Monday, 5 September, Lecture 1, Introduction to Physics
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4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 1 OF 50 College Physics 1 Assignments
Website: http://people.rit.edu/abesps1
PLEASE SIGN THE ATTENDANCE SHEET
GO TO MY WEBSITE… https://people.rit.edu/abesps1 www.masteringphysics.com 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 2 OF 50 College Physics 1 (211) Instructor: Dr. Alan Entenberg, Office 8-3206, 475-5148 (office), 475-2421 (Physics Dept.), Email [email protected] Website for course www.rit.edu/~abesps1 Website for HW www.masteringphysics.com
Schedule Tentative Lecture Workshop Workshop Day Office hours* Sect 04 and 05 Section 04 Section 05 Mon 2:00 – 2:50 PM 4:00 – 6:00 Noon, 8-3305 Tues 2:00 – 2:50 PM 4:00 – 6:00 PM, 8-3345 6:00 – 8:00 PM, 8-3345 Wed 2:00 – 2:50 PM Thursday 2:00 – 2:50 PM 4:00 – 6:00 PM, 8-3345 6:00 – 8:00 PM, 8-3345 Friday** 2:00 – 2:50 PM (Bates Study Center, COS)
*Office hours: You are welcome to come by at anytime. One on one meetings in my office can be scheduled if you are unable to make the above posted office hours. **Office hour will be in the College of Science Bates Study Center. The Center is open every day and is staffed by physics faculty, graduate students, and upper level physics majors. The schedule of the Center is posted on the door. MORE HELP from Academic Support Center: www.rit.edu/asc See this link for tutoring in Math and Physics in room 01-2371. Monday (10-7), Tuesday (10-9), Wednesday (10-9), Thursday (10-4), Friday (10-2)
Course Prerequisites: Competency in algebra, geometry, and trigonometry and passing grade in College Physics 1
Course Goals (1) Understand and use derived concepts of force, energy, and momentum based on the fundamental concepts of matter, space, and time. (2) Describe motion of an object in horizontal and/or “free-fall” motions near the surface of the earth.
Course Text: COLLEGE PHYSICS: A Strategic Approach by Knight, Jones, and Field, Pearson/Addison Wesley, 2007. Chapter 1 Concepts of Motion and Mathematical Background Read: Sections 1 – 7 Chapter 2 Motion in One Dimension Read: Sections 1 – 7 Chapter 3 Vectors and Motion in Two Dimensions Read: Sections 1 – 8 Chapter 4 Forces and Newton’s Laws of Motion Read: Sections 1 – 8 Chapter 5 Applying Newton’s Laws Read: Sections 1 – 5, 6 – 8 wait! Chapter 6 Circular Motion, Orbits, and Gravity Read: Sections 1 – 7 Chapter 7 Rotational Motion Read: Sections 1 – 6 Chapter 8 Equilibrium and Elasticity Read: Sections 1 – 4 Chapter 9 Momentum Read: Sections 1 – 7 Chapter 10 Energy and Work Read: Sections 1 – 10
Homework: You will be assigned about ten problems each week. Some of these will be from the HW website www.masteringphysics.com associated with your text. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 3 OF 50 Grading (VERY TENTATIVE WEIGHTING): A ( > 90%) B ( > 80%) C ( > 65%) D ( > 55%) Homework 15 % Exams 1, 2, 3 (lowest replaced by Final Exam) 50 % Exam1 - March 31, 2008 Final Exam 20 % Cumulative Activities – 15 % Attendance ??? Bonus points (for catching my mistakes made in class) Each point worth about 0.1% on course average).
A FORMULA SHEET WILL BE SUPPLIED FOR EACH EXAM and FOR the joint common FINAL EXAM.
Makeup policy--- It is not possible to makeup an exam. The lowest exam is replaced by the final exam. MAKEUP MUST BE SCHEDULED IN ADVANCE IMMEDIATE NOTIFICATION OF A VERIFIABLE ILLNESS Your academic advisor must also contact me and explain!
It is not possible to makeup an activity. The lowest activity will be dropped. WHEN POSSIBLE, AN OPPORTUNITY TO DO THE ACTIVITY WILL BE GIVEN. There is a automatic online deduction of 10% for each day that a homework assignment is late. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 4 OF 50
Lecture/ Date Schedule and Equipment Needs Workshop Introduction to the course. Discuss units; conversion of units; dimensional analysis; displacement; average velocity; average acceleration; and L1 3/10/08 motion diagrams (1D only). “Estimation” W1 3/11/08 “Unit conversion” “Basic Measurements and Uncertainties Homework” due Discuss uncertainties and error analysis. W2 3/13/08 “Basic Measurements and Uncertainties” Need: 14 aluminum cylinders of varying volumes, 7 triple beam balances, 7 rulers, 7 electronic calipers Discuss instantaneous velocity; instantaneous acceleration; position versus time, velocity versus time, and acceleration versus time graphs; L2 3/17/08 trigonometry; vectors and scalars; and 2D kinematics. “Position-Time and Velocity-Time graphs” “Logger Pro Tutorial” due W3 3/18/08 “Introduction to LabPro and the Force Sensor” Need 14: force sensors with hook, 50 g hangers, mass sets “Acceleration and Deceleration (1D)” W4 3/20/08 “Motion diagrams and Motion Graphs” Discuss free-body diagrams; the gravitational force; the normal force; the tension force; the frictional force; and the spring force. Use “One L3 3/24/08 Dimensional Forces, Translational Equilibrium, Free Body Diagrams” activity as part of discussion. “Ball Drop Homework” due DEMO: “Penny/feather”, need apparatus with pump W5 3/25/08 DEMO: two balls – one dropped and the other fired horizontally, need apparatus “Ball Drop” Need 14: motion detectors and small, well inflated soccer balls “Vector Algebra and Static Translational Equilibrium Homework” due W6 3/27/08 “Vector Algebra and Static Translational Equilibrium” Need: 14 force tables (already set up), 14 mass sets, lots of small 1 g, 2 g, etc. masses for use in determining uncertainty in hanging mass L4 3/31/08 Exam 1. Discuss Newton’s laws. “Interaction Forces” W7 4/1/08 Need: 2 force sensors attached to low friction carts, one 500 g mass