopper, andremove theflaskfrom theicebath. under thewatersurface, placetheglassrod oryour fingerover thehole bath. With theflasktotallysubmerged andtheneckofflaskjust tracted air. The airintheflasknow hasthesametemperature astheice Step 5: 3 minutes. Measure andrecord thetemperature oftheicebath. Step 4: ice bath,andremove theglassrod. the icebath.Hold theflaskandstopperbelow ofthe thewatersurface Remove theclampfrom theflask,andlower theflaskupsidedown into flask tocoolforaminuteorsountilitcanbehandledcomfortably. stand,andlifttheflask,stopper,ring and clampassembly. Allow the the sametemperature astheboilingwater. Loosentheclampfrom the trap alltheairmolecules. Dothisquicklywhiletheairinflaskhas stopperto and quicklyplaceasolidglassrod intotheholeofrubber Step 3: record thewatertemperature. that theairinflaskisheatedtowatertemperature. Measure and beaker (seeFigure A).Boil thewaterforatleast3minutestomakesure the waterwithlevelapproximately 4cmbelow thetopof water, standin stand,andclamptheflasktoring setitonthering a Step 2: large enough tosubmerge a250-mLflask.(Donotputtheflaskinityet.) the temperature, indegrees Celsius, ofabsolutezero. relation. Then you willextrapolate thegraph tozero volumetopredict Step 1: Procedure dry single-hole stopperintotheflask.Half-fill a500-mLbeakerwith Turn offtheburner. Use adamppapertowel tograsp theclamp, Plot the volume of air in the flask (vertical axis)vs.Plot thevolumeofairinflask(vertical thetempera- thevolumeoftrappedDevise amethodtodetermine airat Some waterhasentered theflasktotakeplaceofcon- Hold theflaskupsidedown foratleast underthewatersurface Put onsafetygoggles. Select adry Make anicebathofandwater, usingabucketorcontainer volume ofairattemperature ofboilingwater= ______volume ofairattemperature oficebath= ______temperature oficebath=______temperature______ofboilingwater= 250-mL Florence flask,andfit

© Addison-Wesley Publishing Company, Inc. All rights reserved. 4. 3. 2. 1. Analysis Name volume ofthegasatother temperatures. of thegraphanditsslope.For example,thestudentcouldfind that couldbemadeistotake moredatapointstoimprovetheaccuracy extrapolation willbeoff,too.Thesinglemostimportant improvement slightly off,thenthevalueofabsolutezeroobtainedfrom the defined byonlytwopointsisextrapolatedalongway. Ifeitherpointis Possibly thegreatestsourceoferrorinthisexperiment isthatagraph What canbedonetoimprove theaccuracy ofthisexperiment? can’t take uplessspacethannoat all! compression beyondinfinitedensityiscertainlynotpossible.Amaterial way tozerovolume, that wouldseta lower limiton temperature, for If thestraight-line volume-temperature relationship werevalid all the below absolutezero? In whatwaydoesthisgraph suggestthattemperature cannotdrop were made.Usinggreatcarewillyieldmoreaccurateresults. absolute temperatureatthetemperatureswheremeasurements to tion pointisabsolutezerobecausevolumedirectlyproportional until itcrossesthezero-volumeline.Thetemperatureatthisintersec- 30°C.Thelineinthegraphisextended ± Answers shouldbe–273°C Celsius? Explain how thegraph isusedfortheprediction. What isyour predicted temperature forabsolutezero indegrees in untilthepressureinsideflaskequalsthatoutsideflask. water isgreaterthanthatoftheairinflask,andgetspushed and volumeoftheairinflask.Thepressuresurrounding As thetemperatureofairinflaskdrops,sodoespressure Why didwaterflow intotheflaskinice bath? Period Chapter 24 Thermodynamics Date 219 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage220 220 Laboratory ManualLaboratory 63) (Experiment 5. 7. graph tocheckyour prediction ofthetemperature ofabsolutezero. Use dataplottingsoftware toplotyour data.Use thecomputer-drawn Going Further 6. Various answersinclude:(a) The pressureremained constant. (b) The iment andanalyzingthedata? What are someassumptionsthatyou madeinconductingtheexper- errors students makedrawinggraphs. graph might give a more accuratevaluefor absolute zero because of Although answerswill vary, it’s conceivablethatthecomputer-drawn prediction? How doesthecomputerprediction compare withyour earlier (nitrogen at–196°Candoxygen–183°C). The variousgasesthatmakeupaircondensetotheirliquidstate What happenstoairwhenitgetsextremely cold? toabsolutetemperature. proportion volume oftheglassflask remained constant. (c)Volume variesindirect

Name Period Date

Chapter 25: Vibrations and Waves Period of a Pendulum

64 Tick-Tock

Purpose

To construct a pendulum with a period of one second. Setup: <1 Lab Time: <1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: moderate ring stand stopwatch or wristwatch Mathematical Level: easy pendulum clamp balance pendulum bob meterstick You will capitalize on student string interest by allowing them about 15-20 minutes to complete this lab.

Discussion

A simple pendulum consists of a small heavy ball (the bob) suspended Use of a computer for this lab by a lightweight string from a rigid support. The bob is free to oscillate is not recommended. (swing back and forth) in any direction. A pendulum completes one cycle or oscillation when it swings forth from a position of maximum Activity deflection and then back to that position. The time it takes to complete one cycle is called its period. If, during a 10-second interval, a pendulum completes 5 cycles, its period T is 10 seconds divided by 5 cycles, or 2 seconds. The period is then 2 seconds for this pendulum. What determines the period of a pendulum? You will find out the factors by trying to make your pendulum have a period of exactly one second.

Procedure

Construct a pendulum with a period of exactly one second. To do this, change one variable at a time and keep track of which ones affect the period and which ones do not.

Questions

1. Briefly describe the method you used to construct your pendulum.

Chapter 25 Vibrations and Waves 221 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PMPage222 222 Laboratory ManualLaboratory (Activity 64) 2. 7. 6. 5. 4. 3. 8. Answers willvary. What wasthemassofyour pendulum? Weaker gravityatopMt.Everestwouldcausetheperiodtobelonger less than,thesameas, orgreater thanitwouldbeinyour lab? Why? If you setupyour pendulumatopMt.Everest, be wouldtheperiod precisely inExperiment65,“Grandfather’s Clock.”) (Studentswillexplore therelationmore simple directproportion. The longerthelength,period,butrelationisnota What effect,ifany, ofapendulum? doeslengthhaveontheperiod and solvingforL length The length should be closeto25cm.(Theoretically, the period What wasthelengthofyour pendulum? independent of amplitude. periods thansmallerones.Butforsmallangles,theperiodisessentially For agiven pendulum length,largeamplitudeshave of apendulum? What effect,ifany, doesamplitude(size ofswing)haveontheperiod The periodisindependentofthemass. What effect,ifany, ofapendulum? doesmasshaveontheperiod would notoscillate; it would have no period. In the free fall environment of an orbiting spacevehicle,thependulum be inyour lab? belessthan,thesameas,would theperiod orgreater thanitwould If you setupyour pendulumaboard anorbitingspacevehicle, than atsealevel. L are relatedbytheequation when T is 1.00sgivesL T = 2π√ = 0.248m,or24.8cm.) — L / — g. Using slightly = 9.80m/s longer T and 2

Name Period Date

Chapter 25: Vibrations and Waves Period of a Pendulum

65 Grandfather’s Clock

Purpose

To investigate how the period of a pendulum varies with its length. Setup: <1 Lab Time: >1

Required Equipment/Supplies Learning Cycle: exploratory Experiment Conceptual Level: moderate ring stand stopwatch or Mathematical Level: moderate pendulum clamp computer pendulum bob light probe with interface string ring stands with clamps graph paper or data plotting light source software and printer

Discussion

What characteristics of a pendulum determine its period, the time taken

XXII for one oscillation? Galileo timed the swinging of a chandelier in the XI I X II cathedral at Pisa using his pulse as a clock. He discovered that the time it IX III VIII IV took to oscillate back and forth was the same regardless of its amplitude, VII V VI or the size of its swing. In modern terminology, the period of a pendulum is independent of its amplitude (for small amplitudes, angles less than 10°). Another quantity that does not affect the period of a pendulum is its mass. In Activity 64, “Tick-Tock,” you discovered that a pendulum’s period depends only on its length. In this experiment, you will try to determine exactly how the length and period of a pendulum are related. Replacing Galileo’s pulse, you will use a stopwatch or a computer.

Procedure

Step 1: Set up a pendulum using the listed equipment. Make its length Set up pendulum. 65 cm. Measure its period three times by timing the oscillations with the stopwatch or the computer system. (If you are using a computer to measure the period of your pendulum, set up the light probe. Use clamps and ring stands to position a light source (such as a flashlight) so that the pendulum bob eclipses the light probe somewhere in its path.) Record the average period in Data Table A.

Step 2: Shorten the pendulum length by 5 cm. Measure its period as in Shorten pendulum and repeat. Step 1, and record the average period in Data Table A. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 25 Vibrations and Waves 223 CP02_SE_LAB_Ch57-65 3/5/01 12:09 PM Page 224

Step 3: Complete Data Table A for the remaining pendulum lengths indicated there. Measure periods as you did in Step 1.

Step 4: Make a graph of the period (vertical axis) vs. the length of the pendulum (horizontal axis).

1. Describe your graph. Is it a straight line that shows that the period is directly proportional to the length? Or is it a curve that shows that the relationship between period and length is not a direct proportion?

The graph should be a curve with a decreasing slope.

Step 5: Often data points lie on a curve that is not a straight line. It is very difficult to determine the relationship between two variables from such a curve. It is virtually impossible to extrapolate accurately from a curve. Experimenters instead try to produce a straight-line graph by plotting appropriate functions (squares, cubes, logarithms, etc.) of the variables originally used on the horizontal and vertical axes. When they succeed in producing a straight line, they can more easily determine the relationship between variables. The simplest way to try to “straighten out” a curve is to see if one of the variables is proportional to a power of the other variable. If your graph of period vs. length curves upward (has increasing slope), perhaps period is proportional to the square or the cube of the length. If your graph curves downward (has decreasing slope), perhaps it is the other Data Table A way around; perhaps the square or the cube of the period is proportional to the length. Try plotting simple powers of one variable against To see the curve of the graph the other to see if you can produce a straight line from your data. If you more clearly have your stu- have a computer with data plotting software, use it to discover the math- dents add the point (0,0) to their graphs. ematical relationship between the length and the period. A straight-line plot shows that the relationship between the variables chosen is a direct proportion.

2. What plot of powers of length and/or period results in a straight line?

A plot of the square of the period vs. length results in a straight line.

Predict pendulum length. Step 6: From your graph, predict what length of pendulum has a period of exactly two seconds. The pendulum will be nearly a meter long (99.3 cm). predicted length = ______

Measure pendulum length. Step 7: Measure the length of the pendulum that gives a period of 2.0 s.

measured length = ______

3. Compute the percentage difference between the measured length and the predicted length.

Answers will vary, but using the computer students typically come

224 Laboratory Manual (Experiment 65) CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage225

© Addison-Wesley Publishing Company, Inc. All rights reserved. travels andback. toyour partner Repeat several whathappenstothewave pulseasit times, observing travels toyour partner. Be sure holdstheotherendfixed. your partner shaking ittoonesidethen backsothatyou create awavepulsethat carpeted) floororalongcountertop. Give theSlinky arapid jerk by so asnottogetittangledorkinked—stretch itoutonasmooth(non- Step 1: meaning thatthewavevibrates alongthelineofpropagation. perpendicular tothelineofpropagation. Sound isa Light isatransverse Transverse Waves vs. Longitudinal Part A: Procedure so thatno weak enough,behavethisway. That is, twosoundwavescanoverlap appear ontheotherside!However, soundandwaterwaves, iftheyare you’ve neverseenacueballcollidewithanotherbilliard ballandre- thesize ofbilliard forparticles and isnotobservable balls. Obviously, one uninfluencedby theother. ischaracteristic This property ofwaves region, they continue on their way afterward exactly as they were, each in anyway. If thewavesoverlap onlyforsomeduration andinsome are still there and are separate and independent, not affecting each other waves ateachinstantoftimeandpointinspace. The twowaves When twowavesoverlap, thecompositewaveissumoftwo Discussion 4"-diameter foamball) mountedinside speakerwith9-voltbattery Doppler ball(piezoelectric stereoportable withtwodetachablespeakers tuning fork resonators Slinky™ toy, spring longform Required Equipment/Supplies To waveproperties. important observe Purpose hpe 5 Vibrations and Waves Chapter 25: Name 66 Have holdoneendofalongSlinky your partner andcarefully— sound results! Impressive! wave, meaning thatthewavevibrates backandforth Catch a WaveCatch longitudinal wave, Period Chapter 25 Vibrations and Waves Observe transversewaves. Date Superposition 225

Activity CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage226 226 Observe longitudinal waves. speed. Observe changeinwave Observe reflectionofwaves. Laboratory ManualLaboratory (Activity 66) 1. wave isproduced? Record your observations. alongthedirectionand forth oftheoutstretched Slinky. What kindof Step 4: Does thetensioninSlinky aswell? affectotherwaveproperties along theSlinky. How doesthetensionaffectspeedofpulse? Step 3: 6. along theSlinky. Slinky. Have holdthefree your partner Send endofthestring. apulse Step 2: 5. 4. 3. 2. How doestheSlinky move with respect to the wavepulse? How doesthereflected pulse? pulsedifferfrom theoriginal from your partner? What happenstothewavelengthofpulseasittravels to and How doesthereflected pulse? pulsedifferfrom theoriginal its source? Why doestheamplitudeofpulsedecrease asittravels from Is thepulsetransverse orlongitudinal? Increase thetensioninSlinky by stretching it.Send apulse Repeat steps 1through 3butthistimejerk theSlinky back Attach about50cmlongtooneendofthe apieceofstring

© Addison-Wesley Publishing Company, Inc. All rights reserved. i.A Fig. shown(or thefirstharmonic) inFigure A. mitted waveanditsreflection—a standingwave—likethefundamental untilyou getawavethatisthecombinationoftrans-back andforth Have holdoneendoftheSlinky. your partner Shake theSlinky slowly StandingWaves—Resonance B: Part against eachother. What happenstothevolumenow? pens tothevolumeandfullnessofsound?Bring themfaceto of sound.Gradually thespeakers closertoeachother. bring What hap- apart. The longwavesinterfere destructively, detracting from thefullness are atyour earoutofphasewithwavesfrom arriving theotherspeaker. sound isdifferent—it lacksfullness. Some ofthewavesfrom onespeaker the speakersby interchanging theplusandminuswires. Note thatthe tical. Note thefullnessofsound.Now reverse ofone thepolarity the same).Play inamonomodesothesignalsofeachspeakerare iden- in phase(thatis, withtheplusandminusconnectionstoeachspeaker Step 6: what happensasthepulsesoverlap. Record your observations. on oppositesidesofthelinepropagation. Pay specialattention to ways—that is, withthepulsesonsamesideandthen It mayrequire somepractice togetyour timing synchronized. Try itboth ate equal-sized pulsesatthesametimefrom oppositeendsoftheSlinky. Step 5: Name Now placethepairofspeakersfacingeachotheratarm’s length Detach stereo twospeakersfrom aportable withbothspeakers Now forsomereal fun! This timeyou willcre- andyour partner Period Chapter 25 Vibrations and Waves waves. Observe thesumoftwo waves. Observe interferenceofsound Date 227 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage228 228 Observe Dopplereffect. Observe harmonics. Observe standingwaves. Laboratory ManualLaboratory (Activity 66) movement oftheballaffectpitchsound? Step 9: 7. ing starisseentobe frequency forthelightofareceding stargivesitared shift. motion between thesource andreceiver. For example, thedecrease of light andotherelectromagnetic radiation) wheneverthere isrelative speed creates itsown shockwave—whetherornotitisasoundemitter. boom.” It isinteresting tonotethatanyobjecttraveling atsupersonic Doppler shiftisreplaced by ashockwave, whichproduces a “sonic passes overhead. If theplanemoves fasterthanthespeedofsound, the Dopplereffect. lower whenreceding. This changeoffrequency duetomotioniscalled on theroad, thepitchofitsengineishigherwhenapproaching and or thereceiver ofwavesismoving. For example, whenacarwhizzes by You are now goingto investigatewhathappenswheneitherthesource TheDopplerEffect Part C: observations. Step 8: 8. standingwaveiscreated.harmonic Step 7: How longisthewavecompared tothelength oftheSlinky? The Dopplereffectoccurswithany Similarly, thewhineofanairplaneenginechangesitspitchasit How longisthewavecompared tothelength oftheSlinky? Play usingaDopplerball.How catchwithyour partner doesthe See how you cancreate. manyotherharmonics Record your Now shaketheSlinky atahigherfrequency sothatasecond- blue shifted. The Dopplereffectisfarreaching. wave phenomenon(including An approach-

Name Period Date

Chapter 25: Vibrations and Waves Wave Behavior

Ripple While You 67 Work

Purpose

To observe wave phenomena in a ripple tank. Setup: 1 Lab Time: >1 Learning Cycle: concept Required Equipment/Supplies development ripple tank with light source and bottom screen Conceptual Level: moderate 3/4-inch dowel Mathematical Level: easy paraffin blocks medicine dropper length of large-diameter rubber hose wave generator large glass plate cut rubber stoppers

Discussion Activity Water waves have simple properties when they have small amplitude, and they are familiar to everyone. Observing the behavior of water waves in a ripple tank will introduce you to the analysis of wave motion.

Procedure

Step 1: The ripple tank is set up for you. Turn on its light. Observe the Observe pulse. screen at the base of the tank as you produce a pulse by touching your finger or pencil tip once to the water surface.

1. What is the shape of the pulse?

The shape of the pulse is an expanding circle.

2. Does the speed of the pulse seem to be the same in all directions?

Yes, it seems to be the same in all directions.

