Exercises in Physics Jennifer Bond Hickman Needham, Massachusetts Upper Saddle River, New Jersey Glenview, Illinois To my grandfather, C. Lawrence Bond When I was 10 years old, you paid me 10¢ to write a book for you. I’ve finally finished it! Illustrations by Jennifer Bond Hickman. Cover Photograph: Motor Press Agent/Superstock, Inc. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where such a designation appears in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps (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. 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ISBN 0-13-054275-X 26 V031 13 12 11 Contents Preface to Students: 11 Simple Harmonic Motion 149 Welcome to Physics! iv 11-1 Springs 149 1 Motion 1 11-2 Pendulums 153 1-1 Speed, Velocity, and 12 Waves and Sound 159 Acceleration 1 12-1 Wave Motion 159 1-2 Free Fall 8 12-2 Doppler Effect 161 12-3 Standing Waves 165 2 Vectors and Projectiles 15 2-1 Vectors and Scalars 15 13 Reflection and Refraction 171 2-2 Projectile Motion 21 13-1 The Speed of Light 171 13-2 Reflection 173 3 Forces 29 13-3 Refraction 177 3-1 Forces and Acceleration 29 3-2 Friction 35 14 Lenses, Diffraction, and 3-3 Statics 38 Interference 183 3-4 Pressure 44 14-1 Lenses, Telescopes, and Magnifying Glasses 183 4 Momentum 51 14-2 Eyeglasses 189 4-1 Impulse and Momentum 51 14-3 Diffraction and Interference 192 4-2 Conservation of Momentum 55 15 Electrostatics 197 5 Energy and Machines 63 15-1 Electrostatic Force 197 5-1 Work and Power 63 15-2 Electric Field 200 5-2 Energy 66 15-3 Electrical Potential 5-3 Machines and Efficiency 72 Difference 203 6 Circular and Rotational Motion 81 16 Direct Current Circuits 209 6-1 Centripetal Acceleration and 16-1 Current and Resistance 209 Force 81 16-2 Capacitance 212 6-2 Torque 87 16-3 Power 214 6-3 Moment of Inertia and 16-4 Series and Parallel Circuits 217 Angular Momentum 91 17 Magnetism and Electromagnetic 7 Law of Universal Gravitation 97 Induction 225 7-1 Gravitational Force 97 17-1 Magnetic Forces and Fields 225 7-2 Gravitational Acceleration 101 17-2 Electromagnetic Induction 227 7-3 Escape Speed 104 18 Modern Physics 233 8 Special Relativity 109 18-1 The Atom and the Quantum 233 8-1 Time Dilation 109 18-2 The Photoelectric Effect 236 8-2 Relativistic Length and 18-3 Energy Level Diagrams 239 Energy 113 18-4 Radioactivity 241 9 Solids, Liquids, and Gases 119 Appendix A: Working With 9-1 Density 119 Numbers 247 9-2 Solids 121 Significant Figures 9-3 Liquids 124 Unit Conversions 9-4 Gases 130 Some Simple Trigonometry 10 Temperature and Heat 135 Relationships 10-1 Temperature and Expansion 135 Some Common Prefixes 10-2 Heat 140 Appendix B: Selected Answers 249 iii Welcome to Physics! Studying physics is exciting because it can help you answer many questions about how and why our world works. Your workbook is designed to take some “real-life” situations and examine them with the use of equations, a task often referred to as problem solving. Problem solving, however, is more than just solving numerical exercises by doing calculations. Using mathematics is only one way to obtain a solution. Another effective method of problem solving involves drawing on conceptual understanding to explain how the world works and applying those concepts in the laboratory. Like scientists, we perform experiments to test our hypotheses. Until we can understand the concepts and have the opportunity to make our own discoveries, the numbers and equations of physics are meaningless. In the words of Paul G. Hewitt, author of Conceptual Physics, “Formulas [should be used] as guides to thinking. We [must] learn to conceptualize before we learn to compute.” This book is not meant to stand alone. It is not meant to replace your physics text, the laboratory work that you do, or your physics teacher. Its purpose is to reinforce the concepts that you have already learned in class and to give you the opportunity to try some calculations with your teacher’s help. If you have had difficulty solving word problems in the past, rely on your conceptual understanding of the physics to reason out what should be happening before beginning your mathematical solution. The procedure outlined in the next section will lead you step-by-step through the exercises and make learning to do simple computations a little easier. How to Use This Book As you begin to use this book, you will discover that the word problem has been replaced with the word exercise. A physics exercise does not really become a problem until you accept the challenge it offers and attempt to solve it. Once you have chosen to make it your problem, you have a personal interest in finding the solution. Each chapter of this workbook is divided into two or more topic sections that begin with some physics theory. This theory section provides a very brief review of the concepts and equations your teacher has discussed in class, and is not an introduction to new material. It is presumed that you have already learned everything in the theory section before beginning the exercises. This review is simply a reminder and a place to find all the equations you need. Following the theory, there is a section called Solved Examples, where the theory is applied to exercises similar to those you will be expected to solve later. Solutions are organized to make it easy to follow a calculation from beginning to end. Most solved examples are in the following format. iv Given: States the known values Unknown: Lists the unknown you are in the exercise. looking for. Original equation: Shows the equation in its original form. Solve: Shows the equation set up in terms of the unknown, substitutes the numerical values, and solves for the unknown. The answer is then written with the correct units and shown in boldface type for easy identification. A section of Practice Exercises allows you to apply some of the skills you have learned to new situations. For more practice, at the end of each chapter there is a section of Additional Exercises, which require the same level of understanding as the Practice Exercises. The final section, called Challenge Exercises for Further Study, contains exercises requiring more complex calculations. Challenge Exercises are intended for you to use after you have mastered the skills used in earlier exercises and are anxious to take on some more rigorous computations. At the end of the workbook, some Selected Answers will allow you to check your progress. Using the Right Recipe Solving physics exercises is much like baking a cake. The first time you try to do it, you must read the recipe very carefully and use exactly the ingredients listed. The next time, you are a little less nervous about how well the cake will turn out. Pretty soon you can make the cake without having to read the recipe at all. You eventually become so comfortable making cakes that you are able to experiment by adding ingredients in a different order or changing the recipe slightly to make the cake even better. When solving physics exercises, you will find it easy to follow the prescribed “recipe” shown in the Solved Examples. After trying a few exercises, you will have started to develop a strategy for constructing your solution that you can retain throughout the entire book. As you get better and better at doing calculations and you develop a greater conceptual understanding of the physics involved, you may even come up with an alternative method of solving an exercise that is different from the one used in this book. If so, congratulations! You have done just what the physicist does when he or she tries to find a solution. Be sure to show your teacher and classmates your alternative approach. It is valuable to look at many different solutions to the same exercise. An Alternative to Counting on Your Fingers Early scientists had to make all of their calculations by hand. Later, the slide rule made calculations a little quicker. Today’s tool is the hand-held pocket calculator. To save time, you are encouraged to do your calculations with the use of a calculator, but be sure that you first understand why you are doing them. Remember, it’s important to know how to operate without a calculator as well. Many students rely so heavily on their calculator that they begin to lose the skill of doing calculations by hand. It is extremely important to be able to add, subtract, multiply, divide, and square numbers. You should v practice working with exponents (called scientific notation) and estimating answers to the nearest power of ten because you may not always have a calculator handy! How Much is Too Much? When making measurements, you may have measurement tools that allow you only a certain degree of precision. For example, you may be able to measure your friend’s height to the nearest millimeter, but estimating it any closer is difficult.