bar, and one 1.2 m short track per group “Newton’s Second Law” W8 4/3/08 Need 14 set ups: accelerometer attached to force sensor which is attached to a low friction cart (arrow on accelerometer points away from force sensor hook), short track L5 4/7/08 Discuss uniform circular motion; universal gravitation; and non-uniform circular motion. W9 4/8/08 “Newton’s Second Law Problems” “Motion in 2D (circular track)” W10 4/10/08 Need 42: rulers and protractors L6 4/14/08 Exam 2. Discuss rotational kinematics. W11 4/15/08 “Uniform Circular Motion” Need 14: centripetal force apparatus (already set up), stop watches, rulers, 50 g hangers, mass sets, 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 5 OF 50 Need: 7 digital scales, lots of small 1 g, 2 g, etc. masses for use in determining uncertainty in hanging mass “Rotational Kinematics” W12 4/17/08 Need 14: RMS with aluminum disk attached, crash box Need: 7 blue mass sets, spools of string, scissors Discuss torque; center-of-gravity; moment of inertia; Newton’s second law in rotational form; torque and equilibrium; the spring force; and stress and L7 4/21/08 strain. Use “Torque Calculation” activity as part of discussion. “Torque and Moment of Inertia” W13 4/22/08 Need 14: RMS with aluminum disk attached, crash box, calipers, rulers Need: 7 blue mass sets, 7 digital scales, and spools of string “Torque and Equilibrium” W14 4/24/08 Need 14: meter sticks with drilled holes, 0-5 N and 0-50 N spring scales, 50 g hangers Need: spools of string, scissors, masking tape Discuss impulse; linear momentum; conservation of linear momentum; inelastic collisions; angular momentum; and conservation of angular L8 4/28/08 momentum. “Angular Momentum - Qualitative” W15 4/29/08 Need: 7 low friction bike wheels, 7 platforms, two 500 g mass bars Discuss work; kinetic energy; work-kinetic energy theorem; work done by gravity; work done by an applied force; and conservative forces. Use W16 5/1/08 “Conservative and Non-conservative Forces” activity as part of discussion. L9 5/5/08 Exam 3. Discuss potential energy; mechanical energy; mechanical energy conservation; work done by variable forces; and elastic potential energy. W17 5/6/08 “Energy Graphs” DEMO: “Rotational energy and Rolling Motion” Need set up of two inclined planes; hoop/disk of same radius rolling down one incline and back up another. W18 5/8/08 “Energy Conservation” Need 14: RMS with aluminum disk attached, crash box Need: 7 blue mass sets, spools of string, scissors L10 5/12/08 Discuss energy in collisions and power. 5/13/08 “Rotational Collision” W19 Need 14: RMS with two aluminum disks and specialty brass pin, rulers Need: 7 digital scales W20 5/15/08 Open (“One Dimensional Collision”?) 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 6 OF 50
Notation
Components F + and F + X Y
Magnitude and Angle F = | F | > 0 and + 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 7 OF 50 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 8 OF 50 What is a single “force” on a given object by a given source?
A force is a “push” or a “pull” on an object of mass M.
Object of mass M
Push Pull F FF Force is a “vector quantity.” Force has “magnitude” Force has “direction”
Note: The “tail” of the force vector will usually show where the force acts on the object. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 9 OF 50
Two types of forces
1. Contact forces One object touches another object
Normal force FN N
Tension force F t T
Friction force
o Static friction fs
o Kinetic friction or sliding friction fk 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 10 OF 50 Two types of forces continued
2. Action at a distance forces force seems to act through “empty space”
o Gravitational force
Fg Wt " weight of object "
o Electric and magnetic forces “interaction forces between charges”
Fundamental particles electron, proton, neutron More fundamental proton and neutron are composites of quarks
o Nuclear (strong) and nuclear (weak) forces 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 11 OF 50
PRINCIPLE OF LINEAR SUPERPOSITION FOR FORCES
What is a “net force” on an object? Fnet F F1 F2 F3 F4 ⋯
All of the forces on an object add instantaneously to a single net force. The “resultant force” or “net force” is obtained in the same way a resultant displacement vector is obtained.
NOTE: ZERO NET FORCE DOES NOT MEAN THERE ARE NO FORCES ON AN OBJECT!!
Parallelogram rule for only 2 forces
Pretend force vectors are same as displacement vectors when adding 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 12 OF 50
NEWTON’S FIRST LAW: ENABLES US TO DETERMINE WHETHER THERE IS A “NET FORCE” ON AN OBJECT. (paraphrased below by abe)
EXPERIMENTAL FACT “An object in motion (constant velocity) stays in motion (constant velocity) unless acted upon by a net force.” The constant velocity is non-zero. EXPERIMENTAL FACT “An object at rest stays at rest unless acted upon by a net force.” The constant velocity can even be zero.
“If there is a net force on an object, the velocity must change, i.e., the object must accelerate.” 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 13 OF 50
NEWTON’S THIRD LAW: ALL FORCES OCCUR IN PAIRS!! . “THERE IS NO SUCH THING AS AN ISOLATED FORCE!!” 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 14 OF 50
Ball #1 moves to the right toward Ball #2
Ball #2 is initially at rest
#1 #2
Force on #1 by #2 Force on #2 by #1
Note: Magnitudes are equal
#1 F = F 21 12 #2
At the instant of contact, each ball exerts a force on the other. The pair of forces is called an “action and reaction” pair of forces. Ignore gravitational effects for this example.
QUESTION: CAN YOU TOUCH SOMEONE WITHOUT BEING TOUCHED YOURSELF?