Step 2: Place the dowel in the water. Produce a straight wave front by Generate straight wave front. rolling the dowel forward 1 cm, with the flat of your hand. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 25 Vibrations and Waves 229 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage230 230 by aparabola. Observe wavepulsesreflected Generate circularwavepulses. Observe reflections. Laboratory ManualLaboratory (Activity 67) 7. cine dropper. 6. it. strikes 4. straight thebarrier on. pulse thatstrikes 3. 8. Step 5: Step 4: 5. Step 3: 9. mate shapeofaparabola. Place itinthe tank. Step 6: How dothepulsesreflect from theparaffin block? What istheshapeofreflected pulse? What doesthepulsedowhenitreaches thebarrier? It isamovingstraightlinewithcurvesattheends. What istheshapeofpulse? From whatpointdo thereflected pulsesappeartobeoriginating? They reflectascirculararcs. The shapeofthereflectedpulseisastraightline. The newdirectionofthepulseisstraightback. pulse? thebarrier,After thepulsestrikes whatisthenewdirection ofthe The pulsereflects,orbouncesback. Straight wavesarereflected toa focus. straight pulses? whenyou usethistubingasareflectorWhat doyou observe for far behind the barrierasactual source is infrontofit. A reflectedcircularpulseappearsto have comefrom a point sourceas Produce circular wavepulseswithwaterdrops from themedi- Move theparaffin blocktochangetheangleatwhichpulse Place aparaffin blockinthetank. With thedowel generate a Bend hoseintotheapproxi- alengthoflarge-diameter rubber

© Addison-Wesley Publishing Company, Inc. All rights reserved. 14. parallel to one edge of the glass. covered withwater. Arrange theglasssothatincomingwavefronts are pers sothatitis1.5cmfrom thebottomoftankanditstop isjust Step 10: 13. stand still. astandingwave.The combinationthenforms that thecombinationofincomingandreflected waveappears to thatpassesbythe part it.Adjust thefrequency ofthewavegenerator so aswell ofthestraightas thebarrier thepart wavethatstrikes Observe Step 9: 12. quency ofthewavegenerator. barsinthewaveiswavelength.Adjusttance between bright thefre- Step 8: 11. 10. the focusofparabola. parabola. Generate acircular pulsewiththedropper heldstraight above meet andmark itonthescreen withyour finger. This isthefocus Step 7: Name wavelength decreases. They slowdownandthewavefrontsbunchclosertogether, sothe What happensaswavespassfrom deeptoshallow water? The wavelengthsarethesame. wavelength ofthewavetraveling pastthebarrier? How doesthewavelengthofstandingwavecompare withthe Increasing thefrequencymakeswavelengthshorter. What effectdoesincreasing thefrequency haveonthewavelength? No otherpointsgivethesamepulseshape. Do anyotherpointsgivethesamepulseshape? The reflectedpulse is astraightline. What istheshapeofreflected pulse? Place aparaffin halfwayacross themiddleof tank. barrier Start thewavegenerator toproduce astraight wave. The dis- Find the Support apieceofrectangular stop- slabofglasswithrubber point at whichthestraight pulsesreflected by the hose of the Period Chapter 25 Vibrations and Waves Observe standingwave. Observe frequencychange. ing atthefocus. Observe wavepulsesoriginat- Date 231 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage232 232 Observe wavespreading. Compare wavespeeds. Laboratory ManualLaboratory (Activity 67) 15. incoming wavefronts. Step 11: 18. ings. Generate astraight waveandallow ittopassthrough thepairofopen- nearthecenter. sothatithastwoopeningsabout4cmapart barrier Step 13: 17. the wavegenerator. to sidewithasmallopeninginthemiddle. Generate straight waveswith Step 12: 16. 19. waves. generator. Turn onthewavegenerator toproduce overlapping circular Step 14: Are thewavefronts straight bothoutsideandover theglass? are nodes(minimumdisplacement). regions areantinodes(maximumdisplacement)andthegray“spokes” pattern isformedwhentwocircularwavesintersect.Thestriped The patternshouldlookliketheonesinFig.31.12oftext.This doyou observe? What wavepattern The wavefrontsleavingtheholearecircularornearlycircular. opening? How doesthestraight changeasitpassesthrough the wavepattern The speedisslowerovertheglass. How dothespeedsofwavescompare? Yes, theyarestraightinbothplaces. observed. length isthesame,then samepatternasinStep13willbe If thespacingisaboutsameastwoopeningsand thewave doyou nowWhat pattern observe? Now theglasssothatitsedgeisnolongerparallel turn tothe Using apieceofparaffin about4cmlong,modifyyour paraffin Place paraffin blocksacross thetankuntiltheyreach from side Put twopointsources onthebarofwave about 4cmapart

Name Period Date

Chapter 26: Sound Nature of Sound

68 Chalk Talk

Purpose

To explore the relationship between sound and the vibrations in a Setup: <1 material. Lab Time: <1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: easy Mathematical Level: easy new piece of chalk masking tape chalkboard meterstick Adapted from PRISMS.

Discussion

Every sound has its source in a vibrating object. Some very unusual sounds are sometimes produced by unusual vibrating objects!

Procedure Activity

Step 1: Tape the chalk tightly to the thin edge of the meterstick. The end Tape chalk to meterstick. of the chalk should extend beyond the end of the meterstick by 1 cm.

Step 2: Position the chalk perpendicular to the chalkboard’s surface. Push or pull on meterstick. Hold the meterstick firmly with one hand 15 cm from the chalk; very lightly support the far end with the other hand. Pull the meterstick at a constant speed while maintaining firm contact with the board.

Step 3: Modify the procedure of Step 2 by changing the angle, the contact force, or the distance the chalk protrudes beyond the meterstick. Also try making wavy lines. With the proper technique, the sounds of a trumpet, oboe, flute, train whistle, yelping dog, and a sick Tarzan yell can be produced. Conclude the activity when your instructor can’t stand it any longer! © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 26 Sound 233 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage234 234 Laboratory ManualLaboratory (Activity 68) 1. Analysis 3. 2. 4. What isproducing thesound? the boardandwitharatherhighappliedpressure. A highpitchisbestproducedwiththechalkalmostperpendicularto pitches? What combinationsofangleandpressure tendtoproduce high the meterstick. frequency resultsinalargeramplitudeofvibrationattheotherend because theslippingand sticking ontheboard’s surfaceforalow Low-frequency pitchesareeasiertofeelattheendofmeterstick low pitcheseasiertofeel?Explain. should vibrate indifferent waysforahighandlow pitch.Are highor byThe endofthemeterstickthatislooselysupported thehand through theair. vibration iscarriedtotheobserver’s earsbysoundwavesthattravel meterstick helpstoamplifythesoundthroughforcedvibration.The 29, “Slip-Stick”)ontheboard’s surface.Thisoccursatarapidrate.The board. However, itisactuallyslippingandsticking(recallExperiment The chalkappearstohaveaconstantspeedwhileincontactwiththe observed asaseriesofwell-defined, uniformdots. low enough frequency, the slip-stick natureofthechalk can bereadily together with a verylightpressure,willproducethe lowest note.Ata betweenthe chalkanddirectionofmotion, An angle greaterthan90° pitches? What combinationsofangleandpressure tendtoproduce low

Name Period Date

Chapter 26: Sound Speed of Sound

69 Mach One

Purpose

To determine the speed of sound using the concept of resonance. Setup: <1 Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development resonance tube approximately 50 cm long or golf club tube cut in half Conceptual Level: moderate 1-L plastic graduated cylinder Mathematical Level: moderate meterstick 1 or 2 different tuning forks of 256 Hz or more rubber band Alka-Seltzer® antacid tablet (optional)

Discussion

You are familiar with many applications of resonance. You may have heard a vase across the room rattle when a particular note on a piano was played. The frequency of that note was the same as the natural vibration frequency of the vase. Your textbook has other examples of res- onating objects. Gases can resonate as well. A vibrating tuning fork held over an open tube can cause the air column to vibrate at a natural frequency that matches the frequency of the tuning fork. This is resonance. The length of the air column can be shortened by adding water to the tube. The sound is loudest when the natural vibration frequency of the air column is the same as (resonates with) the frequency of the tuning fork. For a tube open at one end and closed at the other, the lowest frequency of natural vibration is one for which the length of the air column is one fourth the wavelength of the sound wave. In this experiment, you’ll use the concept of resonance to determine the wavelength of a sound wave of known frequency. You can then compute the speed of sound by multiplying the frequency by the wavelength.

Procedure

Step 1: Fill the cylinder with water to about two thirds of its capacity. Place the resonance tube in the cylinder. You can vary the length of the air column in the tube by moving the tube up or down.

Step 2: Select a tuning fork, and record the frequency that is imprinted on it.

Chapter 26 Sound 235 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage236 236 fork. Repeat usingdifferenttuning Compute thespeedofsound. Compute thewavelength. Compute correctedlength. Measure thediameter. Measure aircolumnlength. Laboratory ManualLaboratory 69) (Experiment orce egh=____mwavelength m =______speed ofsoundinair=______lengthofaircolumn=______m/s m corrected m length=______frequency =______Hz Step 8: the speedofsoundinair. Show your work. Step 7: vibrating intheaircolumn.Compute thewavelengthofthatsound. Step 6: accounts fortheairjustabove thetubethat alsovibrates. tube tothemeasured lengthoftheaircolumn. This corrected length Step 5: Step 4: water-level mark. Step 3: bandstretchedfor thisloudestsoundwitharubber around thecylinder. are several loudspots.)sound. (There Mark thewaterlevelontube tube upanddown tofindtheaircolumn length thatgivestheloudest zontally, withitstinesoneabove theother. Move boththefork andthe Hold thetuningfork about1cmabove theopenendoftube, hori- Analysis 2. 1. Strike thetuningfork ontheheelofyour shoe(NOT onthecylinder). % difference = ( accepted value? Compute thepercentage difference. How does your computedspeedofsoundcompare withthe air willaddonlyabout1m/s, aneffectthatcanbeneglected.) speed at20°Cisthus(332m/s)+(12m/s),or344m/s. (Moistureinthe At 20°Cthespeedwillbehigherby(0.6m/s•°C) airatthetemperaturesound indry ofyour room. Celsius above zero. Compute theacceptedvalue forthespeedof 0°C. This speedincreases by 0.6m/sforeachadditionaldegree airis331m/sat The acceptedvalue forthespeedofsoundindry The corrected ofthewavelengthsound lengthisonefourth If timepermits, repeat Steps 2to7using adifferent tuningfork. Using thefrequency andthewavelengthofsound,compute Make acorrected lengthby adding0.4timesthediameterof Measure thediameterofresonance tube. Measure thedistancefrom thetopofresonance tubetothe pe fsudi i ___ m/s speed ofsoundinair=______wavelength = ______m corrected length = ______m diameter oftheresonance m tube=______length ofaircolumn=______m | v measured – v calculated | )/v calculated ) 100% (20°C), or12m/s.The

Name Period Date

Chapter 27: Light Formation of Shadows

70 Shady Business

Purpose

To investigate the nature and formation of shadows. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy bright light source Mathematical Level: none book or other opaque object screen or wall Your follow-up discussion of meterstick this lab is an excellent time to introduce the terms umbra and penumbra in relation to eclipses. Discussion

If you look carefully at a shadow, you will notice that it has a dark central region and a fuzzy and less dark band around the edge of the central region. Why do shadows have two different regions? Activity Procedure

Step 1: Arrange a small light source so that a solid object such as a book Sketch shadow. casts a shadow on a screen or wall. Sketch the shadow formed, noting both its regions. Sketch the relative positions of the book, light source, and shadow.

Step 2: Move the light source away from the object while keeping the Move light source. position of the object fixed. Note and sketch any changes in the shadow. Sketch the new relative position of the light source.

1. What happens to the size of the fuzzy region around the edge of the central region when the light source is moved farther away?

Chapter 27 Light 237 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage238 238 Move object. Laboratory ManualLaboratory (Activity 70) 2. changes intheshadow. Sketch thenewrelative positionoftheobject. screen andthelightsource inthesameposition.Note andsketchany Step 3: 4. 3. Analysis 5. the objectismoved closertothelightsource? What happenstothesize ofthefuzzyregion around theedgewhen region aroundasmallornonexistentcentraldarkregion. the distancefromobjecttoscreen,resultisalargefuzzy When thedistancefromlightsourcetoobjectismuchlessthan region? in alarge fuzzyregion around asmallornonexistentcentral dark Which relative positionsoftheobject,lightsource, andscreen result distinct shadowwithlittleornofuzzyregionarounditsedge. than thedistancefromobjecttoscreen,resultisasharp When thedistancefromlightsourcetoobjectismuchgreater edge? in asharpdistinctshadow withlittleornofuzzyregion around its Which relative positionsoftheobject,lightsource, andscreen result The fuzzyregionaround the edgebecomeswider. the object,aswellrelative distances. the object.Itssizedependsonrelativeof light sourceand The fuzzyregionexistswherethelightsourceis What causesthefuzzyregion around theedgeofashadow? Move theobjectclosertolightsource whilekeepingthe partially blocked by

Name Period Date

Chapter 27: Light Light Intensity 71 Absolutely Relative

Purpose

To investigate how light intensity varies with distance from a light Setup: <1 source. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate computer Mathematical Level: difficult light probe with interface data plotting software Thanks to Scott Ryder for 3-socket outlet extender developing the software for 3 night-lights with clear 7-watt bulbs this experiment. 2 ring stands 2 clamps meterstick

Discussion

The light from your desk lamp may seem almost as bright as the sun. If your desk were only a meter away from the sun, your lamp would not seem bright at all. The brightness of the sun is far greater than that of the lamp, but the intensity of the lamp is almost as great as that of the sun. The intensity of light decreases with distance from the source. In this experiment, you will use a light probe to measure the intensity of light at various distances to see exactly how the intensity varies with the distance.

Procedure

Step 1: Install three night-lights in an outlet extender. Use a clamp to Set up light source and light secure the extender on a ring stand at least 20 cm above the table. This probe. height is necessary to minimize the effect of the light reflected from the table surface. For best results, instruct stu- Clamp the light probe to another ring stand so that it is at the same dents to reduce ambient light height as the night lights and is directly facing them 30 cm away. to a minimum. Turn off room Connect the light probe to the interfacing box. The setup is shown in lights and cover the widows, if Figure A. possible.

Step 2: Set up the light probe so that the computer automatically measures the intensity of light falling on the light probe and displays the intensity. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 27 Light 239 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage240 240 Data TableA Data TableB Laboratory ManualLaboratory 71) (Experiment i.A Fig. 1. Table A. Step 4: Bulbs AandB. Step 3: Record theintensity reading. in Data Table A. Turn offBulb onthethird Bandturn bulb(Bulb C). Leave thelightprobe inthesameposition.Record theintensityreading therefore, expressed relative toBulb A. light intensityofBulb Aatthisdistance. Allfuture intensityreadings are, the computerautomaticallycompares allotherlightintensitiestothe 2. compare withtheirindividualintensityreadings? How dotheintensityreadings forthedifferent bulbcombinations Try itandrecord your data. Now offBulb ononeofthesidebulbs(Bulb turn Aandturn B). Turn onthecenterbulb(Bulb A).Calibrate thelightprobe sothat separately compared withwhentheyare combined? What mightaccountforanydifferences inthereadings ofthebulbs of theindividualbulbintensities. The intensityreadingforeachbulbcombinationshouldequalthesum blocking somelightenteringfrom side bulbs. than centerbulbis; (4) bulbsnotpointsources;(5) the light probe (2) bulbs not of equal brightness; (3) side bulbsfartherfrom lightprobe Differences inthereadings may be caused by: (1)background light; Now allothercombinationsofthebulbstocompleteData try Predict whatintensitythelightprobe willread on whenyou turn predicted intensityreading =______

© Addison-Wesley Publishing Company, Inc. All rights reserved. 7. Analysis 6. 5. that theplotofintensityvs. distanceisastraight line. Step 7: 4. axis) forBulb A.If available, usedataplottingsoftware toplotthegraph. Step 6: 3. ther awayfrom thebulbeachtime. Record your datainData Table B. Bulb A. Take ninemore readings withthelightprobe, moving it5cmfar- Step 5: Name light doesnotdependupon how far youarefromthe source. The brightnessof the bulbremainsconstant.The output of a source of light source insideaballoonoftwicethatradius, 2 oftheballoon.Alsoimaginesame theinsidesurface bulb strikes bulb, atthecenterofaballoonradius r.Allthelightleaving Imagine apointsource oflight,such asasmall1.5-voltflashlight distance. to the inversesquareof The lightintensityvariesin proportion sity andthedistance? What relationship doesyour graph suggestbetween thelightinten- The graphisastraightlinewithpositiveslope. What doesthegraph looklike? intensity decreases,rapidlyat first, thenless rapidly. intensity) as the distanceincreases. As thedistanceincreases,light The graphisacurvethatfallstowardthehorizontalaxis(zero suggest between thelightintensityanddistance? What doesthegraph looklike? What relationship doesyour graph The lightintensitydecreases. from the source? away What happenstothelightintensityasprobe getsfarther the brightness ofthebulbincrease,the brightness decrease, or remain thesame? oftheballoon.Does theinsidesurface leaving thebulbagainstrikes Take anintensityreading withthelightprobe 30cmawayfrom Use dataplottingsoftware thepower tovary ofthex-y axis)vs.Plot the light intensity(vertical distance(horizontal r. Allthelight values so Period Plot data. Vary thepowerofx-yvalues. Chapter 27Light Date 241 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage242 242 Laboratory ManualLaboratory 71) (Experiment 8. 9. loon thanthatofthesmallerballoon? How manytimesgreater area istheinsidesurface ofthelarger bal- as much. covers fourtimesasmucharea,therelativeintensityisonlyonefourth Because thesameamountof light fromthebulbspreadsoutand larger balloon relative tothatforthesmallerballoon? ofthe loon, whatistheintensityoflightatinsidesurface If allthe light spreads ofthelarger bal- outevenlyontothesurface to smaller balloon(sincetheareaofasphereisproportional The inside area of the largerballoonis four times asgreatthe r 2 ).

Name Period Date

Chapter 27: Light Polarization

72 Shades

Purpose

To investigate the effects of polarized light. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: moderate 3 small polarizing filters Mathematical Level: none light source small plane mirror Thanks to Bruce Ratcliffe for his ideas and suggestions for this lab. Discussion

The vibrations of light waves reaching your eyes are mostly randomly oriented; they vibrate in many planes at once. In polarized light, the light waves vibrate in one plane only. Polarized light can be made by blocking all the waves except those in one plane with polarizing filters. The filters can also be used to detect polarized light. Activity

Procedure

Step 1: Position one polarizing filter between your eyes and a light source. Slowly rotate the filter 360°. Observe the intensity of the light as seen through the filter. Note any intensity changes as you rotate the filter.

1. What happens to the intensity of the light as you rotate the filter?

The intensity does not change.

Step 2: Arrange one filter in a fixed position in front of the light source. Rotate second filter. Slowly rotate a second filter held between your eyes and the fixed filter. Note any intensity changes of the light as you rotate the filter 360°.

