The Ultimate Regents Physics Question and Answer Book 2016 Edition edited by Dan Fullerton Webster, NY 14580

Silly Beagle Productions 656 Maris Run Webster, NY 14580 Internet: www.SillyBeagle.com E-Mail: [emailprotected] No part of this book may be reproduced, in whole or in part, by any mechanical, photo- graphic, or electronic process, nor may it be stored in a retrieval system, transmitted, shared, or otherwise copied for public or private use, without the prior written permission of the author. © Copyright 2015 Dan Fullerton [emailprotected] Cover Design: Interior Illustrations by Dan Fullerton and Jupiterimages unless otherwise noted All images and illustrations ©2015 Jupiterimages Corporation and Dan Fullerton Sales and Ordering Information http://www.APlusPhysics.com [emailprotected] Volume discounts available E-book editions available Printed in the United States of America ISBN: 978-0-9907243-3-9 12345678909876

Table of Contents Metric System Waves Metric Estimation 5 Wave Basics 156 Wave Characteristics 161 Kinematics Wave Behaviors 170 Defining Motion 6 Reflection180 Motion Graphs 13 Refraction182 Horizontal Kinematics 17 Diffraction194 Free Fall 22 Electromagnetic Spectrum 197 Projectiles25 Dynamics Modern Physics 200 Wave-Particle Duality 204 Newton’s 1st Law 34 Energy Levels 210 Mass-Energy Equivalence 212 Newton’s 2nd Law 36 The Standard Model Newton’s 3rd Law 45 Friction47 Ramps and Inclines 53 Solutions218 UCM & Gravity Reference Table 238 Circular Motion 55 Gravity64 Momentum & Impulse 71 Momentum & Impulse 75 Conservation of Momentum Work, Energy & Power Work and Power 79 Springs85 Energy and Energy Conservation 93 Electrostatics 109 Electric Charge 112 Coulomb’s Law 117 Electric Field 122 Electric Potential Circuits Electric Current 125 Resistance127 Ohm’s Law 133 Circuit Analysis 140 Magnetism Magnetism153

Name: Period: Metric Estimation 1. What is the approximate width of a person’s little 8. What is the approximate length of a baseball bat? finger? 1. 10-1 m 1. 1 m 2. 100 m 2. 0.1 m 3. 101 m 3. 0.01 m 4. 102 m 4. 0.001 m 9. What is the approximate diameter of an inflated 2. What is the approximate mass of an automobile? basketball? 1. 101 kg 1. 2 × 10-2 m 2. 102 kg 2. 2 × 10-1 m 3. 103 kg 3. 2 × 100 m 4. 106 kg 4. 2 × 101 m 3. The diameter of a United States penny is closest to 10. The length of a football field is closest to 1. 100 m 1. 1000 cm 2. 10-1 m 2. 1000 dm 3. 10-2 m 3. 1000 km 4. 10-3 m 4. 1000 mm 4. An egg is dropped from a third-story window. The 11. The approximate length of an unsharpened No. 2 distance the egg falls from the window to the ground pencil is is closest to 1. 2.0 × 10-2 m 1. 100 m 2. 2.0 × 10-1 m 2. 101 m 3. 2.0 × 100 m 3. 102 m 4. 2.0 × 101 m 4. 103 m 12. The height of a 30-story building is approximately 5. The approximate height of a 12-ounce can of root 1. 100 m beer is 2. 101 m 1. 1.3 × 10-3 m 3. 102 m 2. 1.3 × 10-1 m 4. 103 m 3. 1.3 × 100 m 4. 1.3 × 101 m 13. The diameter of an automobile tire is closest to 1. 10-2 m 6. The mass of a paper clip is approximately 2. 100 m 1. 1 × 106 kg 3. 101 m 2. 1 × 103 kg 4. 102 m 3. 1 × 10-3 kg 4. 1 × 10-6 kg 7. The length of a dollar bill is approximately 1. 1.5 × 10-2 m 2. 1.5 × 10-1 m 3. 1.5 × 101 m 4. 1.5 × 102 m APlusPhysics: Metric Estimation MAT.A1 Page 5