Your Name (Print): Date: Group Members: Group: 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 15 OF 50 Interaction Forces (Modified)
You will explore the relationship between the forces that two interacting objects exert on each other. A force is a push or pull that one body exerts on another. When two bodies interact, they exert forces on each other. When you push down on the table with your hand, the table pushes up on your hand, an effect you can feel. This pushing force is an example of a contact force since the two objects are in contact with each other. As another example, when you drop a pencil, the earth exerts a gravitational force on the pencil pulling it vertically down while the pencil exerts an upward force on the earth. This gravitational force is an example of a non-contact force (or a so called “action-at- a-distance” force) since the two objects do not have to be in physical contact in order to exert the force. Isolated forces do not exist; forces always exist in pairs. Nothing can exert a force without having a force exerted on it.
PREDICTION Two objects, a truck on the left and a car on the right, can move on a horizontal surface. When the truck and car are in contact, there is a horizontal contact force between them, meaning that the truck pushes on the car and the car pushes on the truck. All motion is along a straight line. You are to compare the magnitudes of these two forces in the different situations described in Table 1. In parts (a) through (d), assume the vehicles are of equal weight. In parts (e) through (i), assume the truck is much heavier than the car. Discuss and debate your predictions with the others in your group until you reach a consensus. Record the group’s consensus decision in the second column of Table 1 using “less than” (<), “greater than” (>) or “equal to” (=) signs. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 16 OF 50 Name ______Contact Force on truck by car Contact Force on car by truck Table 1: Summary of Predictions and Measurements regarding PREDICTION MEASUREMENT Explain Reasoning below magnitudes of forces (insert the correct algebraic sign: >, = or <) Magnitude of the (performed after Attach at least one graphical measurement Force on truck by all Predictions from your team’s observations car is are recorded) ( > , = or < ) the magnitude of the Force on car by truck
(a) Equal weights; truck (active) pushes against car (passive) but there is
no motion.
(b) Equal weight; car (active) pushes against truck (passive) but there is no motion.
(c) Equal weight; Truck (more active) pushes car (passive) to the right,
both are moving to the right.
(d) Equal weight; Car (more active) pushes truck (passive) to the left, both
are moving to the left.
(e) Heavy truck (active) pushes on light car (passive) to the right but there is no motion.
(f) Light car (active) pushes on heavy truck (passive) to the left but there is no motion.
(g) Heavy truck (more active) moves to the right and collides with a light car
(passive) that is at rest (in neutral). They separate after the collision.
MEASUREMENT: Connect two force sensors to CH1 and CH2 of the LabPro interface. Connect the LabPro interface to the computer. . Define the truck as the sensor connected to CH1, and the car as the sensor connected to CH2. . Be sure the slide switch on the force sensors is at +50 N. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 17 OF 50 Open the Logger Pro software. Manually set up the sensors if they do not auto-ID. . Reverse the sign of sensor #1 (Experiment->Set Up Sensors->Show All Interfaces, left click the CH1 sensor icon, check Reverse Direction). . Calibrate the sensors using weights corresponding to approximately 1000 g and 500 g suspended from the hook attached to each sensor. Remember to include the mass of the hanger and to convert the mass in grams to a force in Newtons. Replace the hook on each force sensor with a rubber bumper provided by your instructor. . Zero both sensors (Ctrl-0) and check the zero by collecting data with the sensors horizontal and not touching. Push on each bumper with your hand while collecting data to see how data is collected and displayed. . Each force sensor should be securely attached to a low-friction cart that is free to roll along the 1.2 m track. Be sure that neither cart rolls off the end of the track. Now set up experiments to check the results you predicted in parts (a) to (i). Record all your observations regarding the magnitudes of the forces in the third column in the Table 1. (a) - (b) Place the force sensors on the table and push them together in such a way that there is no movement. Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in Table 1. Using Print Graph, Print one graph per group for either part (a) or part (b); append the last names of all members of your group to the bottom of the graph. Be sure the graph includes a title (right click the graph ->Graph Options) and a description. (c) Push on the truck to the right while it is in contact with the car. Hold the car firmly - imagine the car’s brakes are applied, yet the truck still moves the car to the right. Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in Table 1. (d) Push the car to the left while it is in contact with the truck. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 18 OF 50 Hold the truck firmly - imagine the truck’s brakes are applied, yet the car still moves the truck to the left. Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in Table 1.
Add at least one 500 g mass bar to the cart attached to sensor #1 (the truck). Check parts (e) and (f) of your predictions. (e) - (f) Repeat measurements similar to parts (a) and (b). Record the results in Table 1. For one of the experiments (e) or (f), p rint one graph per group (append the last names of all members of your group to the bottom of the graph). Be sure the graph includes a title and a description.
To check your predictions during collisions when the truck and/or the car are initially moving, you must decrease the time of data collection to 5 s and increase the data sampling rate to 1000 samples/second. Click Experiment -> Data Collection. Change the length of data collection to 5 s and the sampling rate to 1000 samples per second. Click Done. Check parts (g) - (i) of your predictions. The graphical display will take a few moments before displaying due to the large amount of data collected. (g) - (i) Gently push the carts as required. Collect data and Autoscale. Change the minimum and maximum values on the time axis so the display includes the time interval from just before the collision to a time just after the collision. To change the maximum value on the time axis, place the cursor near enough to the largest number on the horizontal scale until the cursor changes shape to an “I”, click, then type the appropriate number and hit Enter. Repeat for the smallest number on the horizontal axis. Compare the magnitude of the forces and record your observations in Table 1. Remember to return the time axis to the 0 s to 5 s range after each experiment. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 19 OF 50 For one of the experiments (g) through (i), p rint one graph per group (append the last names of all members of your group to the bottom of the graph). Be sure the graph includes a title and a description.
Reconcile your predictions with your measurements: In what ways were your predictions different from your measurements? In what ways were they the same?
This activity is designed to help you learn something about the forces that two objects exert on each other. The result is known as Newton’s Third Law of Motion. Use the space below to write a clear summary about what you have discovered regarding the interaction force between two objects. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 20 OF 50 Your Name (Print): Date: Group Members: Group:
Interaction Forces
You will explore the relationship between the forces that two interacting objects exert on each other. A force is a push or pull that one body exerts on another. When two bodies interact, they exert forces on each other. When you push down on the table with your hand, the table pushes up on your hand, an effect you can feel. This pushing force is an example of a contact force since the two objects are in contact with each other. As another example, when you drop a pencil, the earth exerts a gravitational force on the pencil pulling it vertically down while the pencil exerts an upward force on the earth. This gravitational force is an example of a non-contact force (or a so called “action-at-a-distance” force) since the two objects do not have to be in physical contact in order to exert the force. Isolated forces do not exist; forces always exist in pairs. Nothing can exert a force without having a force exerted on it.