2. What happens to the intensity of the light as you rotate the filter?

During one complete rotation, the intensity changes through two

Chapter 27 Light 243 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage244 244 View skythroughfilter. reflected offamirror. Rotate singlefilterforlight directions. Rotate bothfiltersinopposite Rotate bothfilters. Rotate otherfilter. Laboratory ManualLaboratory (Activity 72) 6. intensity changesofthelightasyou rotate thefilter. onlythelightcomingfrom themirrorthat yousurface. observe Note any 5. same time, butinoppositedirections. Note anyintensitychanges. 4. same direction atthesametime. Note anyintensitychanges. 3. intensity changesofthelightasfilterrotated. slowly rotates theotherfilternexttolightsource 360°.Note any Step 3: Step 6: Step 5: Step 4: oaetefle 6°whileviewingeach region. Rotate thefilter360° Step 7: 7. What happenstotheintensityoflightasyou rotate thefilter? in oppositedirections? What happenstotheintensityoflightasyou rotate bothfilters together? What happenstotheintensityoflightasyou rotate bothfilters What happenstotheintensityoflightasfilterrotated? metallic). The intensitydoesnotchange(ifthereflectingsurfaceofmirroris The intensitychangesthroughfourcompletecycles. The intensitydoesnotchange. The sameeffectisseenasinStep2. CAUTION: polarized. No, light reflecting off a mirror (andothermetallicsurfaces)is not Is thelightreflected offamirror polarized? View differentView regions oftheskyonasunnydaythrough afilter. Repeat Step 1,except arrange thelightsource andamirror so Rotate bothofthefiltersthrough onecompleterotation atthe Rotate bothofthefiltersthrough onecompleterotation inthe Hold thefilteratyour eye inafixedpositionwhileyour partner Do notlookatthe sun! Do

© Addison-Wesley Publishing Company, Inc. All rights reserved. 12. Analysis 11. 10. using afilter. Rotate thefilter360°,andnoteanyintensitychanges. Step 8: 9. 8. Name glare. so verticallyorientedpolarized sunglassesblockalmost100%ofthe isstronglyhorizontallypolarized, light (glare)fromhorizontalsurfaces First, theyblockonehalftheunpolarizedsunlight.Second, reflected lensesmakegoodsunglasses? Why dopolarized Yes, lightreflected fromanLCDispolarized. Is displaypolarized? thelightcomingfrom aliquidcrystal passes throughonerotatingandfixedfilter. The intensitychangesthroughtwocompletecycles,asforlightthat What happenstointensityofthelightasyou rotate thefilter? tothesun’s directrays. polarization is at90° Yes, thelightofskyispartly polarized. The region of maximum inrelationmum polarization tothepositionofsun? Is If thelightofskypolarized? so, where istheregion ofmaxi- the waytominimumintensityexceptincertainregions. The intensitychangesthroughtwocompletecycles,butdoesnotgoall What happenstotheintensityoflightasyou rotate thefilter? View a liquid crystal display(LCD) orcalculator aliquidcrystal onwristwatch View Period View LCDwithfilter. Chapter 27Light Date 245 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage246 246 Laboratory ManualLaboratory (Activity 72) 14. pair. source getsthrough. Place athird filter between thelightsource andthe 13. 16. angle. ters ata45° Step 11: 15. Step 10: Step 9: Going Further Does anylightgetthrough? The effectofapolarizingfilter on unpolarizedlight is toreducethe Explain why theeffectsseeninSteps 1to 3 occur. Does anylightgetthrough? Same asStep9. Does anylightgetthrough? No more lightgetsthrough if the first pairoffiltersarecrossed at 90°. minimum of light willgetthroughthesecondfilter. light willbefilteredout. If theaxesare crossed at right angles, a in the same direction. Iftheyarecrossedbutnotatright angles, some it encounters a secondfilter, itwillnotbefiltered atall if theaxesare However, when the lightpasses through one filter, itispolarized. When intensity, buttheorientation of the filter does notaffecttheintensity. Figure 27.19ofthetext.) tothecrossedpair. (See maximum whenthatthirdfilterisat45° them passeslightthrough.Theamountofpassing throughis If thefirstpairoffiltersarecrossed,sandwichingathird filterbetween Position apairoffilterssothatminimumlightfrom alight This time, sandwichthethird filterbetween theothertwofil- Place thethird filterbeyond thepair.

Name Period Date

Chapter 28: Color Atomic Spectra

73 Flaming Out

Purpose

To observe the spectra of some metal atoms. Setup: <1 Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development safety goggles 7 20-cm pieces of platinum or Conceptual Level: easy spectroscope nichrome wire with a small Mathematical Level: none incandescent lamp loop at one end Bunsen burner with matches 6 labeled bottles containing salts or igniter of lithium, sodium, potassium, small beaker calcium, strontium, and copper

Discussion

Auguste Compte, a famous French philosopher of the nineteenth century stated that humans would never know what elements made up the distant stars. Soon thereafter, the understanding of spectra made this knowledge easy to obtain. An element emits light of certain frequencies when heated to high enough temperatures. Different frequencies are seen as different colors, and each element emits (and absorbs) its own pattern of colors. This allows us to identify these elements, whether they are nearby or far away.

Procedure

Step 1: Practice using the spectroscope by looking at an incandescent Adjust spectroscope. lamp. The spectrum will appear as a rainbow of colors. Adjust the spectroscope until the spectrum is horizontal and clear.

Step 2: Put on safety goggles. Ignite the Bunsen burner. Adjust it until a blue, nearly invisible flame is obtained.

Step 3: Dip a loop of wire into the bottle of solid sodium chloride. Hold the loop in the flame until the sodium chloride melts and vaporizes. Observe the spectrum of the sodium atoms through the spectroscope. You may also see a long, broad band image due to the glowing wire. Ignore this image. In Data Table A, sketch any major lines you see, in the appropriate position, for the color of the lines.

Step 4: Test each of the other salts as in Step 3. Each wire is to stay in its Sketch spectral lines. proper bottle. Mixing the test wires contaminates them. If you should make a mistake and place a wire in the wrong bottle, burn off all the salt until the wire glows red hot, then return it to its proper bottle. In Data Table A, sketch the major lines emitted by each salt. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 28 Color 247 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage248 248 Observe spectrumof mixture. Laboratory ManualLaboratory 73) (Experiment Data TableA 2. same wire. theresulting throughObserve thespectroscope, spectrum usingthe 1. scope. in theflame, theresulting through andobserve thespectro- spectrum the smallbeaker. Using theextra testwire, holdaloopfulofthemixture 3. Analysis Step 6: Step 5: 5. 4. Did you seethecharacteristic colorsofbothcopperand lithium? tain acombinationofthecopperandlithiumlines? ofthemixtureDoes thespectrum ofcopperandlithiumsaltscon- Several saltsarechlorides,butonlysodiumchloridehas theyellowline inthecompound? chlorine arelooking atsodiumchloride duetothesodiumandnot How doyou know yellow thatthebright when linesyou observed Students willprobablyseethecolorsofboth. Yes, students shouldseethespectrallinesofbothcopperandlithium. lines can be observed. lines canbeobserved. The moltensteelsampleis vaporized sothatthecharacteristicspectral steel inorder toadjustitscomposition. cians inthesteelmillscan tellexactlywhatisinanygivenbatchof are melted tomakenewsteel.Explain how techni- thelaboratory In steelmills, large amountsofscrap steelof unknown composition The elementspresentingreateramountshavebrighter lines. the relative amountsofmetalelementspresent ineachmixture. From inSteps your observations 5and6,draw conclusionsabout (which isactuallytwocloselyspacedlines—adoublet). Mix atrace oflithiumsaltwithalarger amountofcoppersalt. Mix smallandequalamountsofthecopperlithiumsaltsin

Name Period Date

Chapter 29: Reflection and Refraction Parabolic Reflectors

74 Satellite TV

Purpose

To investigate a model design for a satellite TV dish. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: application Conceptual Level: easy small transistor radio Mathematical Level: none large umbrella aluminum foil Adapted from PRISMS.

Remind your students that this is an application of Step 6 of Discussion Activity 67, “Ripple While You Work.” When you can barely hear something, you may cup your hand over your ear to capture more sound energy. Does this really work? The answer is yes. In this activity, you will use an umbrella similarly to capture a signal.

Procedure Activity

Step 1: Line the inside surface of an open umbrella with aluminum foil.

Step 2: Stand near one of the windows of your classroom. Turn on the radio and locate a weak station. Tune the radio until you get the best reception for that weak station.

Step 3: Have a classmate hold the umbrella horizontally, with the handle pointed at, and just touching, the radio.

Step 4: Move the radio back slowly along the line of the handle until you find the most improved reception for the weak station.

Step 5: Repeat the process in other locations and for other stations. Repeat with other stations.

Analysis

1. Why did the umbrella improve the reception of the radio?

Chapter 29 Reflection and Refraction 249 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage250 250 Laboratory ManualLaboratory (Activity 74) 2. Diagram shouldshowraysapproachingtheinsideofumbrella show how themodelsatellite dishactslikeaconcavemirror.TV The umbrella isamodelofsatellite dish.DrawTV adiagram to along thehandle. parallel tothehandle,andbouncingacommonfocusatpoint

Name Period Date

Chapter 29: Reflection and Refraction Formation of Virtual Images

75 Images

Purpose

To formulate ideas about how reflected light travels to your eyes. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: moderate 2 small plane mirrors Mathematical Level: none supports for the mirrors 2 single-hole rubber stoppers Adapted from PRISMS. 2 pencils 2 sheets of paper transparent tape

Discussion

Reflections are interesting. Reflections of reflections are fascinating. Reflections of reflections of reflections are . . . you will see for yourself in Activity this activity.

Procedure

Step 1: Place the pencils in the rubber stoppers. Set one plane mirror upright in the middle of a sheet of paper, as shown in Figure A. Stand one pencil vertically in front of the mirror. Hold your eye steady at the height of the mirror. Locate the image of the pencil formed by the mirror. Place the second pencil where the image of the first appears to be. If you have located the image correctly, the image of the first pencil and Fig. A the second pencil itself will remain “together” as you move your head from side to side.

1. How does the distance from the first pencil to the mirror compare with the distance of the mirror to the image?

The distances are the same.

Step 2: On the sheet of paper, draw the path you think the light takes Fig. B from the first pencil to your eye as you observe the image. Draw a dotted line to where the image appears to be located as seen by the observing © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley eye.

Chapter 29 Reflection and Refraction 251 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage252 252 mirrors. Decrease anglebetween Draw raydiagram. Laboratory ManualLaboratory (Activity 75) 3. Step 5: paths you thinkthelighttakesasitgoesfrom thepenciltoyour eye. 2. Figure B. sheet ofpaper. Place apencilinitsstopperbetween themirrors, asin anglestoeachotherinthemiddleofasecond andatright rors upright Step 3: Step 4: the anglebetween thetwomirrors? What happenstothenumberofimagesyou getwhenyou decrease How manyimagesdoyou see? The numberofimagesincreases. There arethreeimages:oneineachmirrorandthe“crack.” Decrease theanglebetween thetwomirrors. On thepaper, show where theimagesare located. Draw the Hinge twomirrors togetherwithtransparent tape. Set themir-

Name Period Date

Chapter 29: Reflection and Refraction Multiple Reflections

76 Pepper’s Ghost

Purpose

To explore the formation of mirror images by a plate of glass. Setup: <1 Lab Time: 1 Learning Cycle: concept devel- Required Equipment/Supplies opment safety goggles Conceptual Level: moderate two candles of equal size, in holders Mathematical Level: none 1 thick plate of glass, approximately 30 cm × 30 cm × 1 cm 2 supports for the glass plate Thanks to Dave Wall for his matches ideas and suggestions for this lab.

Discussion

John Henry Pepper (1821–1900), a professor in London, used his knowledge of image formation to perform as an illusionist. One of his illusions was based on the fact that glass both reflects and transmits light. Activity

Procedure

Step 1: Put on safety goggles. Light one candle, and place it about 6 cm in front of a vertical thick glass plate. Place a similar, but unlighted, candle at the position on the other side of the glass plate at the point where the flame of the lighted candle appears to be on the unlighted candle.

1. How does the distance from the lighted candle to the glass plate compare with the distance from the glass plate to the unlighted candle?

The distances are the same.

Step 2: Look carefully, and you should see a double image of the candle Find double image. flame.

2. How would you explain the double image?

One image is caused by reflection from the front surface of the thick

Chapter 29 Reflection and Refraction 253 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage254 254 Find multipleimages. Laboratory ManualLaboratory (Activity 76) 3. “ghost” imagesofthecandleflame. oftheglass.small anglewiththesurface You willseethree ormore Step 3: Explain these “ghost” images. These “ghost”imagesarefrommultiplereflectionsinsidetheglass. Look attheglassplatesuchthatyour lineofvisionmakesa

Name Period Date

Chapter 29: Reflection and Refraction Multiple Reflections

77 The Kaleidoscope

Purpose

To apply the concept of reflection to a mirror system with multiple Setup: <1 reflections. Lab Time: 1 Learning Cycle: application Required Equipment/Supplies Conceptual Level: easy Mathematical Level: easy 2 plane mirrors, 4 in. × 5 in. viewing object transparent tape protractor clay toy kaleidoscope (optional)

Discussion

Have you ever held a mirror in front of you and another mirror in back of you in order to see the back of your head? Did what you saw surprise you? Activity Procedure

Step 1: Hinge the two mirrors together with transparent tape to allow them to open at various angles. Use clay and a protractor to hold the two mirrors at an angle of 72°. Place the object to be observed inside the angled mirrors. Count the number of images resulting from this system and record in Data Table A.

Step 2: Reduce the angle of the mirrors by 5 degrees at a time, and count the number of images at each angle. Record your findings in Data Table A.

Step 3: Study and observe the operation of a toy kaleidoscope, if one is available.

Analysis

1. Explain the reason for the multiple images you have observed.

Many images of an object can be seen in a two-mirror system due to

multiple reflections, as the light bounces back and is reflected by Data Table A

Chapter 29 Reflection and Refraction 255 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage256 256 Laboratory ManualLaboratory (Activity 77) 2. 3. The numberofimagesincreasesastheangledecreases. of images? What effectdoestheanglebetween themirrors haveonthenumber result is an infinite pattern made ofsixsymmetrical images. Colored chipsinacompartmentareplacedbetweenthemirrors.The along thelengthofatube. apart facingoneanother60° surfaces A simplekaleidoscopecontainsthree mirrors withtheir reflecting and operation ofatoy kaleidoscope. Using you havegained,explaintheconstruction theinformation

Name Period Date

Chapter 29: Reflection and Refraction Images Formed by a Curved Mirror

78 Funland

Purpose

To investigate the nature, position, and size of images formed by a con- Setup: <1 cave mirror. Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate concave spherical mirror Mathematical Level: moderate cardboard night-light with clear 7-watt bulb Thanks to Michael Zender for small amount of modeling clay his ideas and suggestions for meterstick this lab.

Optional Equipment/Supplies This lab is a mirror image conceptually of Experiment 82, “Bifocals.” If time is short, computer have your students do one or data plotting software the other.

Discussion

The law of reflection states that the angle of reflection equals the angle of incidence. Parallel light rays that strike a plane mirror head on bounce directly backward and are still parallel. If the parallel rays strike that mirror at another angle, each bounces off at the same angle and the rays are again parallel. A plane mirror cannot bring light rays to a focus because the reflected light rays are still parallel and do not converge. Images observed in a plane mirror are always virtual images because real images are made only by converging light. A parabolic mirror is able to focus parallel rays of light to a single point (the focal point) because of its variable curvature. A small spherical mirror has a curvature that deviates only a little from that of a parabolic curve and is cheaper and easier to make. Spherical mirrors can, therefore, be used to make real images, as you will do in this experiment.

Procedure

Step 1: The distance from the center of a spherical mirror surface to the Measure focal length of mirror. focal point is called the focal length. Measure the focal length of your mirror by having it convert a parallel beam of light into a converging beam that comes to a point on a screen. Use the filament of a lit, clear 7-watt bulb as a source of approximately parallel light and a piece of © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 29 Reflection and Refraction 257 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage258 258 Data TableB Find arealimagewithmirror. Laboratory ManualLaboratory 78) (Experiment Data TableA point slightly toonesideofthelight source. The distance between thefocal animageofthe filamentonascreenThe mirror willthenform placed Step 6: this positioninData Table A. appears atall? Where istheobjectinrelation tothefocal length?Record Step 5: the imagereal Record orvirtual? your findingsinData Table A. size of the image (magnified or reduced) compared with the object? Is up(erect)?object whentheimageappearsright-side What istherelative Step 4: findings inData Table A. the imageerect (upsidedown)? up)orinverted (right-side Record your on thescreen? Is itmagnifiedorreduced, compared withtheobject?Is sharp imageofthefilamentonscreen. Can areal imagebeformed than onefocallengthf of theobject,asshown inFigure B. Move themirror sothatitisfarther Figure A.Position your screen sothattheimageisslightlyofftooneside to actasamirror holder. Arrange ascreen andalightsource asshown in Step 3: mirror). Record your measurement tothenearest 0.1cm. source ofparallel lightisavailable, useittofindthefocalpointofyour ror andthe lightsource toseeifthefocallengthchanges. (If abetter ther awayfrom themirror have?Increase thedistancebetween themir- value for thefocallength? What effectwouldmoving thelightsource far- exactly parallel. What effect,ifany, would thishaveonyour measured Step 2: 0.1 cm.Also, record thenumberofyour mirror. cardboard asascreen. Record your measurement below tothenearest i.A Fig. and theobject istheobjectdistanced Where, inrelation toonefocal length from themirror, isthe Position themirror two focal lengthsawayfrom thelightsource. Is there aspacingbetween objectandmirror forwhich noimage Use asmallamountof modelingclayatthebottomofmirror The rays your mirror oflightstriking from thebulbmaynotbe focal lengthf mirror number =______focal length=______cm from thenightlight.Move thescreen a toform ____cm ______= i.B Fig. o and thedistance between

© Addison-Wesley Publishing Company, Inc. All rights reserved. tances 1. your data. thus adirect If proportion? available, usedataplottingsoftware toplot there anycombinationthatmakesalineargraph and through theorigin 2. the pointwhere theycross, animage ofthetiparrow is formed. 3. the focal point. leaves thetipofarrow parallel axis. totheprincipal using theray-diagram method.Draw thepathoflightrays that Step 8: the focalpointandimageisdistanced Step 7: back intofocus. Progressively extend from the lightsource, andreposition thescreen untiltheimagecomes ers ofeachtodiscover themathematicalrelation between ments fivemore times. Record d Name What mathematicalrelationship existsbetween d Where doesthisray goafteritisreflected? Now draw thepathsofthesetwolight rays aftertheyare reflected. At principal axis. The raythatpassesthroughthefocalpointisreflected paralleltothe Where does thislightray goafteritisreflected? Draw thelightray thatleaves thetipofarrow andpassesthrough The rayparallelto the principalaxisisreflectedthrough the focalpoint. the objectdistance, object image (1/d The imagedistance, d You canlocatetheposition oftheimageobjectinFigure C Plot o and d i.C Fig. i d (vertical axis) vs. i in Data Table B. Move away themirror 5cmfarther o ) so the image distance is inversely proportional to ) sotheimagedistanceis inversely proportional d d o i . , is directly proportional to the inverseof the , is directly proportional d o o and (horizontal axis),thendifferent(horizontal pow- d d o i by repeating these5-cmmove- each time. i . Record thedis- i and d d i o and ? d Period o Chapter 29Reflection andRefraction . Is . Date 259 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage260 260 Laboratory ManualLaboratory 78) (Experiment 4. 5. focal pointandisreflected by themirror. heads toward themirror inthesamedirection asifitoriginated axisandisreflectedto theprincipal by themirror. Trace anotherray that Figure D. Draw thepathofray thatleavesthetipofarrow parallel Step 9: Where dothetworeflected rays appear a screen. where the imageappearstobe.Only real imagescan be projected onto No; itisavirtualimage—nolightactuallyconvergesattheposition Could theimagebeprojected ontoascreen? Explain. The tworeflectedraysappeartocrossbehindthemirror. Use theray-diagram methodtolocatetheimageofobjectin i.D Fig. to cross? from the

Name Period Date

Chapter 30: Lenses Pinhole Camera

79 Camera Obscura

Purpose

To observe images formed by a pinhole camera and to compare images Setup: >1 formed with and without a lens. Lab Time: 1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: easy Mathematical Level: none covered shoe box with a pinhole and a converging lens set in one end, an open end opposite, and glassine paper inside the box (as in Figure A) Thanks to Wayne Rosenberger piece of masking tape for his ideas and suggestions for this lab.