Name: Period: Kinematics-Defining Motion 1. A student on her way to school walks four blocks east, three blocks north, and another four blocks east, as shown in the diagram. Compared to the distance she walks, the magnitude of her displacement from home to school is 1. less 2. greater 3. the same 2. A motorboat, which has a speed of 5 meters per sec- 5. On the surface of Earth, a spacecraft has a mass of ond in still water, is headed east as it crosses a river 2.00 × 104 kilograms. What is the mass of the space- flowing south at 3.3 meters per second. What is the craft at a distance of one Earth radius above Earth’s magnitude of the boat’s resultant velocity with respect surface? to the starting point? 1. 5.00 × 103 kg 1. 3.3 m/s 2. 2.00 × 104 kg 2. 5.0 m/s 3. 4.90 × 104 kg 3. 6.0 m/s 4. 1.96 × 105 kg 4. 8.3 m/s 6. An airplane flies with a velocity of 750 kilometers 3. A speedometer in a car does not measure the car’s ve- per hour, 30.0° south of east. What is the magnitude locity because velocity is a of the eastward component of the plane’s velocity? 1. vector quantity and has a direction associated 1. 866 km/h with it 2. 650 km/h 2. vector quantity and does not have a direction 3. 433 km/h associated with it 4. 375 km/h 3. scalar quantity and has a direction associated with it 7. One car travels 40 meters due east in 5 seconds, and 4. scalar quantity and does not have a direction as- a second car travels 64 meters due west in 8 seconds. sociated with it During their periods of travel, the cars definitely had the same 4. A person observes a fireworks display from a safe 1. average velocity distance of 0.750 kilometer. Assuming that sound 2. total displacement travels at 340 meters per second in air, what is the 3. change in momentum time between the person seeing and hearing a fire- 4. average speed works explosion? 1. 0.453 s 8. State the two general characteristics that are used to 2. 2.21 s define a vector quantity. 3. 410 s 4. 2.55 × 105 s Page 6 VEL.A1, ACC.A1 APlusPhysics: Kinematics-Defining Motion

Name: Period: Kinematics-Defining Motion Base your answers to questions 9 through 12 on the information and diagram below. A model airplane heads due east at 1.50 meters per second, while the wind blows due north at 0.70 meter per second. The scaled diagram below represents these vector quantities. 9. Using a ruler, determine the scale used in the vector diagram. 1 cm = ____________ m/s 10. On the diagram above, use a protractor and a ruler to construct a vector to represent the resultant velocity of the airplane. Label the vector R. 11. Determine the magnitude of the resultant velocity. 12. Determine the angle between north and the resultant velocity. 13. A baseball player runs 27.4 meters from the batter’s 15. A girl leaves a history classroom and walks 10 me- box to first base, overruns first base by 3.0 meters, ters north to a drinking fountain. Then she turns and and then returns to first base. Compared to the total walks 30 meters south to an art classroom. What is distance traveled by the player, the magnitude of the the girl’s total displacement from the history class- player’s total displacement from the batter’s box is room to the art classroom? 1. 3 m shorter 1. 20 m south 2. 6 m shorter 2. 20 m north 3. 3 m longer 3. 40 m south 4. 6 m longer 4. 40 m north 14. In a 4-kilometer race, a runner completes the first ki- 16. Which is a vector quantity? lometer in 5.9 minutes, the second kilometer in 6.2 1. speed minutes, the third kilometer in 6.3 minutes, and the 2. work final kilometer in 6 minutes. The average speed of the 3. mass runner for the race is approximately 4. displacement 1. 0.16 km/min 2. 0.33 km/min 17. A cart travels 4 meters east and then 4 meters north. 3. 12 km/min Determine the magnitude of the cart’s resultant dis- 4. 24 km/min placement. APlusPhysics: Kinematics-Defining Motion VEL.A1, ACC.A1 Page 7

Name: Period: Kinematics-Defining Motion Base your answers to questions 18 through 20 on the in- 23. The diagram below shows a resultant vector, R. formation and vector diagram below. A dog walks 8 meters due north and then 6 meters due east. Which diagram below best represents a pair of com- ponent vectors, A and B, that would combine to form resultant vector R? 18. Using a metric ruler and the vector diagram, deter- mine the scale used in the diagram. 1 cm = ______________ m Base your answers to questions 24 and 25 on the infor- mation below. 19. On the diagram above, construct the re- sultant vector that represents the dog’s A stream is 30 meters wide and its current flows south- total displacement. ward at 1.5 meters per second. A toy boat is launched with a velocity of 2.0 meters per second eastward from 20. Determine the magnitude of the dog’s the west bank of the stream. total displacement. 24. What is the magnitude of the boat’s resultant veloc- ity as it crosses the stream? 1. 0.5 m/s 2. 2.5 m/s 3. 3.0 m/s 4. 3.5 m/s 21. On a highway, a car is driven 80 kilometers during the 25. How much time is required for the boat to reach the first hour of travel, 50 kilometers during the next 0.50 opposite bank of the stream? hour, and 40 kilometers in the final 0.50 hour. What 1. 8.6 s is the car’s average speed for the entire trip? 2. 12 s 1. 45 km/h 3. 15 s 2. 60 km/h 4. 60 s 3. 85 km/h 4. 170 km/h 26. A person walks 150 meters due east and then walks 30 meters due west. The entire trip takes the person 22. Explain the difference between a scalar and a vector 10 minutes. Determine the magnitude and direction quantity. of the person’s total displacement. Page 8 VEL.A1, ACC.A1 APlusPhysics: Kinematics-Defining Motion