PREDICTION Two objects, a truck on the left and a car on the right, can move on a horizontal surface. When the truck and car are in contact, there is a horizontal contact force between them, meaning that the truck pushes on the car and the car pushes on the truck. All motion is along a straight line. You are to compare the magnitudes of these two forces in the different situations described in Table 1. In parts (a) through (d), assume the vehicles are of equal weight. In parts (e) through (i), assume the truck is much heavier than the car. Discuss and debate your predictions with the others in your group until you reach a consensus. Record the group’s consensus decision in the second column of Table 1 using “less than” (<), “greater than” (>) or “equal to” (=) signs. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 21 OF 50 Table 1: Summary of Predictions and Measurements regarding magnitudes of forces (insert the correct algebraic sign: >, = or <) PREDICTION Magnitude of the force of MEASUREMENT car on truck is (>, = or (performed after <) all Predictions the magnitude of the are recorded) force of truck on car (a) Equal weight; truck pushes against car but there is no motion. (b) Equal weight; car pushes against truck but there is no motion. (c) Equal weight; truck pushes car to the right, both are moving to the right. (d) Equal weight; car pushes truck to the left, both are moving to the left. (e) Heavy truck pushes on light car to the right but there is no motion. (f) Light car pushes on heavy truck to the left but there is no motion. (g) Heavy truck moves to the right and collides with a light car that is at rest (in neutral). They separate after the collision. (h) Light car moves to the left and collides with a heavy truck that is at rest (in neutral). They separate after the collision. (i) Heavy truck moves to the right and collides with a light car that is moving to the left. They separate after the collision.
Summarize your “PREDICTIONS” by describing the reason(s) you chose the predicted responses. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 22 OF 50 MEASUREMENT: Connect two force sensors to CH1 and CH2 of the LabPro interface. Connect the LabPro interface to the computer. Define the truck as the sensor connected to CH1, and the car as the sensor connected to CH2. Be sure the slide switch on the force sensors is at +50 N. Open the Logger Pro software. Manually set up the sensors if they do not auto-ID. Reverse the sign of sensor #1 (Experiment->Set Up Sensors->Show All Interfaces, left click the CH1 sensor icon, check Reverse Direction). Calibrate the sensors using weights corresponding to approximately 1000 g and 500 g suspended from the hook attached to each sensor. Remember to include the mass of the hanger and to convert the mass in grams to a force in Newtons. Replace the hook on each force sensor with a rubber bumper provided by your instructor. Zero both sensors (Ctrl-0) and check the zero by collecting data with the sensors horizontal and not touching. Push on each bumper with your hand while collecting data to see how data is collected and displayed. Each force sensor should be securely attached to a low-friction cart that is free to roll along the 1.2 m track. Be sure that neither cart rolls off the end of the track. Now set up experiments to check the results you predicted in parts (a) to (i). Record all your observations regarding the magnitudes of the forces in the third column in the Table 1.
(a) - (b) Place the force sensors on the table and push them together in such a way that there is no movement. Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in Table 1. Using Print Graph, Print one graph per group for either part (a) or part (b); append the last names of all members of your group to the bottom of the graph. Be sure the graph includes a title (right click the graph ->Graph Options) and a description. (c) Push on the truck to the right while it is in contact with the car. Hold the car firmly - imagine the car’s brakes are applied, yet the truck still moves the car to the right. Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in Table 1. (d) Push the car to the left while it is in contact with the truck. Hold the truck firmly - imagine the truck’s brakes are applied, yet the car still moves the truck to the left. Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in Table 1.
Add at least one 500 g mass bar to the cart attached to sensor #1 (the truck). Check parts (e) and (f) of your predictions. (e) - (f) Repeat measurements similar to parts (a) and (b). Record the results in Table 1. For one of the experiments (e) or (f), p rint one graph per group (append the last names of all members of your group to the bottom of the graph). Be sure the graph includes a title and a description.
To check your predictions during collisions when the truck and/or the car are initially moving, you must decrease the time of data collection to 5 s and increase the data sampling rate to 1000 samples/second. Click Experiment -> Data Collection. Change the length of data collection to 5 s and the sampling rate to 1000 samples per second. Click Done. Check parts (g) - (i) of your predictions. The graphical display will take a few moments before displaying due to the large amount of data collected. (g) - (i) Gently push the carts as required. Collect data and Autoscale. Change the minimum and maximum values on the time axis so the display includes the time interval from just before the collision to a time just after the collision. To change the maximum value on the time axis, place the cursor near enough to the largest number on the horizontal scale until the cursor changes shape to an “I”, click, then type the appropriate number and hit Enter. Repeat for the smallest number on the horizontal axis. Compare the magnitude of the forces and record your observations in Table 1. Remember to return the time axis to the 0 s to 5 s range after each experiment. For one of the experiments (g) through (i), p rint one graph per group (append the last names of all members of your group to the bottom of the graph). Be sure the graph includes a title and a description.
Reconcile your predictions with your measurements: In what ways were your predictions different from your measurements? In what ways were they the same? This activity is designed to help you learn something about the forces that two objects exert on each other. The result is known as Newton’s Third Law of Motion. Use the space below to write a clear summary about what you have discovered regarding the interaction force between two objects. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 23 OF 50 NEWTON’S SECOND LAW: PROVIDES US WITH AN OPERATIONAL DEFINITION OF A NET FORCE. Vector equation F F F F F F ⋯ Fnet M a net 1 2 3 4
Fnet = M a Magnitude equation
Two observations Observation #1: For a fixed acceleration, force is proportional to “acceleration” or “rate of velocity change” Force acceleration Note: or “alpha” means “proportional to”
o How would you design an experiment to test this statement? Use a stretched spring to define a “unit of force” F0 For a fixed mass M, measure acceleration for 1 spring, 2 springs, 3 springs, etc. Plot acceleration a versus F = N F0 to see if F and a are linearly proportional.