See Teacher Notes for refer- Discussion ences on how to build actual pinhole cameras. The first camera, known as a camera obscura, used a pinhole opening to let light in. The light that passes through the pinhole forms an image on the inner back wall of the camera. Because the opening is small, a long time is required to expose the film sufficiently. A lens allows more light Activity to pass through and still focuses the light onto the film. Cameras with lenses require much less time for exposure, and the pictures have come to be called “snapshots.”

Procedure

Step 1: Use a pinhole camera constructed as in Figure A. Tape the foil Observe images on screen of flap down over the lens so that only the pinhole is exposed. Hold the camera with pinhole. camera with the pinhole toward a brightly illuminated scene, such as the scene through a window during the daytime. Light enters the pinhole and falls on the glassine paper. Observe the image of the scene on the glassine paper.

1. Is the image on the screen upside down (inverted)?

Yes, the image is upside down.

2. Is the image on the screen reversed left to right?

Yes, left and right are reversed. Fig. A

Step 2: Now seal off the pinhole with a piece of masking tape, and open Observe images with lens. the foil door to allow light through the lens. Move the camera around. You can watch people or cars moving by. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 30 Lenses 261 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage262 262 information ontechniques. Diego, CA92115,formore Crawford HighSchool,San Wayne Rosenbergerat develop thefilm.Contact graphic processingcan already familiarwithphoto- photographs. Astudent your studentsshootpinhole Extend this activity byhaving Draw raydiagram. Laboratory ManualLaboratory (Activity 79) 7. 6. Analysis screen by thepinhole. through thepinholeandontoscreen. Show theimagecreated onthe Draw anotherray forlightthatpassesfrom thebottomofobject from thetopofadistantobjectthrough apinholeandontoscreen. 5. focuses onnearby objects. Point thecamera lensatanearby whetherthelens objecttodetermine 3. Step 4: Step 3: 4. produces focusedimageswithout alens. contact lenses,youmaysee clearlywithoutthembecauseapinhole resembles apinholecamera.Then,ifyounormallywear glassesor very brightlight,thesizeofyourpupilbecomessosmall thatyoureye side up,eventhoughyoureyedoesnot down. Your brain,however, interpretstheupside-down image as right- The lensofyoureyeformsanimageonretinathat ontheretinaimages formed ofyour eye are upsidedown? How isapinholecamera similartoyour eye? Doyou thinkthatthe The pinholeadmitsmuchlesslight. ated by thelens? Why istheimagecreated by thepinholedimmerthanone cre- Does thelensfocusonnearby objects? Yes, theimageisupsidedown. Is theimageonscreen upsidedown (inverted)? as sharplyobjectsthatareclose. A lensthatisadjustedtosharplyfocusdistantobjectsdoesnot Yes, leftandright are reversed. Is theimageonscreen reversed lefttoright? Draw aray diagram asfollows. Draw aray forlightthatpasses A pinholecamera focusesequallywell onobjectsatalldistances. have aright-side-upimage!In is upside

Name Period Date

Chapter 30: Lenses Convex and Concave Lenses

80 Thin Lens

Purpose

To acquire a qualitative understanding of concave and convex lenses. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy convex lens Good Stuff software Mathematical Level: none concave lens computer Thanks to Robert H. Good for developing the software that makes this lab possible. Discussion

Lenses are not to read about, but to experiment with. Before studying Chapter 30 in the text, some hands-on experience is important for understanding lenses. This activity should help guide you to discover It is best if students have a some of their interesting properties. lens in their hand as they investigate the formation of images on the computer. Procedure Activity

Move an object to different distances from a convex lens and observe the image formed. Select the “Thin Lens” program from Good Stuff and the option for a converging lens. A ray diagram consisting of an object arrow and its image as formed by the rays will appear. The focal length, f, of the lens is the distance from its center to the point where light parallel to the lens axis (principal axis) converges to a focus. Initially, the object and image are located at a distance 2f from the lens. Use the arrow keys to move the object along the principal axis. Is the image larger or smaller than the object? Is the image erect (right-side up) or inverted (upside down)? Can the image be projected (a real image) or not (a virtual image)? Is there any position of the object for which no image is formed? Record your observations as to the nature of the image you observe on the computer in Data Table A and Data Table B for both kinds of lenses. Check to see how the image on the screen cor- responds to images of objects formed by real lenses in your hand!

Analysis

1. When the image appears right-side up (erect) using a converging lens, how many focal lengths is the object from the lens?

Chapter 30 Lenses 263 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PM Page 264

2. Under what circumstances is the image formed by a converging lens magnified? Under what circumstances is it reduced? When is it real? When is it virtual?

The image is virtual and magnified when the object is less than one

focal length distant from the lens. It is real and magnified when the

object is between one and two focal lengths from the lens. It is real and

reduced when the object is more than two focal lengths from the lens.

3. Can an object be located in a position where a converging lens forms no real image?

Yes, whenever the object distance ≤ one focal length.

4. For a diverging lens, is the virtual image enlarged or reduced?

Reduced.

5. Can you form a real image with a diverging lens?

No.

6. When the object is moved, does the image formed by a converging lens always move in the same direction? What about the image formed by a diverging lens?

For both lenses, the image always moves in the same direction as the

object (except that for a converging lens, the image jumps in the

opposite direction from infinite distance on one side to infinite distance

on the other side when the object distance passes through the focal

distance).

Data Table A Data Table B

NATURE OF IMAGE NATURE OF IMAGE - CONVERGING LENS - DIVERGING LENS

POSITION REAL MAGNIFIED INVERTED POSITION REAL MAGNIFIED INVERTED OF OBJECT OR VIRTUAL OR REDUCED OR ERECT OF OBJECT OR VIRTUAL OR REDUCED OR ERECT

BEYOND 2f REAL REDUCED INVERTED BEYOND 2f VIRTUAL REDUCED ERECT AT 2f REAL SAME SIZE INVERTED AT 2f VIRTUAL REDUCED ERECT AT f NO IMAGE NO IMAGE NO IMAGE AT f VIRTUAL REDUCED ERECT WITHIN f VIRTUAL MAGNIFIED ERECT WITHIN f VIRTUAL REDUCED ERECT © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

264 Laboratory Manual (Activity 80) CP02_SE_LAB_Ch66-85 3/5/01 12:11 PM Page 265

Name Period Date

Chapter 30: Lenses Pinhole “Lens”

81 Lensless Lens

Purpose

To investigate the operation of a pinhole “lens.” Setup: <1 Lab Time: <1 Learning Cycle: concept Required Equipment/Supplies development

3" × 5" card Conceptual Level: moderate straight pin Mathematical Level: none meterstick Thanks to Lonnie Grimes for his ideas and suggestions for this lab. Discussion

The image formed through a pinhole is in focus no matter where the object is located. In this activity, you will use a pinhole to enable you to see nearby objects more clearly than you can without it.

Procedure Activity

Step 1: Bring this printed page closer and closer to your eye until you Look at print close up. cannot focus on it any longer. Even though your pupil is relatively small, your eye does not function as a pinhole camera because it does not focus well on nearby objects.

Step 2: With a straight pin, poke a pinhole about 1 cm from the edge of a 3" × 5" card. Hold the card in front of your eye and read these instructions through the pinhole. Bright light is needed. Bring the page closer and closer to your eye until it is a few centimeters away. You should be able to read clearly. Quickly take the pinhole away and see if you can still read the words. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 30 Lenses 265 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage266 266 Laboratory ManualLaboratory (Activity 81) 1. 4. 3. 2. Analysis The printdoesappearmagnified. through thepinhole? appearmagnifiedwhenobserved Did theprint The pinholefocusesanimageontheretina,which uncorrectedeye it!) sighted yourself, try through apinhole. Explain how thisispossible. (Andifyou are near- rective lenses. Yet, such apersoncanseedistantobjectsclearly A nearsightedpersoncannotseedistantobjectsclearlywithoutcor- The pinholeadmitsmuchlesslight than thepupil(opening) of theeye. pinhole thanwhenseenusingyour eye alone? dimmerwhenseenthrough the Why wasthepageofinstructions the imageissamesizebutblurry. if thepagewereatnormalreadingdistance.Withoutpinhole, magnified becauseitiscloser, makingtheimagelargerthanitwouldbe matter how closetheobjectis to youreye.Theobjectseems Not inthe ordinary sense. Thepinholefocuses images onyour retina no Did thepinhole actuallymagnifytheprint? is unabletodo. to be

Name Period Date

Chapter 30: Lenses Images Formed by a Convex Lens

82 Bifocals

Purpose

To investigate the nature, position, and size of images formed by a con- Setup: <1 verging lens. Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate converging lens Mathematical Level: moderate small amount of modeling clay cardboard Thanks to Floyd Judd for his meterstick ideas and suggestions for night-light with clear, 7-watt bulb this lab.

Optional Equipment/Supplies This lab is a mirror image conceptually of Experiment 78, “Funland.” If time is short, data plotting software have your students do one or computer the other.

Discussion

The use of lenses to aid vision may have occurred as early as the tenth century in China. Eyeglasses came into more common use in Europe in the fifteenth century. Have you ever wondered how they work? In Experiment 78, “Funland,” you learned that the size and location of an image formed by a concave mirror is determined by the size and location of the object. In this experiment, you will investigate these relationships for a converging glass lens.

Procedure

Step 1: A converging lens focuses parallel light rays to a focal point. The Measure focal length. distance from the center of a lens to the focal point is called the focal length, f. Measure the focal length of the lens by having it convert a parallel beam of light into a converging beam that comes to a small spot on a screen. Use the filament of a lit, clear, 7-watt bulb as a source of approximately parallel light and a piece of cardboard as a small screen. Record your measurement below to the nearest 0.1 cm. Also, record the number of your lens.

focal length = ______cm

Chapter 30 Lenses 267 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage268 268 Measure d Find erectimagewithlens. Find invertedimagewithlens. i.A Fig. Data TableB Laboratory ManualLaboratory 82) (Experiment i and d Data TableA o . 1. your data. thus, adirect If proportion? available, usedataplottingsoftware toplot these 5-cmmovements fivemore times, recording d reposition the screen untiltheimagecomesbackintofocus. Repeat Table B. Move awayfrom thelightsource, thelens5cmfarther and image isthedistanced distance The distancebetween theobjectandfocalpoint animageonthescreenform ontheothersideoflensasinFigure A. Step 6: Record thisposition in Data Table A. appears atall?If so, whatisthis distancerelative tothefocallength? Step 5: your findingsinData Table A. the imagecompared withtheobject?Is theimagereal Record orvirtual? up(erect)?when theimageappearsright-side What istherelative size of Step 4: d Step 7: powers ofeach,todiscover themathematical relation between Record your findingsinData Table A. or reduced) andtheobject(thefilament)?Is theimagereal orvirtual? upside down (inverted)? What istherelative size oftheimage(magnified to onefocallengthfrom thelens, istheobjectwhenimageappears until theimageoffilamentisassharppossible. Where, inrelation theimageoffilamentonscreen,Observe andmove thescreen a lensholder. Arrange ascreen andalightsource asshown inFigure A. Step 3: of your lens.) a bettersource ofparallel lightisavailable, useittofindthefocallength Move awayandrecord itfarther thefocallengthtonearest 0.1cm.(If length? What effectwouldmoving thelightsource awayhave? farther effect, ifany, wouldthishaveonyour measured value forthe focal Step 2: o . Doesanycombinationgivealineargraph and, through theorigin What mathematicalrelationship exists between d Image distanced Where, inrelation toonefocallengthfrom thelens, istheobject Position thelenstwofocallengthsawayfrom thelightsource to Is there adistanceoftheobjectfrom thelensforwhichnoimage Plot The rays thelensmaynotbeparallel. oflightstriking What Use asmallamountofmodelingclayatthebottomlensas d o , andthedistancebetween theotherfocalpointand d i (vertical axis)vs.(vertical focal lengthf i , is inversely proportional totheobjectdistance, , isinverselyproportional i . Record thedistancesd d ____cm ______= o (horizontal axis), thendifferent(horizontal o closest toitisthe and i o and and d d i d o each time. ? i in Data d i and d o .

© Addison-Wesley Publishing Company, Inc. All rights reserved. 4. focal pointandisrefracted by thelens. heads toward thelensinsamedirection asifitoriginated to the principal axisandisrefractedto theprincipal by thelens. Trace another ray that Figure C.Draw thepathofray thatleavesthetipofarrow parallel Step 9: At thepointwhere theycross, animageofthetiparrow isformed. 3. the focal point. 2. the arrow parallel axis. totheprincipal ray-diagram method.Draw thepathoflightray thatleavesthetipof Step 8: Name Do therefracted rays actually No, theydonotcross. Now, draw thepathsofthesetwolightrays aftertheyare refracted. The refracted ray is parallel to theprincipal axis. Where doesthislightray goafteritisrefracted? Draw thelightray thatleavesthetipofarrow andpassesthrough The refracted ray goesthroughthe focal point. Where doesthisray goafteritisrefracted? i.C Fig. i.B Fig. You canlocatethepositionofimageinFigure Busingthe Use theray-diagram method tolocatetheimageofobjectin cross? from the Period Chapter 30Lenses Date 269 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage270 270 Laboratory ManualLaboratory 82) (Experiment 5. classes today!) telescope, your namewouldbetheanswer toquestionsinscience have discovered, 400years ago, thattwoconverging lensescanmakea relative positionsandfocallengths. (Had you beenthefirst image ofadistantobject.Sketch your arrangement oflenseswiththeir Step 10: Going Further 6. They appeartocrossonthesamesideoflensasimage. Where dotheyappear its focallength.) the realimage.Theeyepiecemustbealittleclosertoimagethan at itsfocallength.Theeyepieceservesasamagnifyingglasstolook f then thetwolensesshouldbeseparatedbyadistancelittlelessthan and If No, itisavirtualimage. Could theimagebeprojected ontoascreen? o f + o f is thefocallengthofobjective(thelensclosertoobject) f e e Use twoconverging lensestoseeifyou cancreate amagnified (the sumofthefocallengths).(Theobjectivecreatesarealimage is thefocallengthofeyepiece(thelensclosertoeye), to cross? person to

Name Period Date

Chapter 30: Lenses Focal Length of a Diverging Lens

83 Where’s the Point?

Purpose

To measure the focal length of a diverging lens. Setup: <1 Lab Time: >1

Learning Cycle: concept Experiment Required Equipment/Supplies development low-powered helium-neon laser Conceptual Level: moderate diverging lens Mathematical Level: moderate sheet of white paper meterstick Thanks to Herb Gottlieb for graph paper (if computer is not used) his ideas and suggestions for this lab. Optional Equipment/Supplies

computer data plotting software printer

Discussion

Parallel light rays are brought to a focus at the focal point of a converging lens. Ray diagrams are useful for understanding this. Parallel light rays are not brought to a focus by a diverging lens. Ray diagrams or other techniques are essential for understanding this. In this experiment, you will use a laser to simulate a ray diagram for a diverging lens. Lasers are fun!

Procedure

Step 1: Carefully (lasers are delicate!) place the laser on a table. Do not Set up laser. point it at any mirrors, windows, or persons.

Step 2: Place a diverging lens in front of the laser. Turn on the laser. Use Observe diverging laser beam. the sheet of white paper to observe that the beam is very narrow as it comes out of the laser, but after going through the lens, it spreads out into an ever-widening cone.

Step 3: Place the sheet of paper against a book. Hold the paper 5 cm beyond the lens that is in the laser beam. The red spot made by the beam should be in the center of the paper. With a pen or pencil, trace the outline of the red spot. Label the outline “distance 5 cm.” © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 30 Lenses 271 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage272 272 Data TableA Laboratory ManualLaboratory 83) (Experiment of the graph with your lab report. diverging lens. If you are usingdataplottingsoftware, includeaprintout axisisthefocallengthof negative distancealongthehorizontal would bezero, extendyour axis. lineuntilitintersectsthehorizontal The Step 7: use data plotting software to plot your data. graph axis.) fornegativedistances(totheleftofvertical If available, axis)between(horizontal thelensandpaper. Allow room onyour Step 6: tances from thelensinData Table A. paper foreachpositionofthepaper. Record thesediametersanddis- Step 5: paper. lens andthepaperby untilthespotcompletelyfills 5-cmintervals, distance. Repeat thisprocedure, increasing thedistancebetween the the outlineofspotthatisproduced. Labeltheoutlinewithnew Step 4: focal lengthofadiverging lensinthismanner? allel lightrays are brought toafocus. Why isitimpossibletofindthe The focallengthofaconvexlensisthedistancefrom thelenswhere par- Analysis appear to thelens from a point behind converge to a focus.The focal lengthofadiverging lens is thedistance manner asthatofa convex lens, becausetheparallellightraysnever The focallengthofadiverging lens cannotbefoundinthesame To findthedistancefrom thelensatwhichbeamdiameter Plot agraph axis)vs. ofthebeamdiameter(vertical thedistance Measure thediametersoftraces ofthelaserbeamon Move awayfrom thelens, thepaper5cmfarther andagaintrace to haveoriginated. focal lengthoflens=______cm the lensfromwhichdiverginglightrays

Name Period Date

Chapter 30: Lenses Refraction in Air

84 Air Lens

Purpose

To apply your knowledge of light behavior and glass lenses to a different Setup: 1 type of lens system. Lab Time: <1 Learning Cycle: application Required Equipment/Supplies Conceptual Level: easy Mathematical Level: none 2 depression microscope slides light source Adapted from PRISMS. screen

Discussion

Ordinary lenses are made of glass. A glass lens that is thicker at the center than at the edge is convex in shape, converges light, and is called a converging lens. A glass lens that is thinner at the middle than at the edge is concave in shape, diverges light, and is called a diverging lens. Activity Suppose you had an air space that was thicker at the center than at the edges and was surrounded by glass. This would comprise a sort of “convex air lens.” What would it do to light? This activity will let you find out. Fig. A Procedure

Step 1: A convex air lens encased in glass can be produced by placing Construct convex air lens. two depression microscope slides together, as shown in Figure A.