Observation #2: For a fixed acceleration, force is proportional to “mass” Force Mass
o How would you design an experiment to test this statement? Start with the gravitational field at the earth’s surface; this will provide a constant acceleration Determine the force on an object of mass M, 2 M, 3 M, etc. Plot mass (M, 2 M, 3 M, …) versus force (F, 2 F, 3 F, …) to see if there is a linear relationship. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 24 OF 50 NEWTON’S SECOND LAW: PROVIDES US WITH AN OPERATIONAL DEFINITION OF A NET FORCE. SUMMARY F F F F F F ⋯ Fnet M a Vector equation net 1 2 3 4
Fnet = M a Magnitude equation
The force on an object is proportional to the acceleration of the object. (The greater the velocity change per unit time, the bigger the force.)
To obtain the same acceleration with a bigger mass, a bigger force is required.
UNITS…. 2 SI Unit the Newton N = kg m/s 2 CGS Unit the dyne g cm/s 2 BE Unit the pound slug ft/s 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 25 OF 50
The Force of Gravity Consider an object in “free gall” at the Earth’s surface. The acceleration has magnitude |a| = g = +9.80 m/s2 in the downward direction. Hence, there is a gravitational force on the object
“ Magnitude and angle vector description” Magnitude: Fg = M a = M g = “Wt” the weight of the object Direction: “Down”
“ Component vector description” X component: FX = M aX = 0 aX = 0 2 Y component: FY = M aY = – M g aY = – g where g = + 9.80 m/s
Y axis a F Note that with respect to the y axis which points upward, a = - g = - 9.80 m/s2 and a = 0 Y X 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 26 OF 50
FREE BODY DIAGRAMS AND FREE BODY EQUATIONS FOR STATIC EQUILIBRIUM
IN ONE DIMENSION…
Newton’s 2nd Law for linear motion
Fx = M ax or FnetX = M ax where FnetX = Fx
Translational static equilibrium ACCELERATION IS ZERO!!!! HENCE…
Fx = M ax = 0
Examples DO EACH IN CLASS!
An object at rest on a flat table Show that FN = M g
An object hanging from a rope Show that Ft = M g
An object at rest on an incline Show that FN = M g cos
Other examples 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 27 OF 50 Your Name (Print): Date: Group Members: Group: Newton’s Second Law Fnet m a You will explore the relationship between the net force applied to an object and the object’s resulting acceleration. PREDICTION You pull a low-friction cart along a straight horizontal track, as shown in Figure 1. The cart starts from rest at point A and stops at point B, a distance of approximately 75 cm. You never let go of the cart. The cart only moves to the right.
Cart y t i A B c o l e V Figure 1 Cart pulled along straight horizontal line from point A to point B Time
On the grids to the right, carefully sketch the Velocity of
the cart as a function of Time and the Position of the cart as a n o i t i
function of Time. THE TIME AXES ARE IDENTICAL. s o Remember that velocity is a vector – be careful with its P Time algebraic sign. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 28 OF 50
n o i The cart starts from rest at point A, moves only to the right, t a r e l and stops at point B. On the grid to the right, sketch a graph of e Time c c the resulting Acceleration of the cart versus Time. A
BASED ON YOUR ACCELERATION-TIME SKETCH, carefully sketch the horizontal Force applied to the cart as a function of Time. e c
THE TIME AXES ARE IDENTICAL. Remember that force and r o acceleration are vectors – be careful with algebraic signs. F Time 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 29 OF 50 In the grid below, sketch a predicted graph of Force versus Acceleration. Force and acceleration are vectors – be careful with algebraic signs. Why do you expect this particular shape? What would happen to the shape of the curve if the mass of the cart were increased?
Force
Acceleration 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 30 OF 50 MEASUREMENT This activity is your first introduction to an electronic accelerometer: The “Low-g Accelerometer” measures acceleration along the line marked by the arrow on the label (a “single- axis” accelerometer). The accelerometer can measure accelerations in the range of -5g to +5g, where one g is the magnitude of the earth’s gravitational acceleration (g = 9.80 m/s2). The accelerometer also senses the effect of gravity and uses this property to calibrate the sensor. The accelerometer is attached to a force sensor which is attached to a low friction cart. Be certain the arrow on the accelerometer is parallel to the long side of the force sensor and points away from the force sensor hook. The force sensor must be set to the ±10 N range. Connect the force sensor to channel 1 (CH1) and the accelerometer to channel 2 (CH2) on the interface. An experiment file is available for this activity. From the desktop, click on Start then on My Computer. Double click on the Student Shares on ‘svphy01’ (S:) folder. Open the College Physics Students folder and then open Team Physics 211. Select and drag the experiment file titled Newton’s Second Law into the My Documents folder. Close the My Computer folder and launch the experiment file from the My Documents folder. Click OK if you receive a sensor error message (“Sensors specified in experiment file do not match detected sensors”). When properly configured, two graphs (Force versus Time and Acceleration versus Time) should be displayed. Ignore: “The sensors should not need to be calibrated.” If your instructor recommends you calibrate the sensors, then follow the calibration procedure outlined below. Calibrate the force sensor – Suspend the sensor assembly vertically and use approximately 500 g and 1000 g masses as the force calibration points. Remember to include the mass of the hanger and to convert the mass in grams to a force in Newtons. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 31 OF 50 Calibrate the accelerometer - Suspend the accelerometer at rest with the arrow pointing vertically up. Define this calibration point as +9.80 m/s2. Suspend the accelerometer at rest with the arrow pointing vertically down and define this calibration point as -9.80 m/s2. Place the sensor assembly horizontal and at rest. Press the TARE button on the side of the force sensor. When the sensor readings stabilize, zero the sensors (Ctrl 0). Repeat this process prior to collecting any experimental data. Starting with the cart initially at rest, Collect data, pull on the force sensor hook and move the cart back and forth along a straight line. Do not let go of the force sensor. Pull in such a way that your forearm is HORIZONTAL and PARALLEL to the track. Pick up and move the sensor cables with the cart. Don’t let any cables or other material obstruct the motion of the cart. Good results are obtained with accelerations in the range -5 m/s2 to +5 m/s2. A schematic of the setup is shown in Figure 2.
Accele- rometer Force Sensor Cart
Figure 2 Cart with sensors attached Print a copy of the observed Force versus Time and Acceleration versus Time graphs. Append the names of all participating group members to the graph. Be sure the graph is carefully labeled. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 32 OF 50 Describe the observed relationship between the Force-Time and the Acceleration-Time graphs.
Change one of the graphs to display Force versus Acceleration (Force on the vertical axis and Acceleration on the horizontal axis). Based on this graph, what can you conclude about the relationship between the applied force and the resulting acceleration? Remember, force and acceleration are vectors.
Explain how your measured Force-Acceleration graph compares to your predicted Force- Acceleration graph. How are they similar; how are they different?
Determine and record the slope of the linear portion of the Force-Acceleration line (INCLUDE UNCERTAINTY AND UNITS). Note that you will need to sort the acceleration data before you can perform the fit.
Write (and simplify) the slope’s units in terms of the basic SI units (the “Newton” is a derived unit).
What physical quantity does the slope correspond to? 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 33 OF 50
Print a copy of the observed Force-Acceleration graph with the curve fitting parameter box clearly displayed (and not covering any relevant portion of the graph). Click on the Force-Acceleration graph and use Print Graph. Append the names of all participating group members to the graph. Be sure the graph is carefully labeled.
DESIGN AND PERFORM a measurement to verify your hypothesis regarding the physical significance of the slope. Clearly describe the experimental procedure and include NUMERICAL results supporting your hypothesis.
Summarize the results of this activity in the context of Newton’s Second Law. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 34 OF 50 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 35 OF 50
Example 5.2 “Readying a wrecking ball” 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 36 OF 50 Example 5.2 “Readying a wrecking ball” according to abe’s variation
(a) Review of tension force “T” in a rope (4 possible tension forces!!) Consider a vertically hanging wrecking ball on a rope. What are the four tension forces associated with the rope? Make a FBD for the just the wrecking ball. What is the magnitude of the tension force on the ball? (2500. N)
(b) Let’s redraw the free body diagram for just the ball. Write down Newton’s 2nd Law equations for static equilibrium Note the difference between “force magnitudes” and “force components”
Equation 1 X equation - T1 + T2 sin + 0 = 0
Equation 2 Y equation 0 + T2 cos + (- 2500. N) = 0
We have 2 simultaneous equations. Solve (8th grade) 3 T2 = 2.66 x 10 N T1 = 910. N 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 37 OF 50 Example 5.3 Tension in towing a car at a constant velocity (zero acceleration or “dynamic equilibrium”) Note: Fnet = 0 even though the car is in moving!!
Sketch free body diagram Note force magnitudes (+) T, f, n, Wt Wt = 1500.· 9.80 = 1.47 x 104 N Note force components (+) Tx, Ty, fx, fy, nx, ny, Wtx, Wty
#1 X equation T cos + (- 320. N) + 0 + 0 = 0 T = 341. N
#2 Y equation T sin + 0 + n + (- Wt) = 0 n = 1.46 x 104 N < Wt 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 38 OF 50 Example 5.5 Tension in towing a car with constant acceleration (not in equilibrium!)
Find the tension T in the rope. Draw motion diagram Draw free body diagram Note force magnitudes (+) T, f, n, Wt Wt = 1500.· 9.80 = 1.47 x 104 N Note force components (+) Tx, Ty, fx, fy, nx, ny, Wtx, Wty
#1 X equation T cos + (- 320. N) + 0 + 0 = M aX
2 3 find aX = VX / t = 1.20 m/s T = 2.26 X 10 N
Note: If you have time, use the Y equation to find the normal force magnitude n.
#2 Y equation T sin + 0 + n + (- Wt) = M aY 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 39 OF 50 More on Friction Forces
Static friction “model” f s fS ≤ fSMax fSMax = S FN
S = Coefficient of static friction for a “rough” surface
(for a “smooth” frictionless surface, S = 0 ) With “static” friction, the object does not move on the surface.
Note that (for this model) the static MAXIMUM friction force is proportional to the normal force. o This should be “intuitive.” Let’s demonstrate. Try to move a book on the desk surface while I push down on the book. The harder I push down on the book, the harder it is for you to move the book.
Kinetic friction “model” for sliding friction fK = K FN fk K = Coefficient of kinetic friction for a “rough” surface
(for a “smooth” frictionless surface, K = 0 ) With “kinetic” friction, the object slides on the surface. Magnitude of friction force f versus magnitude of applied force Fa Friction force axis f
Static friction Kinetic friction
f smax
Note f = F = CONSTANT < f K K N SMAX
F = f F axis a smax applied 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 40 OF 50
Magnitude of friction force f versus magnitude of applied force F Friction force a f ≤ f f = F axis f S SMax SMax S N
Static friction Kinetic friction f smax
Note f = F = CONSTANT < f K K N SMAX
F = f F axis a smax applied 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 41 OF 50 Figure 5.17 Static friction keeps an object from slipping
4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 42 OF 50 Figure 5.19 The kinetic friction force is opposite to the direction of motion. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 43 OF 50 A box of books is initially at rest on a floor. The mass of the box is 90.0 kg. The coefficients of static and kinetic friction for the bottom of the box and the floor are µs = 0.700 and µk = 0.600 . Let the applied force Fapp on the box be horizontal.
(a) On the above figure, sketch and label the remaining forces on the box. (b) Calculate the magnitude of the normal force. (c) For the following table, calculate the magnitude of the friction force and state whether the box is moving or not.