1. Predict whether this arrangement makes a diverging or converging lens. Explain your prediction.

Some students may realize that, just as light bends toward the normal

as it goes from air to glass, it bends away from the normal as it goes

from glass into air. These students should accurately predict that the

convex air lens acts the opposite from the convex glass lens and

Chapter 30 Lenses 273 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage274 274 Laboratory ManualLaboratory (Activity 84) 2. prediction. Step 2: 4. 3. Analysis What doyou discover? Draw ray diagrams forbothaconvex surrounding medium. whether lighttravelsfasterorslowerinthelensthan You needto knowmorethantheshape.You alsoneedtoknow converging ordiverging lens” notalwaystrue? Why isthestatement whetheritisa shapeofalens determines “The diverging lens. the screen.Theyshouldinferthat the convexair lens behavesasa Students willnotbe able to form animage of a distant lightsourceon them. in glasstoshow whattheselensesdotolightrays passingthrough Use your lenswithalightsource andscreen tocheckyour and aconcave air lensencased

Name Period Date

Chapter 31: Diffraction and Interference Thin-Film Interference

Rainbows Without 85 Rain

Purpose

To observe and develop a hypothesis about a phenomenon of light inter- Setup: 1 ference. Lab Time: 1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: none soap-bubble solution wire frame for soap films Adapted from PRISMS. large, flat, rimmed pan (such as a cookie sheet) oil 2 microscope slides or glass plates 2 rubber bands

Discussion

A rainbow is produced by the refraction and reflection of light from Activity drops of water in the sky. Rainbow colors, however, can be produced in a variety of ways. Some of these ways will be explored in this lab activity.

Procedure

Step 1: Pour some of the bubble solution into the flat pan. Place the loop of the wire frame into the solution. Hold the frame in a vertical position. Look at the soap film with the room lights behind you, reflecting off the film.

1. List as many observations as you can of what you saw in the soap film.

Students should note many different colors. If the film is held vertically

for a long enough time, the top will become dark.

2. How would you explain these observations?

Answers will vary widely. See Teacher Notes for this activity in the

front of the teacher’s edition for a full explanation.

Step 2: During or after a rainfall, you may have noticed brilliant colors on a wet driveway or parking lot where oil has dripped from a car © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley engine. To reproduce this situation, cover the bottom of the pan with a

Chapter 31 Diffraction and Interference 275 CP02_SE_LAB_Ch66-85 3/5/01 12:11 PMPage276 276 Laboratory ManualLaboratory (Activity 85) 5. small repeating colored bandsintheairwedge. the two. Fasten bands. bothendstogetherwithrubber Try toobserve scope slides. You candothisby placingahairacross oneendbetween 3. anglesofincidentlight. slick withvarious thin layer ofwater. Place adrop ofoilonthewater, andlookattheoil 6. Step 3: 4. 7. Analysis List your observations. asyou canoftheoilonwater.List asmanyobservations Answers willvarywidely. SeeTeacher Notesforafullexplanation. How wouldyou explaintheseobservations? patterns becauseofslightirregularitiesinthesurfaces. of glass,theinterferencebandswillstillbetherebutnotinstraight straight across the plates.If you usemicroscopeslidesor longer strips With opticallyflatplatesofglass,theinterferencebandswillbefairly Answers willvarywidely. SeeTeacher Notesforafullexplanation. How wouldyou explaintheseobservations? angle atwhichthey look at the film. Students shouldsee different colorsinthe oil film,depending on the out. Allthreesituationsinvolve interferenceofreflectedwaves. In all three situations, most or all colors oflightareselectively blocked Summarize inyour observations. anypatterns Make a very thinwedgeMake ofairbetween twoglassplatesormicro- avery

Name Period Date

Chapter 32: Electrostatics Static Electricity

86 Static Cling

Purpose

To observe some of the effects of static electricity. Setup: <1 Lab Time: 1 Learning Cycle: concept Required Equipment/Supplies development electroscope Conceptual Level: moderate hard rubber rod and fur or glass rod and silk Mathematical Level: none plastic golf-club tube foam rubber Styrofoam (plastic foam) “peanuts” or packing material coin with insulated connected string empty can from soup or soda pop, with insulated connecting string

Discussion

Have you ever been shocked after walking on a carpet and reaching for a Activity doorknob? Have you ever found your sock hiding inside one of your shirts just after it came out of the clothes dryer? Have you ever seen a lightning bolt from closer range than you might like? All of these situations arise due to static electricity. After this activity, you should understand its behavior a bit better.

Procedure

Step 1: Make sure the electroscope is discharged (neutral) by touching the probe with your finger. The leaves will drop down as far as possible.

CAUTION: Do not open the electroscope in an effort to adjust the position of the leaves. NEVER touch the leaves.

Step 2: Rub a hard rubber rod with fur, or a glass rod with silk. The rubber rod will become negatively charged, while the glass rod will become positively charged. Touch the probe of the electroscope with the charged rod.

1. What happens to the leaves of the electroscope?

Chapter 32 Electrostatics 277 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage278 278 Explore Styrofoam“peanuts.” Test chargeonelectroscope. induction. Charge electroscopeby Charge plastictube. Explore chargeontube. Laboratory ManualLaboratory (Activity 86) 2. whether thecharge ontheelectroscope is positive ornegative. Each time, charge theelectroscope by induction,asin Step 4,andtest Step 7: 6. make the “peanuts” interact withthecharged tube. pour someover thecharged tube. See how manydifferent waysyou can “peanuts” outonthetable. Try topickthemupwiththecharged tube, or Step 6: 5. rod acharged closeto(butnottouching)theprobe. glassorrubber bringing Step 5: 4. charged plastic tube but without touching the tube to the probe. Step 4: 3. not touching)theelectroscope, andthenmove thetubeaway. the charged whathappenswhenyou tubecloseto(but bring Observe ger. Charge aplastictubeby itwithapieceoffoamrubber. rubbing Step 3: The chargeonthe leaves willbethesame as on the chargedrod What kindofcharge isontheleaves? The “peanuts”jumpandhopareattractedtothe tube. andexplain thebehaviorof Describe “peanuts.” apart. spread farther collapse, whileapositively charged glass rodwillmakethe leaves Positive. Anegativelychargedrubber rod willcause the leavesto you can tell. Is thecharge ontheelectroscope positive ornegative? Explain how tube away, liftyourfingerofftheprobe.Thenmovetubeaway. probe, andtouchtheprobewithyourfinger. Withoutmovingthe Bring thechargedtubeupto(butnottouching)electroscope Record themethodyou used tocharge theelectroscope by induction. tube ismovedaway. The leavesspreadapartwhenthetubeisclose,butcollapse Record whathappens. (negative ifarubberrodisused, positive ifaglassrodisused). Test whether the charge on the electroscope is positive or negative by Charge theplastictubeby itwith different rubbing materials. Charge theplastictube. Now putsomeStyrofoam packing Devise a waytoleaveacharge ontheelectroscope, usingthe Discharge theelectroscope by touchingtheprobe withyour fin-

Name Period Date

Chapter 34: Electric Current Simple Series and Parallel Circuits

Sparky, the 87 Electrician

Purpose

To study various arrangements of a battery and bulbs and the effects of Setup: <1 those arrangements on bulb brightness. Lab Time: >1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: moderate size-D dry cell (battery) 6 pieces of bare copper wire Adapted from PRISMS. 3 flashlight bulbs 3 bulb holders second size-D dry cell (optional)

Discussion

A dry cell (commonly called a battery) is a source of electric energy. Many arrangements are possible to get this energy from dry cells to Activity flashlight bulbs. In this activity, you will test these arrangements to see which makes the bulbs brightest.

Procedure

Step 1: Arrange one bulb (without a holder), one battery, and wire in as many ways as you can to make the bulb emit light. Sketch each of your arrangements, including failures as well as successes. Label the sketches of the successes.

1. Describe the similarities among your successful trials.

There must be a direct connection (by wire or contact) between the

metal bottom of the bulb and one end of the battery. There must also

be a direct connection between the metal side of the bulb and the

opposite end of the battery. There can be no direct connection between

the two ends of the battery or between the metal side and bottom of

Chapter 34 Electric Current 279 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage280 280 Laboratory ManualLaboratory (Activity 87) circuits. circuit diagram ofFigure B. Circuits liketheseare examplesof i.A Fig. Figure A. 3. Sketch eachofyour arrangements, andnotetheonesthatwork. 2. light. and wire. Arrange theseinasmanywaysyou cantomakethebulb Step 2: Step 4: Step 3: Connect thebulbsinholders, onebattery, andwire asshown ineach ment(s), usingonlyonebattery, madethemostbulbsglow? Compare your results withthoseofotherstudents. What arrange- ofthebulbdoesholdermakecontactwith? What twoparts most successfulinlightingthebulbswithonebattery. If studentsdiscoverthem,parallelarrangementsofthebulbswillbe of thebulb. The holdermakescontactwiththemetalsideandbottom i.B Fig. Diagrams circuits forelectric usesymbolsliketheonesin Using onebattery, lightasmanybulbsinholdersyou can. Use abulbinholder(insteadofbare bulb),onebattery, series

© Addison-Wesley Publishing Company, Inc. All rights reserved. 8. 7. Step 7: 6. cuit likethisiscalledaparallel circuit Step 6: 5. Step 5: 4. Name dependence vs.independenceofcircuitelements. Answers mayemphasizethesinglevs.separatepaths orthe allel circuits. In your own words, thedifferences describe andpar- between series The otherbulbremainslit. What happenstotheotherbulb? The bulbsshouldlightifthecircuitisconnectedproperly. Do bothbulbslightinthisparallel circuit? The otherbulbgoesout. What happenstotheotherbulb? bulbs inserieswillbelessbrightthanthesinglebulb. The bulbsshouldlightifthecircuitisconnectedproperly, butthetwo circuits?Do thebulbslightineachoftheseseries Unscrew oneofthebulbsinparallel circuit. Set upthecircuit shown inthecircuit diagram ofFigure C.Acir- In thecircuit withtwobulbs, unscrew oneofthebulbs. i.C Fig. . Period Chapter 34 Electric CurrentChapter 34Electric Date 281 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage282 282 Laboratory ManualLaboratory (Activity 87) arrangements, onthesketches. andnotethebulbbrightness that givedifferent degrees ofbulbbrightness. Sketch eachofyour 9. of your arrangements, andnotetheonesthatwork. Step 8: Going Further so itsbrightnessmayincreaseslightly. ing wireisappreciablecomparedwiththatoftheremainingbulb, ness. Withflashlightbulbs,however, theresistanceofconnect- bulb normallynotonlyremainslitbutmaintainsthesamebright- When oneoftwobulbsinaparallelcircuitisunscrewed,theother Step 9: 10. What arrangement(s), usingtwobatteries, litthemostbulbs? of onetotheoppositeendother(putbatteriesinseries). The mosteffectivewaytousethetwobatteriesisconnectend is toputthebatteriesinseries andthebulbsinparallel. is toputthebatteriesinparallelandbulbsseries; thestrongest There arequiteanumberofdegreesbrightness.The weakest setup arrangements? three Did otherstudentsusedifferent bulbs andtwobatteries? How manydifferent degrees couldyou obtainusing ofbrightness Using three bulbsandtwobatteries, discover thearrangements Using twobatteries, lightasmanybulbsyou can.Sketch each

Name Period Date

Chapter 34: Electric Current Capacitors

88 Brown Out

Purpose

To investigate charging and discharging a capacitor through a bulb. Setup: <1 Lab Time: <1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: moderate CASTLE Kit (available from PASCO) Mathematical Level: none or 1 25,000 µF capacitor (20 volts nonpolar) It’s important to use a voltage 2 #14 lightbulbs (round) (no substitutions allowed!) source between 3.6 and 4.5 2 #48 lightbulbs (long) (no substitutions allowed!) volts (3 D-cells) for the speci- 4 lightbulb sockets fied bulbs. A greater voltage 1 packet of 12 alligator leads is likely to burn out the bulbs; 1 D-cell battery holder and 3 D-cells a smaller voltage is not sufficient.

Discussion

When you switch on a flashlight, the maximum brightness of the bulb Activity occurs immediately. If a capacitor is in the circuit, however, there is a noticeable delay before maximum brightness occurs. When the circuit contains a capacitor, the flow of charge through the circuit may take a noticeable time. How much time depends upon the resistance of the resistor and the charge capacity of the capacitor. In this activity, we will place a resistor (lightbulb) between the battery and the capacitor to be charged. By using bulbs of different resistances, the charging and discharging times are easily observed.

Procedure

Step 1: Connect a battery, two long bulbs, and a blue capacitor Assemble the circuit and (25,000 µF) as shown in Figure A. Leave one wire (lead) to the battery charge the capacitor. disconnected. Close the circuit by connecting the lead to the battery and observe how long the bulb remains lit. You are charging the capacitor.

Step 2: Disconnect the leads from the battery and remove the battery from the circuit. Connect the two leads that were connected to the bat- Fig. A tery to each other as shown in Figure B. Observe the length of time the bulbs remain lit. This process is called discharging the capacitor.

Step 3: Replace the long (#48) bulbs in the circuit with round (#12) bulbs and charge the capacitor. Observe the length of time the bulbs remain lit. Remove the battery from the circuit as in Step 2 and discharge Fig. B the capacitor through the round bulbs. Observe the time the bulbs

© Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley remain lit. Which bulbs remain lit longer as the capacitor charges and discharges—long or round bulbs? Chapter 34 Electric Current 283 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage284 284 Discharge thecapacitor. Charge thecapacitor. Laboratory ManualLaboratory (Activity 88) Is thetimebulbsremain litlonger, shorter, orthesameasinStep 3? 1. careful nottoaccidentallydischarge thecapacitor. long bulbsfrom theirsocketsandreplace themwithround bulbs, being Step 4: If, however, bulbsaffecttherate ofcharge flow rather thanthe amount • If bulbsaffecttheamountofcharge thatpassesthrough them,bulbs • following hypotheses: 3. Analysis Step 5: 2. 4. time during whichcharge flowstime during through them. of charge thatflows, thenbulbsthatremain litlongerwillincrease the charge would bestored inthecapacitor. that remain litlongerallow more charge topassthrough them. The when thecapacitorwascharged through round bulbstakemore, less, orthesametimeasinStep 3— what typeofbulbsare charging. usedduring Will discharging Suppose thecapacitorstores thesameamountofcharge nomatter To accountforthedifferent timesthebulbsare lit,we canmakethe The longbulbsremainlitalongertimethantheroundbulbs. To store charge (somewhatlikeabattery, but with important (a) What isoneuseofacapacitor? through twosimilarbulbs. The dischargingtimethrough the singlebulbissomewhatshorterthan The dischargingwilltakemoretime. as itdidinStep 4? charging now through round bulbstakemore, less, orthesametime charging time,the capacitorthanoccurswithashorter willdis- If, instead,alongercharging timeindicatesmore charge isstored in The dischargingshouldtakethesametime. True, evidencedby the differencebetween theroundand long bulbs. Why orwhynot? Is thatthetypeofbulbaffectsrate ittrue charge flows through it? change thedischargetime. No. Switchingthebulbsaftercapacitorhasbeencharged doesnot type ofbulbsthrough whichitwascharged? Explain. (b) Doestheamountofcharge stored inacapacitordependonthe differences). Remove from thecircuit thebattery anddischarge the capacitor. Charge the capacitorthrough twolongbulbs. Now remove the through round bulbs?

Name Period Date

Chapter 34: Electric Current Ohm’s Law 89 Ohm Sweet Ohm

Purpose

To investigate how the current in a circuit varies with voltage and Setup: 1 resistance. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate nichrome wire apparatus with bulb Mathematical Level: none 2 1.5-volt batteries or 2 Genecon® handheld generators

Discussion

Normally, it is desirable for wires in an electric circuit to stay cool. Red- hot wires can melt and cause short circuits. There are notable exceptions, however. Nichrome wire is a high-resistance wire capable of glowing red-hot without melting. It is commonly used as the heating element in toasters, ovens, stoves, hair dryers, and so forth. In this experiment, nichrome wire is used as a variable resistor. Doubling the length of a piece of wire doubles the resistance; tripling the length triples the resistance, and so on. Tungsten wire is capable of glowing white-hot and is used as filaments in lightbulbs. Light and heat are generated as the current heats the high-resistance tungsten filament. The hotter the filament, the brighter the bulb. For the same voltage, a bright bulb (such as a 100-watt bulb) has a lower resistance than a dimmer bulb (such as a 25-watt bulb). Just as water flows with more difficulty through a thinner pipe, electrical resistance is greater for a thinner wire. Manufacturers make bulbs of different wattages by varying the thickness of the filaments, so we find that a 100-W bulb has a lower resistance and a thicker filament than a 25-W bulb. In this lab, the brightness of the bulb will be used as a current indi- cator. A bright glow indicates a large current is flowing through the bulb; a dim glow means a small current is flowing.

Procedure Assemble the battery with four D-cells. Step 1: Connect four D-cell batteries in series, so that the positive termi- Be sure students understand nal is connected to the negative terminal in a battery holder as shown in the circuit before attempting to Figure A. This arrangement, with Terminal #1 as ground, will provide you do this lab. with a variable voltage supply as indicated in Table A. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 34 Electric Current 285 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage286 286 A Fig. Repeat withthinnerwire. bulb. Observe the brightness of the a circuitdiagram. Assemble the circuit and draw Laboratory ManualLaboratory 89) (Experiment Post A. ofthebulbasyou movebrightness thebulb’s leadclosertoBinding Step 4: 1. move thetestbulbleadfrom bindingPost Btoward A. circuit by theintensityofbulbasyou closing theswitch.Observe Step 3: thereby changingitsresistance. and heatthewire, power oninthecircuit forlongperiodsoftimewilldrain yourbatteries to make your measurements and then open the switch. make yourmeasurements quickly. cuit elements, draw adiagram thatrepresents this binding Post BtobindingPost A.Using thestandard symbols for thecir- the resistance inthecircuit by moving theclipleadoftestbulb from through tworesistances: thebulbandnichrome wire. You willvary Post Bonthenichrome wire. test bulb. Attach theotherclipleadoftestbulbtobinding Connect the3-voltlead(#3)from thevoltagesupplytoaclipleadof side oftheswitchtobindingPost Aonthe thickestnichrome wire. (#1) ofthevoltagesupplytoonesideaknifeswitch.Connect theother post ofthenichrome wire “A” andtheother “B”. Attach theground lead Step 2: i.B Fig. The brightnessofthebulbdecreasesfromBtoA. Binding Post BtoA? ofthebulbasyou moveWhat happenstothebrightness itfrom Note: The voltagesupplyisnow connectedsothatthecurrent passes Repeat usingthethinnernichrome wire. therelative Observe After carefully checkingallyour connections, applypower tothe Assemble thecircuit asshown inFigure B. Labelonebinding Data TableA Always applypower packsby closingaswitchand from battery Leave thepower onjustlongenough series Leaving the circuit.