Fapplied Friction Force Does box move ? If so, what is the acceleration a X? ______50 N ______100 N ______250 N ______400 N ______600 N ______650 N ______700 N ______A box of mass M = 15.0 kg is motionless on a rough inclined plane at an angle of 35.0 degrees with respect to the horizontal. The coefficient of static friction for the box and plane is .800. Hint: Use tilted coordinate system for this problem. (a) Illustrate all forces acting on the box. (b) On a diagram, show the x and y components of the gravitational force. Also, calculate these components. (84.4 N, -120. N) (c) Use the equilibrium condition for y-components of force to calculate the magnitude of the normal force. (d) Calculate the magnitude of the friction force. (e) If the mass of the box is increased sufficiently, will it start to slide ? (f) At what angle will the box start to slide? 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 44 OF 50 Two types of forces continued
2. Action at a distance forces force seems to act through “empty space”
o Gravitational force Weight = “Wt” = M g
Fg Wt "weight of object "
o Electric and magnetic forces
Fundamental particles electron, proton, neutron More fundamental proton and neutron are composites of quarks
o Nuclear (strong) and nuclear (weak) forces 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 45 OF 50 Newton’s Law of Universal Gravitation Fundamental Law of Gravity between any two objects in the universe (includes Solar System and beyond. The force seems to have an infinite range. This is an exact law with only tiny corrections from General Relativity.
F F on 1 by 2 on 2 by 1
M 1 M 2
r
F = F = F = G M M / r 2 on 1 by 2 on 2 by 1 1 2
G = 6.67 x 10-11 N m2 / kg2 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 46 OF 50 What is the relation between G and g = 9.80 m / s2 ? Consider the gravitational force on a basketball at the surface of the Earth.
F F = M g on E by B on B by E B
M ball M Earth
r = R + R E B
R R B r ≈ R E E r 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 47 OF 50
F = F = F = G M M / r 2 EB BE E B
F = M g = F = G M M / r 2 BE B E B
M g = G M M / R 2 B E B E
g = G M / R 2 E E
On the surface of the Earth g = (6.67 x 10-11) (5.98 x 1024) / (6.38 x 106)2 g = 9.80 m / s2 (SI units)
g = 980. cm / s2 (CGS units) g = 32.2 ft /s2 (BE units)
On the surface of the Moon g = (6.67 x 10-11) (7.35 x 1022) / (1.74 x 106)2 Moon g = 1.62 m / s2 Moon
Memorize: Newton’s Laws and corresponding formulas; formulas for static and kinetic friction forces. 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 48 OF 50
MORE Optional HOMEWORK PROBLEMS WITH ANSWERS All SI, BE, and CGS units defined until present assignment.
(1) A constant force of 3.75 N is applied to a hockey puck in the positive x-direction. (Note: A hockey stick remains in contact with the puck in order to apply the constant force.) The puck is initially at rest at the origin; its mass is .150 kg. Assume there is no friction between the puck and the ice. (a) What is the acceleration in the x-direction ? (b) At what time t will the puck have a speed of 5.20 m/s ? (c) How far has the puck moved at the time from part (b) ? [HRF3,5-4E] ( 25.0 m/s2, .208 s, .541 m )
(2) A 200 kg boat is being pulled in the water by two ropes. The first rope exerts a force magnitude F1 of 700. N in the positive x-direction; the second rope exerts a force magnitude F2 of 900 N at an angle of 30.0 degrees CCL with respect to the positive x-direction. (a) Make a vector diagram which illustrates the two forces and their resultant force FR . (You may wish to use the “parallelogram rule”.) (b) Calculate the x and y components of FR. (c) Calculate the x and y components of the acceleration vector of the boat. (d) Calculate the magnitude and angle of the acceleration vector. (e) Assuming the boat starts from rest, find where its coordinates after 8.00 s and the distance which it has moved. (1.48 . 103 N, 450. N, 7.40 m/s2, 2.25 m/s2, 7.73 m/s2, 16.9 degrees CCL WRT + x direction, 237.,72.0, 247.)
(3) Given a 5 kg box which is resting on the surface of the earth. (a) Make a free body diagram of the box. Sketch and label all forces which act on the box. (b) Calculate the magnitude of each force acting on the box. (c) Make a “cartoon” sketch of the box sitting on the earth. Illustrate action and reaction pairs.
(4) Given a 5 kg box which is hanging by a rope. (a) Make a free body diagram of the box. Sketch and label all forces which act on the box. (b) Calculate the magnitude of each force acting on the box. (c) Sketch the box hanging from the ceiling. Illustrate action and reaction pairs.
(5) A woman is walking on the floor. What is the origin of the force which causes her to move forward? Make a sketch to illustrate.
(6) Calculate the "weight" and "mass" for each of the following. Use SI units for your answer. (a) a "5.00 lb" bag of sugar. (b) a "240 lb" fullback. (c) a "1.80 ton" automobile. [HRF3,5-15E] (22.2 N, 2.27 kg, 1.07x103 N, 109. kg, 1.60x104 N, 1.63x103 kg)
(7) A man “weighs” 150 lbs. (a) Calculate his weight and mass in SI units. (b) Calculate his weight and mass in BE units. (c) Calculate his weight and mass in CGS units.
WAIT (8) Sketch and calculate the magnitudes of the tension forces for each of the following ? Let M = 5 kg. Assume frictionless and massless pulleys. (49.0 N, 24.5 N, 24.5 N) Can you design a system which reduces the tension below 15 N. See “Solved Problem 1” in Cutnell and Johnson.
(9) An automobile which weighs 3800 lbs is accelerating at 12.0 ft/s2 along the positive x-axis. (a) Calculate the mass of the automobile in British units. (b) Calculate the force on the automobile in British units. (c) What is applying the force to move the automobile? [HRF3,5-20E] (119 slugs, 1.43x10 3 lbs, to be discussed in class)
(10.0) Given two boxes stacked on the floor. The top box is 5 kg and the bottom box is 8 kg. Sketch the boxes and show all forces acting on the system. Which forces are “action & reaction” pairs ? Where do the missing “reaction” forces act ? Make a free-body diagram for the bottom box. Calculate the magnitude of each force on the bottom box.
(10.1) You are walking on the floor. What is the origin of the force which causes you to move forward? Which of Newton’s three laws applies? Make a sketch to illustrate your answer. (11.0) Two railroad cars are being pulled along the positive x-axis by an engine which exerts a force F of magnitude 6500 N. The two cars are connected by a rope with tension FT . Assume there is no rolling friction. The masses are as follows: M1= 1200 kg and M2 = 2400 kg . Calculate the magnitude “ a” of the 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 49 OF 50 2 3 acceleration of the system of the two railroad cars and the tension “FT” in the rope. [HRF3,5-43P] (1.81 m/s , 4.34 . 10 N) Suggested approach: set up a free- body diagram and free-body equations for each car; get two simultaneous equations in “a” and “FT”.
(11.1) See figure below. Given an Atwood’s machine (two masses hanging on a frictionless pulley). Let M2 > M1. Show that the magnitude of the acceleration is given by a = g (M2 - M1)/(M1 + M2) and that the tension in the string is FT = 2 M1 M2 g/(M1 + M2). Hint: Set up free-body diagrams. What is the relation between a1y , a2y , and a ?
y axis a M 1 a F FT T
M M 2 2 x axis
M 1
(11.2) See right hand figure above. Given the following simple machine. Let M1 = 4 kg and M2 = 2 kg. Find the tension in the string and the magnitude of the acceleration. Assume that M1 slides on a frictionless surface. Hint: Set up free-body diagrams. What is the relation between a1x , a2y , and a ? [HRF3,5-23E] (13.1 N, 3.27 m/s2)
(11.3) See right hand figure above. Given the following system of two masses. The the surface on which M1 rests has a coefficient of kinetic friction equal to 0.150. Let M1 = 4 kg and M2 = 2 kg. Find the tension in the string and the magnitude of the acceleration of the system. Hint: Set up free-body diagrams and free- 2 body equations. What is the relation between a1x and a , and, between a2y and a ? (15.0 N, 2.29 m/s ) Note: Do not use any formulas from text; start with free body diagrams and free body equations (Newton’s Second Law) to arrive at answers.
WAIT (11.3) Given the following machine. Let a1 = 6 m/s2. Determine a2. What are the x and y components of a1 and a2 ?
(12) A 160 lb man stands on a bathroom scale in an elevator which is at rest. (a) When the elevator starts moving the scale reads 200 lbs. Find the accleration (magnitude and direction) of the elevator. (b) The elevator is again at rest. But, when the elevator starts to move this time, the scale reads 120 lbs. Find the accleration (magnitude and direction) of the elevator. (c) If the scale reads zero, should the man worry? Explain. (+8 ft/s2, -8 ft/s2, Yes!....) (new)
(13) Given an acrobat of mass M hangs in the middle of a tightrope. Show that the tension in the rope is given by
FT = M g /(2 sin( )) . The angle is the angle between the horizontal and the rope at the points where it is tied.
(14) Given a 3 kg metal puck which is sliding on ice. The coefficient of kinetic friction between the puck and the ice is 0.0255 . At t = 0 , the speed of the puck is 5 m/s. (a) Sketch all forces on the moving puck. (b) Calculate the magnitude of the force of kinetic friction on the puck. (c) Calculate the x-component of acceleration. (d) Estimate when the puck will come to rest. (e) How far will the puck have moved? (0.750 N, -.250 m/s2,20.0 s, 50.0 m)
(15) A box of books is initially at rest on a floor. The mass of the box is 80 kg. The coefficients for static and kinetic friction between the bottom of the box and the floor are 0.750 and 0.650. A horizontal force is applied to the box in the positive x-direction. (a) Sketch the box and show all forces acting on it. (b) Calculate the magnitude of the force of friction and state whether the box moves for each of the following applied forces: 150 N, 450 N, 575 N, 720 N, 985 N. Hint: Do a 4/6/18, 11:08 AM 05beb6a244744b50140c7c12a2f88a8a.doc PAGE 50 OF 50 quick calculation with the coefficient of static friction first. (150 N, No; 450 N, No; 575 N, No; 510 N, Yes; 510 N, Yes)
(16) A dockworker loading crates on a ship finds that a 20 kg crate, initially at rest on a rough horizontal surface, requires a 75 N horizontal force to set it in motion. However, after it is in motion, horizontal force of 60 N is required to keep the crate moving with a constant speed. Find the coefficients of static and kinetic friction between the crate and the floor. (.383,.306)
(18) To move a box of books along the floor, it is necessary for a rope to have a tension of 80.0 N at an angle of 35.0 degrees. The box of books has a mass of 25.0 kg and the coefficient of kinetic friction between the box and the floor is 0.300. (a) Make a free-body diagram of all the forces acting on the box. On your diagram, illustrate the x and y components of the tension force of the rope on the box; also, calculate these components. (b) Calculate the normal force on the box. (c) Calculate the magnitude of the kinetic force of friction on the box. (d) Use Newton's second law to calculate the horizontal acceleration of the box. [SF2, Example 3.5] (65.5 N,45.9 N,199 N,59.7 N,0.232 m/s2)
(19) A man is applying a horizontal force to drag a 200. kg box of books on a floor whose static and kinetic coefficients of friction are 0.500 and 0.450. The box is moving with a constant speed of 2 m/s. Calculate the magnitude of the force that the man applies to the box. (882. N) (new)
Given the following object of mass M = 15.0 kg which is hanging from the ceiling as shown.
M
(a) With a free-body diagram, illustrate the tension forces on the knot. Sketch the x and y components of tension forces T1 and T2 on the knot. (b) Apply the equilibrium condition to the hanging mass in order to calculate the tension T3. (T3 = 147. N) (c) Specify the x and y components of the three tension forces on the knot in terms of the magnitude of the tension force and, if necessary, the appropriate trigonometric function. (d) Using the equilibrium condition for forces, write down the two x and y free-body equations for the knot. (e) Solve for the magnitudes of the tensions, T1 and T2 . (T1 = 147. N, T2 = 134. N)
(20) Does the following conversion equation make sense “physically” ? 1 lb = 2.20 kg Explain how it should be corrected to read in terms of exclusively mass units and in terms of exclusively force units.