© Addison-Wesley Publishing Company, Inc. All rights reserved. power isapplied. polarity oftheleadsifneedle ofthemetergoeswrong way(–)when prevent draining thebatteries. Repeat using thethinnerwire. B toA.Be sure toapplypower Measure thecurrent inthecircuit asyou move thetestbulbleadfrom ply andtheswitch. The ammeterwillread totalcurrent inthecircuit. withthevoltagesupplybetween in series Terminal #1ofthevoltagesup- With thethickerpieceofnichrome wire inthecircuit, place the ammeter Step 6: Going Further 6. 5. 3-volt leads. Step 5: 4. 3. 2. Name Note: increases. The currentincreasesasvoltageanddecreasesresistance rent inthecircuit depend uponvoltageandresistance? Combining your results from Questions 4and5,how doesthecur- to A,justasinthecasewith3volts. as theresistanceofcircuitincreasesyoumoveleadfromB The brightnessofthebulbisgreaterwithvoltage,butdims nichrome wires using4.5voltsinsteadof3volts? How ofthetestbulb compare doesthebrightness forthetwo decreases astheresistanceincreases. Based uponthebrightnessofbulb,currentincircuit the resistance ofthecircuit increase ordecrease? lead closertoBinding Post B?Asyou move theleadfrom BtoA,does Does thecurrent ofthecircuit increase ordecrease asyou move the sectional area)ofthewire. increases withlengthanddecreasesdiameter(andhencecross- Based uponthebrightnessofbulb,resistanceapparently resistance? What effectsdothethicknessandlengthofwire haveonits position anddimswhentheleadismovedfromBtoA. The bulbisdimmerwhentheconnectedinsamerelative ofthebulbwhenconnectedtoathicker wire?with thebrightness How ofthebulbwiththinnerwire doesthebrightness compare Now anammeterintothecircuit insert asillustrated inFigure C. Repeat Steps 1–2usingthe4.5and6-voltleadsinsteadof fyuaentuigadgtlmtr youmayhave toreverse the If youare notusingadigitalmeter, only while makingthemeasurements to Period Chapter 34 Electric CurrentChapter 34Electric and measure current. Install ammeterinthecircuit Date 287 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage288 288 Laboratory ManualLaboratory 89) (Experiment 9. 8. 7. i.C Fig. The currentislessinthethinnerwire.Ithasgreaterresistance. the samevoltageisappliedtolengthsofwire? How dothecurrents inthethickerandthinnerwires compare when Yes, thecurrent increasesasthevoltageincreases. increased? Do your results show anincrease incurrent asthevoltageis Yes, thecurrentdecreasesaslengthofwireincreases. length ofthewire) isincreased? Do your results show adecrease incurrent astheresistance (or

Name Period Date

Chapter 35: Electric Circuits Current Flow in Circuits

90 Getting Wired

Purpose

To build a model that illustrates electric current. Setup: 1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy 4 D-cells (1.5 volt) Mathematical Level: none D-cell battery holder 3 alligator clip leads 2 bulbs and bulb holders

Discussion

While we can float on a raft gliding down the Mississippi or ride in cars moving in traffic, nobody can see electric current flow. Even in the case of lightning, we are seeing the flash of hot glowing gases produced by electric current—not the current itself. However, we can infer the pres- Activity ence of electric current using lightbulbs and magnetic compasses in much the same way as a flag indicates the presence of wind. In this activity, you will build a model to study electric current.

Part A: What Is Happening in the Wires? Procedure

Step 1: With the circuit arranged as shown in Figure A, turn the bulbs on Observe the wires when the and off by connecting and disconnecting one of the wires. circuit is closed.

Encourage students to visual- ize what is going on in the wires.

Chapter 35 Electric Circuits 289 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage290 290 neath thewire. Position acompassunder- Laboratory ManualLaboratory (Activity 90) 2. whether the bulbs must be lit to deflect the compass needle. the amountofneedle’s deflectionisthesameasbefore. Also, observe to see if the needle deflects in the same direction as before. Look to see if theneedleasyou openandclosethecircuitObserve several times. Look cuit. Be sure theneedleisparallel tothewire whenthebulbsare notlit. Step 3: 3. Observe whathappenstotheneedlewhenbulbsgoout. Observe pass needle. whathappensto theneedlewhenbulblights. Observe disconnect aleadinthecircuit thecom- several timeswhileyou observe on topofthecompassparallel totheneedleasinFigure B. Connect and needle pointingtothe “N.” With thebulbs unlit,placeoneofthewires 1. Step 2: the wires while thebulbsare energized? thenotionthatsomethingishappeningin What evidencesupports same everywhereinthecircuit. The sizeanddirectionofthe deflectionofthecompassneedleis ofthecircuit? inallparts occurs uniformly thenotionthatwhateverishappening What evidencesupports while thebulbislit. The deflectionofthecompassneedleindicatessomething isgoingon brighter thantheother? brighter before theother?Doesonebulbgooutbefore theother?Is onebulb circuit whenthebulbsare lit?For example, doesonebulblight Is there anyvisualevidencethatsomethingismoving around the bulb willgooutbeforetheotherwhendisconnected. bulbs arethesame,theywillhavesamebrightness,andneither least nothingismovingataspeedthatnoticeable.Aslongasthe Nothing visuallyindicatessomethingismovingintheclosedcircuit—at Place thecompassbeneathwire indifferent ofthecir- parts Place amagnetic compassonthetablenearcircuit withthe i.B Fig.

© Addison-Wesley Publishing Company, Inc. All rights reserved. and 5. D-cells. Carefully deflectionof theneedleasyou repeat observe Steps 4 Step 7: 6. deflection oftheneedlewhileyou repeat Steps 4and5. holderonlyhastwocellsinsteadofthree.battery Carefully observe Step 6: 5. 4. counterclockwise. needle. Watch theneedledeflectandnotewhetheritisclockwiseor Open andclosethecircuitterminal. whileyou watchthecompass withtheleadconnectedtonegative ofthebattery positive terminal and compass. Dothisby simplyexchanging theleadconnectedto Step 5: clockwise orcounterclockwise. you carefully theneedle. observe Note whethertheneedledeflects of thecompassparallel totheneedle. Open andclosethecircuit while Step 4: Happening intheCircuit? Is There Directionality to What Is Part B: Name as withthreeD-cells. The deflectionofthecompassneedleislessbutin samedirection compare when you usetwocellsinsteadofthree? How dothesize anddirection ofthecompassneedle’s deflections of the flow in the wires. The directionofthecompassneedle’s deflection is duetothe direction the direction oftheflow? tion Suppose somethingisflowing inthewires. Doyou thinkthedirec- opposite directionasinStep4. The deflectionofthecompassneedleisinsameamountbut deflection thesameasbefore? wereleads tothebattery reversed? Is theamountofneedle’s Is thedirection ofthedeflectionsameasinStep 4,before the Install twomore holdersothatithasfour D-cellsinthebattery Remove holdersothatthe oneoftheD-cellsfrom thebattery Reverse thecircuit withoutaltering theleadsfrom thebattery Arrange thecircuit asinFigure A.Place oneofthewires ontop the needleisdeflectedcausedby theamountofflow or Period Chapter 35 Electric CircuitsChapter 35Electric tion ofthecompass. battery and observe thedeflec- Reverse the leadsfrom compass. Observe thedeflectionof Add two cells to the battery. the battery. Remove oneofthe cells from Date 291 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage292 292 Laboratory ManualLaboratory (Activity 90) 7. 11. 10. 9. 8. Analysis flow? deflection iscausedby amountoftheflow with twoandthree D-cells?Doyou thinkthesize How dothedeflectionsofcompassneedlecompare withthose The batteryisasourceof energy thatsuppliesthecurrent,or does? What doyou thinkthebattery More electricalenergymovesinthecircuit. needle’s deflectionincreases ordecreases. Hypothesize whatishappeninginthewires whentheamountof The current, or the electricity, reverses direction. the compassdeflectionreverses. Hypothesize whatishappeninginthecircuit whenthedirection of Some formofelectricalenergyismovinginthecircuit. Hypothesize whatishappeninginthecircuit whenbulbsare lit. brightest—i.e., whenastrongerbatteryisused. the amountofflow—deflectionismorevigorouswhenbulbsare direction aswiththreeD-cells.Thesizeofthedeflectiondependson The deflectionofthecompassneedleisgreaterbutinsame electricity that flows throughthecircuit. or thedirection ofthe of theneedle’s

Name Period Date

Chapter 35: Electric Circuits Series and Parallel Circuits

91 Cranking Up

Purpose

To observe and compare the work done in a series circuit and the work Setup: 1 done in a parallel circuit. Lab Time: 1

Learning Cycle: concept Experiment Required Equipment/Supplies development Conceptual Level: moderate 4 lightbulbs, sockets and clip leads voltmeter Mathematical Level: moderate Genecon ammeter parallel bulb apparatus

Discussion

Part A: Qualitative Investigation

Step 1: Assemble four bulbs in series as shown in Figure A. Screw all the Assemble the circuit and crank bulbs into their sockets. Connect the sockets with clip leads. the Genecon as you unscrew Connect one lead of a Genecon to one end of the string of bulbs and bulbs in series. the other lead to the other end of the string. Crank the Genecon so that all the bulbs light up. Now, disconnect one of the bulbs from the string and reconnect the Genecon. Crank the Genecon so that the three remaining bulbs are energized to the same brightness as the four-bulb arrangement. How does the crank feel now? Repeat, removing one bulb at a time and comparing the cranking torque each time.

The series arrangements require bulbs of identical resistance (or as nearly so as possible) if they are to flow reasonably well with D-cells. This subtlety can be very confusing for students if their bulbs have different resistances.

Fig. A Fig. B

Step 2: Assemble the circuit with the parallel bulb apparatus as shown in Assemble the parallel circuit Figure B. Each end of the bulb apparatus has two terminals. Connect the and crank the Genecon as you leads of a voltmeter to one pair of terminals on one end of the apparatus. screw in the bulbs. Connect the leads of the Genecon to the terminals on the other end of the apparatus. Crank the Genecon with all the bulbs unscrewed in the sockets so that they don’t light. Then, have your partner screw them in

© Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley one at a time as you crank on the Genecon. Try to keep the bulbs energized at the same brightness as each bulb is screwed into its socket. Chapter 35 Electric Circuits 293 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage294 294 titative data. for gettingaccuratequan- ence, itisnotagoodtool great forhands-onexperi- Although theGeneconis best tousebatteries. and parallelcircuits,itis ferences betweenseries To seethequantitativedif- Assemble thecircuitinseries. Laboratory ManualLaboratory 91) (Experiment i.C Fig. and repeat themeasurements. Record your datainData Table A. the otherbulbsoneatatime, closing thegapincircuit eachtime, the circuit, andrepeat your measurements forthree bulbs. Then remove Step 4: each bulb. Record your results inData Table A. in thecircuit, thevoltageappliedtocircuit, andthevoltageacross when power isapplied. polarity oftheleadsifneedlemetergoes wrong way (–) bulbs. The ammeterwillmeasure thetotal Connect ofthe theotherleadofammetertosecondterminal nal ofthebulbsandground connectiontooneleadofanammeter. each bulb. Connect the3-voltleadfrom thevoltage supplytoonetermi- connect itinparallel withsinglebulbstomeasure thevoltageacross so you canmeasure thetotalvoltageappliedtocircuit. Then you will shown inFigure C.Connect thevoltmeterinparallel withallfourbulbs 1. Step 3: ammeter. Now repeat Part Ainaquantitativefashionusing avoltmeterandan Resistors inSeries QuantitativeInvestigation— Part B: 3. 2. Close theswitch,applypower tothecircuit, andmeasure thecurrent Note: More torqueisrequired. at aconstantspeedasmore bulbsare addedtothecircuit? What doyou noticeaboutthetorque Yes. Genecon) thesame? brightly, istheenergy expended(thework you are doingtocrank the andparallelIf allthe bulbs intheseries circuits are glowing equally The torqueisthesame. required forfourbulbsinparallel? Genecon toenergize compared fourbulbsinseries withthat How theamountoftorque wouldyou required describe tocrank the Now remove closethegapin oneofthebulbsfrom thestring, Assemble four bulbs in a series circuitAssemble fourbulbsinaseries andconnectthemetersas fyuaentuigdgtlmtr,youmayhave toreverse the If youare notusingdigitalmeters, i.D Fig. required tocrank theGenecon current inthecircuit.

© Addison-Wesley Publishing Company, Inc. All rights reserved. unscrew the bulbs one at a time. and applypower ofthebulbs, tothecircuit. thebrightness then Observe measure thetotalcurrent inthecircuit. oftheparallelthe secondterminal bulbapparatus. The ammeterwill connecttheother leadoftheammeterto ply tooneleadofanammeter; parallel bulbapparatus. Connect theground leadfrom thevoltagesup- Connect ofthe the3-voltleadfrom thevoltagesupplytooneterminal ononeendoftheparallelvoltmeter totwoterminals bulbapparatus. D. Connect thevoltmeterinparallel withthebulbsby connectingthe Step 6: Resistors inParallel QuantitativeInvestigation— Part C: 8. 7. 6. 5. 4. Recordof the3-voltterminal. your datainData Table B. Step 5: Name Data TableA Make sure thebulbsare notlooseintheirsockets. Closetheswitch No. change whenyou applied4.5 voltsinstead of3volts? youDid discovered anyoftherules relating voltagesandcurrents Total current inthecircuitdecreasesasnumberofbulbsincreases. bulbs are added? How doesthecurrent suppliedby changewhenmore thebattery voltage dropsacrossallthebulbsequalsappliedvoltage. The voltagedropacrossallbulbsisaboutthesame.sumof How are thevoltagesacross each bulbrelated totheappliedvoltage? No, thevoltageremainsunchangedregardlessofnumberbulbs. bulbs? Does thevoltageappliedincircuit changeasyou addmore Yes, thebrightness decreasesasmorebulbsareaddedtothecircuit. Is there asthenumber ofbulbschanges? anychangeinbrightness Assemble thecircuit andconnectthemetersasshown inFigure Repeat ofthevoltagesupplyinstead usingthe4.5-voltterminal Data TableB Period Chapter 35 Electric CircuitsChapter 35Electric Assemble thecircuitinparallel. voltage. Repeat usingadifferent Date 295 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage296 296 voltage. Repeat usingadifferent current and voltage. Record your measurements of Data TableC Laboratory ManualLaboratory 91) (Experiment 9. Recordsupply insteadofthe3-voltterminal. your datainData Table D. Step 8: 13. 12. 11. 10. drop across eachbulb. Record your datainData Table C. current inthecircuit, thevoltageappliedtocircuit, andthevoltage Step 7: Is there asthenumberofbulbschanges? anychangeinbrightness No; theratioofvoltagetocurrentequalsresistance. volts instead of 3 volts? Did theratio ofvoltageandcurrent changewhenyou applied4.5 internal resistance)ofthebatteryasmorebulbsareadded tothecircuit. decreases slightlyduetothedrop in the terminal voltage (due to the currentamountstoabout 0.2 amp/bulb. The amount ofincrease to thenumber of bulbs.When3voltsisapplied, In direct proportion of bulbsinthecircuit changes? How doesthecurrent suppliedby changeasthenumber thebattery No, not appreciably. bulbs? Does theappliedvoltagetocircuit changeasyou addmore No, not appreciably. to or subtracted from the circuit? Does thevoltageacross eachbulbchangeasmore bulbsare added No, thistimethebulbsremainsamebrightness. Repeat Steps ofthevoltage 3and4usingthe4.5-voltterminal Screw thebulbsbackin,oneatatime, the eachtimemeasuring Data TableD

Name Period Date

Chapter 35: Electric Circuits Household Circuits

92 3-Way Switch

Purpose

To explore ways to turn a lightbulb on or off from either one of two Setup: <1 switches. Lab Time: 1 Learning Cycle: application Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: none 2.5-V dc lightbulb with socket connecting wire Thanks to Manuel DaCosta for 2 single-pole double-throw switches his ideas and suggestions for 2 1.5-V size-D dry cells connected in series in a holder this lab.

Discussion

Frequently, multistory homes have hallways with ceiling lights. It is convenient if you can turn a hallway light on or off from a switch located at either the top or bottom of the staircase. Each switch should be able to Activity turn the light on or off, regardless of the previous setting of either switch. The same arrangement is often adopted in a room with two doors. In this activity, you will see how simple, but tricky, such a common circuit really is!

Procedure

Step 1: Examine a 3-volt battery (formed from two 1.5-volt dry cells with the positive terminal of one connected to the negative terminal of the other). Connect a wire from the positive terminal of the battery to the center terminal of a single-pole double-throw switch. Connect a wire from the negative terminal of the same battery to one terminal of the lightbulb socket. Connect the other terminal of the lightbulb socket to the center terminal of the other switch.

Step 2: Now interconnect the free terminals of the switches so that the Devise working circuit. bulb turns on or off from either switch. That is, when both switches are closed in either direction, moving either switch from one side to the other will always turn an unlit bulb on or a lit bulb off.

Chapter 35 Electric Circuits 297 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage298 298 Interchange batteryandbulb. Reverse polarityofbattery. Laboratory ManualLaboratory (Activity 92) versa. nect thecircuit iswhere sothatthebattery thelightbulbisnow, andvice Step 5: your successful circuit willwork ifyou reverse ofthebattery. thepolarity the connectionstopositiveandnegativeterminals. Predict whether Step 4: pendently ofhow theotherswitchisset? tings oneachswitchhave?Can eithersettingkeepthecircuit openinde- switches you usedinthisactivity, whatfunctiondothetwo “closed” set- point, andan “off” setting,whichopensthecircuit atthatpoint.Onthe An ordinary switchhasan “on” setting, whichclosesthecircuit atthat Analysis Now itandrecord try your results. Now reverse andrecord thepolarity theresult. independently ofthesettingonotherswitch. other travelwire.Thus,neithersettingcankeepthecircuitopen connection butclosesthebetweenswitchand between theswitchandonetravelwire.Theothersettingopensthat (called The twoswitchesareconnectedtoeachotherbywiresinparallel The polarity of a battery canbereversed ofabattery inacircuitThe polarity by switching Predict whetheryour successfulcircuit willwork ifyou recon- travel wires).Onesettingofeachswitchclosestheconnection results: ______results: ______prediction: ______result: ______prediction: The circuitwillwork. The circuitwillwork.

Name Period Date

Chapter 36: Magnetism Magnetic Field Lines

93 3-D Magnetic Field

Purpose

To explore the shape of magnetic fields. Setup: <1 Lab Time: 1 Required Equipment/Supplies Learning Cycle: exploratory Conceptual Level: easy 2 bar magnets 5 to 10 small compasses Mathematical Level: none iron filings jar of iron filings in oil strong horseshoe magnet paper Adapted from PRISMS. sheet of clear plastic

Discussion

A magnetic field cannot be seen directly, but its overall shape can be seen by the effect it has on iron filings.

Procedure Activity

Step 1: Vigorously shake the jar of iron filings. Select the strongest horseshoe magnet available. Place the jar over one of the poles of the magnet and observe carefully. Place the jar at other locations around the magnet to observe how the filings line up.

1. What happened to the iron filings when they were acted upon by the magnetic field of the magnet?

The iron filings align along paths that are closer together near the poles

of the magnet. (A torque on the magnetic domains of the iron filings

aligns them along the direction of the magnetic field lines.) At the

poles, the filings accumulate like spikes radiating outward.

Step 2: From all your observations, draw a sketch showing the direction Sketch magnetic field. of the magnetic field all around your magnet, as observed from the side. Also, draw a sketch as viewed from the end of the magnet. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 36 Magnetism 299 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage300 300 Repeat usingtwomagnets. Sketch magneticfieldlines. Trace magneticfieldlines. compasses. Observe orientationof Laboratory ManualLaboratory (Activity 93) 2. other. Sketch ofthefilingsinbothsituations. thepattern other, suchasNandorSS,withunlikepolesfacingeach Step 6: 4. 3. ings make. Repeat thisstepusingtheotherbarmagnet. the magneticfield.In the following space, thatthefil- sketchthepattern tly taporjiggletheplasticsheet. The filingswilllinethemselvesupwith small quantityofiron filingsover theplastic. It togen- maybenecessary tic. Place theplasticontopofonebarmagnets, a andsprinkle Step 5: show themagneticfield. point ateachlocation.Linkthearrows togetherby continuouslinesto passes around themagnet,andusearrows todraw thedirections they Step 4: end. north-pointing with theactivity, represent eachcompassasanarrow whosepointisthe which endofeachcompasspointstoward Asyou proceed thenorth. Step 3: in obtainingaquickandaccurate picture ofthemagneticfield. Compare themethodsofSteps oftheirusefulness 4and5interms direction andstrengthofthe magneticfield. one nearby).Also, the fieldlines never cross.Fieldlinesindicatethe The fieldlinesbeginandend on amagnet(eitherthe same magnetor What generalizations canyou makeabout magneticfieldlines? difficult tosee. filings clumpintounevenpilesandmakethemagnetic fieldlines The compassesdonotalignwellifthemagneticfield is weak.Theiron Are there anylimitationstoeithermethod? together, thefieldisstrongest. magnetic fieldlinesinaplane.Also,wheretheironfilingsareclosest their locations.Theironfilingsgiveaquickindicationoftheoverall The smallcompassesindicatethedirectionofmagneticfieldat Repeat Step 5fortwobarmagnetswithlikepolesfacingeach Trace oneofthebarmagnetsonapiecepaper. Move thecom- Obtain asmallquantityofiron filingsandasheetofclearplas- Obtain twobarmagnetsand5to10smallcompasses. Note

Name Period Date

Chapter 36: Magnetism Force on Moving Charges

94 You’re Repulsive

Purpose

To observe the force on an electric charge moving in a magnetic field, Setup: <1 and the current induced in a conductor moving in a magnetic field. Lab Time: 1 Learning Cycle: exploratory Required Equipment/Supplies Conceptual Level: moderate Mathematical Level: none cathode ray oscilloscope or computer with monitor horseshoe magnet Adapted from PRISMS. bar magnet compass 50 cm insulated wire galvanometer or sensitive milliammeter masking tape

Discussion Activity In this lab activity, you will explore the relationship between the mag- CAUTION: Do not bring a netic field of a horseshoe magnet and the force that acts on a beam of strong, demonstration magnet electrons that move through the field. You will see that you can deflect near a color TV or monitor. the beam with different orientations of the magnet. If you had more control over the strength and orientation of the magnetic field, you could use it to “paint” a picture on the inside of a cathode ray tube with the electron beam. This is what happens in a television set. A moving magnetic field can do something besides make a television picture. It can induce the electricity at the generating station to power the television set. You will explore this idea, too.

Procedure

Step 1: If you are using an oscilloscope, adjust it so that only a spot Adjust monitor or oscilloscope occurs in the middle of the screen. This will occur when there is no hori- so dot is centered. zontal sweep. If you are using a computer monitor for the cathode ray tube, use a graphics program to create a spot at the center of the screen. Make a white spot on a black background. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 36 Magnetism 301 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage302 302 on spot. Note effects of bar magnet entations of the magnet. Make sketches ofdifferent ori- Laboratory ManualLaboratory (Activity 94) 2. your observations. Step 3: the spot moves. Try ofthemagnet,andmakesketchestoshow otherorientations how Figure Atoindicatethedirection inwhichthespotmoves ineachcase. ofthemagnetshownthe orientations inFigure A.Sketch arrows on can causepermanentdamage. asthey Such magnetsshouldnot bebrought closetoanycathoderay tube, label itwithtape. orsouthpole, whetherapoleisnorth use acompasstodetermine and 1. Step 2: force onthebeamrelated tothedirection ofthemagneticfield? magnetic force onthebeam.How isthedirection ofthemagnetic poletothesouthpole.north The spotmoves inthedirection ofthe Recall from the thatthemagneticfieldlinesoutsideamagnetrun electron beam. The spotdoesnotmovewhenthemagneticfieldisparallel tothe the beamisperpendiculartomagneticfield. along thescreenperpendiculartomagneticfield.Thusforceon When themagneticfieldisparalleltoscreen,beamdeflected Place the polesofthehorseshoemagnet1cmfrom thescreen. Try CAUTION: screen. In whatdirection are theelectrons moving? The dotonthescreen iscausedby anelectron beamthathitsthe The electronsaremovingstraighttowardthescreenfromback. Aim onepoleofabarmagnetdirectly toward thespot.Record If the north andsouthpolesofyourIf magnetsare thenorth notmarked, ontuelre demonstration magnetsinthisactivity. notuselarge, Do i.A Fig.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 5. 4. differentloops inthecoil,andtry strengths ofmagnets. directions, poles, and speedsofthemagnet.Also, thenumberof vary currentinduce electric andcausethegalvanometer todeflect. Vary the ter. Explore theeffectsofmoving abarmagnetintoandoutofthecoilto the wire ofagalvanometer orsensitivemilliamme- tothetwoterminals ter ofapproximately 8cm. Tape theloopstogether. Connect theendsof Step 5: 3. one sideofthespot.Record your observations. Step 4: Name magnet moves (while keeping the orientation of themagnet the same). direction of motion the same);(2)reversingdirection in whichthe changing whichpolemoves through thecoilfirst(while keeping the The galvanometercan be deflectedintheopposite direction by(1) opposite direction? What doyou needtodocausethegalvanometer todeflectinthe of wire onthecoil,and(3)using strongest barmagnet. the coilas quickly as possible;(2)usingthe maximum number of turns The largest current canbeinduced by (1)thrustingthemagnetthrough the largest deflectionofthegalvanometer? Under whatconditions canyou inducethelargest current andget beam areallperpendiculartotheeachother. The electronbeam,themagneticfield,andforceon deflection oftheelectron beam? magnetic field,andtheforce onthebeamformaximum In general, whatare therelative directions oftheelectron beam,the electron beam. The spotshouldmovewhenthemagneticfieldisatanangleto With alonginsulatedwire, makeathree-loop coilwithadiame- Change your aimsothatthepoleofbarmagnetpointsto Period affects coilofwire. Explore howmovingmagnet Chapter 36Magnetism Date 303 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PM Page 304 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PM Page 305

Name Period Date

Chapter 37: Electromagnetic Induction Electromagnetic Induction

Jump Rope 95 Generator

Purpose

To demonstrate the generator effect of a conductor cutting through the Setup: <1 earth’s magnetic field. Lab Time: 1 Learning Cycle: application Required Equipment/Supplies Conceptual Level: easy Mathematical Level: none 50-ft extension cord with ground prong galvanometer Adapted from PRISMS. 2 lead wires with alligator clips at one end

Discussion

When the net magnetic field threading through a loop of wire is changed, a voltage and, hence, a current are induced in the loop. This is what happens when the armature in a generator is rotated, when an iron car drives over a loop of wire embedded in the roadway to activate a traf- Activity fic light, and when a piece of wire is twirled like a jump rope in the earth’s magnetic field.

Since the deflection is small, the more sensitive the galvanometer the better. Digital meters are commonly very sensitive, but it is much more difficult for students to see the sinusoidal variation. The galvanometer must respond rapidly enough so that it doesn’t average out the alternating input.

Procedure

Step 1: Attach an alligator clip to the ground prong of the extension cord (see Figure A). Attach the wire’s other end to the galvanometer. Jam the other alligator clip into the ground receptacle on the other end of the extension cord. Attach the other end of this second wire to the other Fig. A contact on the galvanometer. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 37 Electromagnetic Induction 305 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage306 306 Change directions. cord. Jump ropewiththeextension Laboratory ManualLaboratory (Activity 95) 2. direction. thedifference Observe inthedeflectionongalvanometer. 1. galvanometer. Twirl thecord faster, thegalvanometer. andobserve the twirl itlikeajumprope withthehelpofanotherperson.Observe ends oftheextensioncord ontheground, pickupthemiddlehalfand Step 2: 3. Analysis Step 3: 4. Is itharder tospinthecord inonedirection ortheother? tion of the galvanometer? What effectdoestherotational speedofthecord haveonthedeflec- magnetic fieldlinesarecutperunittime.) west direction.(Undertheseconditions,thegreatestnumberof extension cordisatamaximumandthealignedineast- The maximumcurrentoccurswhentherotationalspeedof through thegalvanometer. theconditionsinwhichyouDescribe hadmaximumcurrent east-west direction,butthedifference may beimperceptible. It is slightly harder to spin the extensioncordwhenitisaligned inthe the galvanometer. Increasing therotationalspeedincreasesalternatingdeflectionon aligned in the north-south direction. aligned in the north-south The minimum current occurs whenthe speed is small and thecord is the galvanometer. theconditions inwhichyouDescribe hadminimumcurrent through Repeat Step 2,butaligntheextensioncord inthenorth-south Align theextensioncord intheeast-west direction. Leavingboth

Name Period Date

Chapter 38: The Atom and the Quantum Photoelectric Effect

96 Particular Waves

Purpose

To observe the photoelectric effect. Setup: 1 Lab Time: 1 Learning Cycle: concept Required Equipment/Supplies development electroscope Conceptual Level: moderate electrostatic kit, containing strips of white plastic and clear acetate and Mathematical Level: none swatches of wool and silk zinc plate (approximately 5 cm 5 cm 0.1 cm) or magnesium ribbon, Thanks to Lonnie Grimes for 10 cm long his ideas and suggestions for steel wool this lab. lamp with 200-watt bulb 60-watt ultraviolet light source (mercury vapor lamp)

Discussion Activity Albert Einstein was best known for his discovery of special and general relativity. Interestingly enough, he was awarded the Nobel Prize for something entirely different—the rules governing the photoelectric effect. In this activity, you will observe the photoelectric effect, which is the ejection of electrons from certain metals (in this case, zinc or magnesium) when exposed to light.

Procedure

Step 1: Scrub the zinc plate (or magnesium ribbon) with the steel wool Scrub metal until shiny. to make it shiny; then place the plate on the probe of the electroscope.

Step 2: Rub the white plastic strip with the wool cloth to charge the strip Observe electroscope. negatively. Touch the strip to the zinc plate on the electroscope. Notice that the leaves separate—evidence that the electroscope is charged.

Step 3: Observe the leaves of the electroscope for one minute.

1. Did the electroscope discharge by itself during that time?

Chapter 38 The Atom and the Quantum 307 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage308 308 zinc plate. Shine weakultravioletlighton watt bulbonzincplate. Shine whitelightfrom200- Laboratory ManualLaboratory (Activity 96) 4. watt lightbulbontothezincplatefrom adistanceof10cm. the electroscope negatively, asinStep 2.Shine whitelightfrom a200- charged electroscope by bombarding itwithhigh-intensitylight.Charge 3. electroscope discharges. the leavesforoneminute. Now touchthe zincplatetoseewhetherthe positively. Touch tothezincplateonelectroscope. thestrip Observe 2. that theelectroscope discharges. Step 4: Step 6: Step 5: ultraviolet light on the zinc plate again. tive. withapositivecharge Charge asinStep thestrip 5,andshinethe Step 8: 5. Now shinelightfrom a60-wattultraviolet lightsource onthezincplate. Step 7: How doestheelectroscope react tothehigh-intensitywhitelight? tothezincplate.touched thecharged acetatestrip whathappenedtotheelectroscopeDescribe from thetimeyou Why didtheelectroscope discharge whenyou touchedit? The leavesremaininthe“charged”position. The high-intensitywhitelighthaslittleornoeffectontheelectroscope. finger. leaves spreadapart.Theydropwhenthezinc plate is touched bya When thepositivelychargedstripistouchedtozincplate, electroscope onlyiftheyhaveaconductivepathtocarrythem. repelled tothegroundviayourfinger. Electronscanflowontooroffthe The excesselectronsonthenegativelychargedelectroscopeare negatively chargedelectroscope. The electroscopeleavesdrop,indicatingthatelectrons leavethe How doestheelectroscope react totheweak, ultraviolet light? Touch thezincplateonelectroscope withyour finger. Note Perhaps electrons canbe “blown away”from anegatively Rub withthesilkclothtocharge thestrip theclearacetatestrip Possibly theultraviolet lightissomehow makingtheairconduc- Recharge theelectroscope negatively ifitsleaveshavedropped.

© Addison-Wesley Publishing Company, Inc. All rights reserved. 9. 8. 7. Analysis yourscope discharged tests. during Step 9: 6. Name light. A photonofultravioletlight has more energythanaphotonofvisible have more energy—those ofvisiblelightorthoseultraviolet light? absorbs it.According toyour data, which typeofphotonsseemto energy. When aphotonisabsorbed,itsenergy isgiventowhatever adiscrete calledphotons.Eachphotoncarries of particles amountof Although lightisawavephenomenon,italsobehaves like astream Ultraviolet lighthashigherfrequenciesthanvisiblelight. ent from visiblelight? the lightdidnotcauseittodischarge. How isultraviolet lightdiffer- light, butwasdischarged by weak, ultraviolet light,the If theelectroscope couldnotbedischarged by high-intensitywhite The 200-wattlightbulbshoulddischargebetter. scope, whichlightsource shoulddischarge theelectroscope better? If theintensity electroscope. No. Ultravioletlightdoesnotdischargeapositivelycharged Does theelectroscope discharge? Data TableA In Data Table A,indicateineachbox whetherornottheelectro- of thelightisresponsible fordischarging theelectro- intensity Chapter 38 The Atom andtheQuantum Period of Date 309 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage310 310 Laboratory ManualLaboratory (Activity 96) 10. 11. ultraviolet light? tively charged, whydiditnotdischarge whenitwasexposedto electrons trapped inthezincmetal. When theelectroscope wasposi- Photons ofultraviolet lightpossessenoughenergy to “kick free” The energy tothefrequency ofaphotonisproportional ofthelight. electrons fromametalsurface. have evenlessenergythanphotonsofvisiblelightandcannoteject more energythanphotonsfromanultravioletsource.Infrared The X-raymachineisbetterbecausethephotonsitemitshaveeven scope, aninfrared heatlamporadentist’s X-ray machine? Why? Which wouldbebetteratdischarging anegativelycharged electro- back tothepositivesurface. Thefreedelectronsaredrawn net positivechargeofthezincsurface. Any electrons“kickedfree”bytheultravioletlightonlyincrease

Name Period Date

Chapter 39: The Atomic Nucleus and Radioactivity Nuclear Scattering

97 Nuclear Marbles

Purpose

To determine the diameter of a marble by indirect measurement. Setup: <1 Lab Time: 1 Learning Cycle: concept Required Equipment/Supplies development 7 to 10 marbles Conceptual Level: moderate 3 metersticks Mathematical Level: moderate

Adapted from PRISMS. Discussion

People sometimes have to resort to something besides their sense of sight to determine the shape and size of things, especially for things smaller than the wavelength of light. One way to do this is to fire particles at the object to be investigated, and to study the paths of the particles that are deflected by the object. Physicists do this with particle accelerators. Ernest Rutherford discovered the tiny atomic nucleus in his Activity gold-foil experiment. In this activity, you will try a simpler but similar method with marbles. You are not allowed to use a ruler or meterstick to measure the marbles directly. Instead, you will roll other marbles at the target “nuclear” marbles and, from the percentage of rolls that lead to collisions, determine their size. This is a little bit like throwing snowballs at a tree trunk while blindfolded. If only a few of your throws result in hits, you can infer that the trunk is small. First, use a bit of reasoning to arrive at a formula for the diameter of the nuclear marbles (NM). Then, at the end of the experiment, you can measure the marbles directly and compare your results. Fig. A When you roll a marble toward a nuclear marble, you have a certain probability of a hit between the rolling marble (RM) and the nuclear marble (NM). One expression of the probability P of a hit is the ratio of the path width required for a hit to the width L of the target area (see Figure A). The path width is equal to two RM radii plus the diameter of the NM, as shown in Figure B. The probability P that a rolling marble will hit a lone nuclear marble in the target area is

Chapter 39 The Atomic Nucleus and Radioactivity 311 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage312 312 Set upnucleartargets. Laboratory ManualLaboratory (Activity 97) rolling marble willhitoneoftheN probability ofmultiplecollisionsissmall). Thus, theprobability thatthe a hitisincreased by afactorofN and expression for of themarbles. Combine thelasttwoequationsfor nuclear marbleare equal,thenR expressions maybeequated.If theradii oftherolling marbleand and where the ratio ofthenumberhitstotrials. where Procedure number of trials T number oftrials statistically significant.Record your totalnumberofhits trials—more than200—needtobemadebefore theresults become the 60-cm-widearea, Asignificantnumberof donotcountthattrial. nuclear marbles, countjustone hit.If a rolling marble goesoutside whole target area from the release point.If arolling marblehitstwo Figure A.Roll additionalmarblesrandomly, oneatatime, toward the Step 1: If thenumber ofnuclearmarblesisincreased toN,theprobability of This is the formula you areThis istheformula now goingtotest. You now havetwoexpressions fortheprobability ofahit. These two by experimentally The probability ofahitcanalsobedetermined Place 6to9marblesinanarea 60cmwide(L R d in terms ofH, in terms + P H . r R marble diameterd T H P T L r = ______= = thewidthoftarget area. = thedistancebetween thecentersofanRMand = thenumberoftrials. = thenumberofhits = = theradius oftheRM = theradius oftheNM ———– = = ——— = ———— = ______= 2N(R NM thatare touching — T H 2R L L + 2r + r) T, (provided N, andL. + widely spacednuclearmarblesis r = = ______= d 2(R , where d L + N r) _____ is smallenoughthatthe 2TN HL is thediameterofany , and write an P, andwrite = 60cm),asin H and total

© Addison-Wesley Publishing Company, Inc. All rights reserved. 2. 1. Analysis Step 3: the marble. Show your work. Step 2: Name experiment. It ispossibletoinferthesizeofsomethingindirectlyinacollision State aconclusionyou candraw from thisexperiment. the marblejustbyrollingmarblesintoatargetarea. they gotasclosedidtothemeasuredvaluefordiameterof the directlymeasureddiameter. Studentsshouldbeimpressedthat The collisionexperimentshouldyieldadiameterthatiswithin20%of centage difference thediameter? inthesetwowaysofmeasuring anddirectlycollision experiment by measurement. What istheper- Compare your results indirectly forthediameterdetermined in the Measure thediameterofonemarble. Use from your theDiscussion formula tofindthediameterof measured diameter=______computed diameter=______Chapter 39 The Atomic Nucleus andRadioactivity Period Date 313 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PM Page 314 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PM Page 315

Name Period Date

Chapter 39: The Atomic Nucleus and Radioactivity Half-Life

98 Half-Life

Purpose

To develop an understanding of half-life and radioactive decay. Setup: <1 Lab Time: 1 Learning Cycle: concept Required Equipment/Supplies development shoe box and lid Conceptual Level: easy 200 or more pennies Mathematical Level: easy graph paper Adapted from PRISMS. Optional Equipment/Supplies

jar of 200 brass fasteners computer data plotting software

Discussion Activity

Many things grow at what is called an exponential rate: population, money bearing interest in the bank, and the thickness of paper that is repeatedly folded over onto itself. Many other things decrease exponentially: the value of money stuffed under a mattress, the amount of vacant area in a place where population is growing, and the remaining amount of a material that is undergoing radioactive decay. A useful way to describe the rate of decrease is in terms of half-life—the time it takes for the quantity to be reduced to half its initial value. For exponential decrease, the half-life stays the same. This means that the time to go from 100% of the quantity to 50% is the same as the time to go from 50% to 25% or from 25% to 12.5%, or from 4% to 2%. Radioactive materials are characterized by their rates of decay and are rated in terms of their half-lives. You will explore this idea in this activity.

Procedure

Step 1: Place the pennies in a shoe box, and place the lid on the box. Remove all pennies with head- Shake the box for several seconds. Open the box and remove all the pen- side up. nies with the head-side up. Count these and record the number in Data Table A. Do not put the removed pennies back in the box.

Step 2: Repeat Step 1 over and over until one or no pennies remain. Repeat Step 1. Record the number of pennies removed each time in Data Table A. © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 39 The Atomic Nucleus and Radioactivity 315 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage316 316 Plot yourdata. remaining eachtime. Compute numberofpennies Data TableA Laboratory ManualLaboratory (Activity 98) points. axis).Drawnumber ofshakes(horizontal asmoothlinethatbest fitsthe Step 4: number remaining, andrecord inData Table A. subtracting thenumberofpenniesremoved eachtimefrom theprevious pennies. Now, findthenumberofpennies remaining aftereachshakeby 3. 2. 1. Analysis Step 3: tance ifyou needhelp. will makeyour graph comeoutastraight line. Askyour teacher for assis- to discover what changesinthevalue axis orhorizontal ofyour vertical Step 6: the pennieswithhead sideup. Repeat untilallthefasteners are gone. table. Remove thefastenersthatare standingon theirheads, asyou did Step 5: Going Further half-life? Each shakerepresents ahalf-lifeforthepennies. What ismeant by a penny hasa50%chanceof landing with its headsideup. About 50%ofthepennies are removedafter each shake,because on eachshake? Why? Approximately whatpercent oftheremaining pennieswere removed (in thiscase50%—seeanswertoQuestion2). number ofpennies remaining isreducedbyaboutthesamepercentage The graphisa“decaycurve”forthepennies.Aftereachshake, What isthemeaningofgraph you obtained? reduced to half its original value, or fromanyvalueto half that value. A half-lifeisthe time ittakesfor the amountofsomething tobe Shake ajarofbrass paperfastenersandpourthem ontothe Graph thenumberofpenniesremaining axis)vs. (vertical the Add thenumbersofpenniesremoved tofindthetotalnumberof Plot your dataonthecomputer, usingdataplottingsoftware. Try

Name Period Date

Chapter 40: Nuclear Fission and Fusion Chain Reaction

99 Chain Reaction

Purpose

To simulate a simple chain reaction. Setup: <1 Lab Time: <1 Learning Cycle: concept Required Equipment/Supplies development 100 dominoes Conceptual Level: easy large table or floor space Mathematical Level: none stopwatch Adapted from PRISMS.

Discussion

You could give your cold to two people; they in turn could give it to two others, each of whom in turn could give it to two others. Before you knew it, everyone in school would be sneezing. You would have set off a chain reaction. Similarly, electrons in a photomultiplier tube in an electronic instrument multiply in a chain reaction so that a tiny input pro- Activity duces a huge output. Another example of a chain reaction occurs when one neutron triggers the release of two or more neutrons in a piece of uranium, and each of these neutrons triggers the release of more neutrons (along with the release of nuclear energy). The results of this kind of chain reaction can be devastating. In this activity, you will explore chain reactions using dominoes.

Procedure

Step 1: Set up a string of dominoes about half a domino length apart in Set up dominoes in a straight a straight line, as you did back in Activity 3, “The Domino Effect.” Push line. the first domino and measure how long it takes for the entire string to fall over. Also notice whether the number of dominoes being knocked over per second increases, decreases, or remains about the same as the pulse runs down the row of dominoes.

Step 2: Set up the dominoes in an arrangement similar to the one in Figure A. When one domino falls, another one or two will be knocked over. When you finish setting up all your dominoes, push the first domino over, and time how long it takes for all or most of the dominoes to fall over. Also, notice whether the number of dominoes being knocked over per unit time increases, decreases, or remains about the same. Fig. A © Addison-Wesley Publishing Company, Inc. All rights reserved. Inc. Company, Publishing © Addison-Wesley

Chapter 40 Nuclear Fission and Fusion 317 CP02_SE_LAB_Ch86-99 3/5/01 12:20 PMPage318 318 Laboratory ManualLaboratory (Activity 99) 1. Analysis 5. 4. 3. 2. arranged dominoes? dominoes, theonewithalineofdominoesorrandomly Which approach results timetoknockover intheshorter allthe process? How isthedominoreaction inStep 2dissimilartotheatomicfission (in theformofdominopotentialenergy)toallowprocesscontinue. increases overtime.Thisincreasecontinuesuntilthereisnomore“fuel” a chainreactioninwhichthenumberofatoms(dominoes)involved The dominoreactionofStep2issimilartothefissionprocessinthatit reaction inStep 2similartotheatomicfissionprocess? explosion wouldthenresult inasplitsecond.How isthedomino chain reaction continuestogrow ifthere are nocontrols. Anatomic and causethemtofission.In abigenoughpieceofuranium, this nucleus ofeachfissioninguranium atomhitotheruranium nuclei Neutronsnium atomswhentheyfission(splitapart). from the Imagine thatthedominoesrepresent theneutrons released by ura- dominoes is exhausted. Each stopswhenthepotentialenergyrepresentedby the upright What madeeachsequenceoffallingdominoes? unit timeremainsthe same. Intheprocedure of Step 2, itincreases. In the procedureofStep1, the numberofdominoesknockedoverper change ineachprocedure? How didthenumberofdominoesbeingknockedover perunittime it proceeds. since thereaction“grows”—involvesmoredominoesperunittime—as The procedureof Step 2willknock over the dominoes inashortertime, fission processdoesnothave. (dominoes tendtofallforward)that the it hasadirectional property over by onedomino)islessthan the neutronmultiplication factor, and it is slower, the “multiplicationfactor”(number of dominoes tipped The dominoreactioninStep2is dissimilar tothe fission processinthat

Appendix: Significant Figures and Uncertainty in Measurement

Units of Measurement cision of your measuring instruments cannot be avoided. All measurements consist of a unit that tells what Uncertainty in a measurement can be illus- was measured and a number that tells how many trated by the two different metersticks in Figure A. units were measured. Both are necessary. If you The measurements are of the length of a tabletop. say that a friend is going to give you 10, you are Assuming that the zero end of the meterstick has telling only how many. You also need to tell what: been carefully and accurately positioned at the left 10 fingers, 10 cents, 10 dollars, or 10 corny jokes. If end of the table, how long is the table? your teacher asks you to measure the length of a piece of wood, saying that the answer is 36 is not correct. She or he needs to know whether the length is 36 centimeters, feet, or meters. All measurements must be expressed using a number and an appropriate unit. Units of measurement are more fully covered in Appendix A of the Conceptual Physics text.

Numbers

Two kinds of numbers are used in science—those that are counted or defined and those that are measured. There is a great difference between a counted or defined number and a measured number. The exact value of a counted or defined number can be stated, but the exact value of a measured number cannot be known. For example, you can count the number of chairs in your classroom, the number of fingers on Fig. A your hand, or the number of nickels in your pocket with absolute certainty. Counted numbers are not subject to error (unless the number counted is so The upper scale in the figure is marked off in large that you can’t be sure of the count!). centimeter intervals. Using this scale, you can say Defined numbers are about exact relations, with certainty that the length is between 82 and 83 defined to be true. The exact number of seconds in centimeters. You can say further that it is closer to an hour and the exact number of sides on a square 82 centimeters than to 83 centimeters; you can are examples. Defined numbers also are not sub- estimate it to be 82.2 centimeters. ject to error. The lower scale has more subdivisions and has Every measured number, no matter how care- a greater precision because it is marked off in fully measured, has some degree of uncertainty. millimeters. With this meterstick, you can say What is the width of your desk? Is it 98.5 centime- that the length is definitely between 82.2 and ters, 98.52 centimeters, 98.520 centimeters, or 82.3 centimeters, and you can estimate it to be 98.5201 centimeters? You cannot state its exact 82.25 centimeters. measurement with absolute certainty. Note how both readings contain some digits that are exactly known, and one digit (the last one) Uncertainty in Measurement that is estimated. Note also that the uncertainty in the reading of the lower meterstick is less than that The uncertainty in a measurement depends on the of the top meterstick. The lower meterstick can precision of the measuring device and the skill of give a reading to the hundredths place, and the top the person who uses it. There are nearly always meterstick to the tenths place. The lower meter- some human limitations in a measurement. In stick is more precise than the top one. addition, uncertainties contributed by limited pre-

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No measurements are exact. A reported mea- Examples: surement conveys two kinds of information: (1) 43 two significant figures the magnitude of the measurement and (2) the 43.0 three significant figures precision of the measurement. The location of the 43.00 four significant figures decimal point and the number value gives the 0.00200 three significant figures magnitude. The precision is indicated by the num- 0.40050 five significant figures ber of significant figures recorded. Rule 5: In a number that has no decimal point, and Significant Figures that ends in one or more zeros (such as 3600), the zeros that end the number may or may not be sig- Significant figures are the digits in any measure- nificant. The number is ambiguous in terms of sig- ment that are known with certainty plus one digit nificant figures. Before the number of significant that is uncertain. The measurement 82.2 centime- figures can be specified, further information is ters (made with the top meterstick in Figure A) has needed about how the number was obtained. If it three significant figures, and the measurement is a measured number, the zeros are probably not 82.25 centimeters (made with the lower meter- significant. If the number is a defined or counted stick) has four significant figures. The right-most number, all the digits are significant (assuming digit is always an estimated digit. Only one esti- perfect counting!). mated digit is ever recorded as part of a measure- Confusion is avoided when numbers are ment. It would be incorrect to report that, in Figure expressed in scientific notation. All digits are taken A, the length of the table as measured with the to be significant when expressed this way. lower meterstick is 82.253 centimeters. This five- Examples: significant-figure value would have two estimated 3.6 105 two significant figures digits (the 5 and 3) and would be incorrect because 3.60 105 three significant figures it indicates a precision greater than the meterstick 3.600 105 four significant figures can provide. 2 10–5 one significant figure Standard rules have been developed for 2.0 10–5 two significant figures writing and using significant figures, both in 2.00 10–5 three significant figures measurements and in values calculated from measurements. Rule 1: In numbers that do not contain zeros, all the digits are significant. Examples: 3.1428 five significant figures 3.14 three significant figures 469 three significant figures

Rule 2: All zeros between significant digits are significant. Examples: 7.053 four significant figures 7053 four significant figures 302 three significant figures

Rule 3: Zeros to the left of the first nonzero digit serve only to fix the position of the decimal point and are not significant. Examples: 0.0056 two significant figures 0.0789 three significant figures 0.000001 one significant figure

Rule 4: In a number with digits to the right of a decimal point, zeros to the right of the last nonzero digit are significant.

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Rounding Off multiplication and division, and for addition and subtraction. A calculator displays eight or more digits. How do Multiplication and Division For multipli- you round off such a display of digits to, say, three cation and division, an answer should have the significant figures? Three simple rules govern the number of significant figures found in the number process of deleting unwanted (nonsignificant) dig- with the fewest significant figures. For the density its from a calculator number. example above, the answer would be rounded off Rule 1: If the first digit to be dropped is less than 5, to one significant figure, 0.7 gram per cubic cen- that digit and all the digits that follow it are simply timeter. If the mass were measured to be 2.0 dropped. grams, and if the volume were still taken to be 3 cubic centimeters, the answer would still be Example: rounded to one significant figure, 0.7 gram per 54.234 rounded off to three significant figures cubic centimeter. If the mass were measured to be becomes 54.2. 2.0 grams and the volume to be 3.0 or 3.00 cubic centimeters, the answer would be be rounded off Rule 2: If the first digit to be dropped is a digit to two significant figures: 0.67 gram per cubic greater than 5, or if it is a 5 followed by digits other centimeter. than zero, the excess digits are all dropped and the last retained digit is increased in value by one unit. Study the following examples. Assume that the numbers being multiplied or divided are mea- Example: sured numbers. 54.36, 54.359, and 54.3598 rounded off to three Example A: significant figures all become 54.4. 8.536 0.47 = 4.01192 (calculator answer) Rule 3: If the first digit to be dropped is a 5 not fol- The input with the fewest significant figures lowed by any other digit, or if it is a 5 followed only is 0.47, which has two significant figures. by zeros, an odd-even rule is applied. That is, if the Therefore, the calculator answer 4.01192 last retained digit is even, its value is not changed, must be rounded off to 4.0. and the 5 and any zeros that follow are dropped. But if the last digit is odd, its value is increased by Example B: one. The intention of this odd-even rule is to aver- 3840 285.3 13.459516 (calculator answer) age the effects of rounding off. The input with the fewest significant figures is Examples: 3840, which has three significant figures. Therefore, the calculator answer 13.459516 54.2500 to three significant figures becomes 54.2. must be rounded off to 13.5. 54.3500 to three significant figures becomes 54.4. Example C: Significant Figures and 360.0 3.000 12 (calculator answer) Calculated Quantities Both inputs contain four significant figures. Therefore, the correct answer must also contain Suppose that you measure the mass of a small four significant figures, and the calculator wooden block to be 2 grams on a balance, and you answer 12 must be written as 12.00. In this case, find that its volume is 3 cubic centimeters by pok- the calculator gave too few significant figures. ing it beneath the surface of water in a graduated Addition and Subtraction For addition or cylinder. The density of the piece of wood is its subtraction, the answer should not have digits mass divided by its volume. If you divide 2 by 3 on beyond the last digit position common to all the your calculator, the reading on the display is numbers being added and subtracted. Study the 0.6666666. It would be incorrect to report that the following examples: density of the block of wood is 0.6666666 gram per cubic centimeter. To do so would be claiming a Example A: degree of precision that is not warranted. Your 34.6 answer should be rounded off to a sensible num- 17.8 ber of significant figures. 15 The number of significant figures allowable in a 67.4 (calculator answer) calculated result depends on the number of significant figures in the data used to obtain the result, The last digit position common to all numbers and on the type of mathematical operation(s) used is the units place. Therefore, the calculator to obtain the result. There are separate rules for answer of 67.4 must be rounded off to the units place to become 67.

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Example B: Percentage Error 20.02 20.002 Uncertainty and error can easily be confused. 20.0002 Uncertainty gives the range within which the 60.0222 (calculator answer) actual value is likely to lie relative to the measured value. It is used when the actual value is not known The last digit position common to all numbers for sure, but is only inferred from the measure- is the hundredths place. Therefore, the calcula- ments. Uncertainty is reflected in the number of tor answer of 60.0222 must be rounded off to significant figures used in reporting a measure- the hundredths place, 60.02. ment. Example C: The error of a measurement is the amount by which the measurement differs from a known, 345.56 245.5 100.06 (calculator answer) accepted value as determined by skilled observers The last digit position common to both num- using high-precision equipment. It is a measure of bers in this subtraction operation is the tenths the accuracy of the method of measurement as place. Therefore, the answer should be rounded well as the skill of the person making the measure- off to 100.1. ment. The percentage error, which is usually more important than the actual error, is found by divid- Percentage Uncertainty ing the difference between the measured value and the accepted value of a quantity by the If your aunt told you that she had made $100 in the accepted value, and then multiplying this quotient stock market, you would be more impressed if this by 100%. gain were on a $100 investment than if it were on a % error = $10 000 investment. In the first case, she would accepted value measured value have doubled her investment and made a 100% ______ 100% gain. In the second case, she would have made a accepted value 1% gain. For example, suppose that the measured value In laboratory measurements, the percentage of the acceleration of gravity is found to be uncertainty is usually more important than the 9.44 m/s2. The accepted value is 9.80 m/s2. The dif- size of the uncertainty. Measuring something to ference between these two values is (9.80 m/s2) within 1 centimeter may be good or poor, depend- (9.44 m/s2), or 0.36 m/s2. ing on the length of the object you are measuring. Measuring the length of a 10-centimeter pencil to ______0.36 m/s2 1 centimeter is quite a bit different from measur- % error 9.80 m/s2 100% ing the length of a 100-meter track to the same 1 centimeter. The measurement of the pencil 3.7% shows a relative uncertainty of 10%. The track measurement is uncertain by only 1 part in 10 000, or 0.01%.

322 Appendix