Name: Period: Kinematics-Defining Motion 27. A high-speed train in Japan travels a distance of 300 Base your answers to questions 32 and 33 on the follow- kilometers in 3.60 × 103 seconds. What is the average ing information. speed of this train? A hiker walks 5 kilometers due north and then 7 kilome- 1. 1.20 × 10-2 m/s ters due east. 2. 8.33 × 10-2 m/s 32. What is the magnitude of her resultant 3. 12.0 m/s 4. 83.3 m/s displacement? 28. A child walks 5 meters north, then 4 meters east, 33. What total distance has she traveled? and finally 2 meters south. What is the magnitude of the resultant displacement of the child after the entire walk? 1. 1.0 m 2. 5.0 m 3. 3.0 m 4. 11.0 m 29. Scalar is to vector as Base your answers to questions 34 and 35 on the infor- 1. speed is to velocity mation below. 2. displacement is to distance 3. displacement is to velocity In a drill during basketball practice, a player runs the 4. speed is to distance length of the 30-meter court and back. The player does this three times in 60 seconds. 30. A car travels 90 meters due north in 15 seconds. Then the car turns around and travels 40 meters due south in 5 seconds. What is the magnitude of the average velocity of the car during this 20-second interval? 1. 2.5 m/s 2. 5.0 m/s 3. 6.5 m/s 4. 7.0 m/s 31. Velocity is to speed as displacement is to 34. The magnitude of the player’s total displacement 1. acceleration after running the drill is 2. time 1. 0.0 m 3. momentum 2. 30 m 4. distance 3. 60 m 4. 180 m 35. The average speed of the player during the drill is 1. 0.0 m/s 2. 0.50 m/s 3. 3.0 m/s 4. 30 m/s APlusPhysics: Kinematics-Defining Motion VEL.A1, ACC.A1 Page 9

Name: Period: Kinematics-Defining Motion Base your answers to questions 36 through 38 on the information below. A river has a current flowing with a velocity of 2 meters per second due east. A boat is 75 meters from the north riverbank. It travels at 3 meters per second relative to the river and is headed due north. In the diagram below, the vector starting at point P represents the velocity of the boat relative to the river water. 36. Calculate the time required for the boat to cross the river. [Show all work, including the equation and substitu- tion with units.] 37. On the diagram, use a ruler and protractor to construct a vector representing the velocity of the river current. Begin the vector at point P and use a scale of 1 cm = 0.50 meter per second. 38. Calculate or find graphically the magnitude of the resultant velocity of the boat. [Show all work, including the equation and substitution with units or construct the resultant velocity vector on the diagram, using the scale given. The value of the magnitude must be written below. Page 10 VEL.A1, ACC.A1 APlusPhysics: Kinematics-Defining Motion

Name: Period: Kinematics-Defining Motion Base your answers to questions 39 through 42 on the information below. A girl rides her bicycle 1.40 kilometers west, 0.70 kilometer south, and 0.30 kilometer east in 12 minutes. The vector diagram in your answer booklet represents the girl’s first two displacements in sequence from point P. The scale used in the diagram is 1.0 centimeter = 0.20 kilometer. 39. On the vector diagram below, using a ruler and protractor, construct the following vectors: • Starting at the arrowhead of the second displacement vector, draw a vector to represent the 0.30 kilometer east displacement. Label the vector with its magnitude. • Draw the vector representing the resultant displacement of the girl for the entire bicycle trip and label the vector R. 40. Calculate the girl’s average speed for the entire bicycle trip. [Show all work, including the equation and substitution with units.] 41. Determine the magnitude of the girl’s resultant displacement for the entire bicycle trip, in kilometers. 42. Determine the measure of the angle, in degrees, between the resultant and the 1.40-kilometer displacement vector. APlusPhysics: Kinematics-Defining Motion VEL.A1, ACC.A1 Page 11

Name: Period: Kinematics-Defining Motion 43. An airplane traveling north at 220 meters per second encounters a 50.0-meters-per-second crosswind from west to east, as represented in the diagram below. What is the resultant speed of the plane? 1. 170 m/s 2. 214 m/s 3. 226 m/s 4. 270 m/s 44. The vector diagram below represents the velocity of a car traveling 24 meters per second 35° east of north. What is the magnitude of the component of the car’s velocity that is directed eastward? 1. 14 m/s 2. 20 m/s 3. 29 m/s 4. 42 m/s Page 12 VEL.A1, ACC.A1 APlusPhysics: Kinematics-Defining Motion

Name: Period: Kinematics-Motion Graphs 1. A cart travels with a constant nonzero acceleration along a straight line. Which graph best represents the rela- tionship between the distance the cart travels and time of travel? Base your answers to questions 2 through 4 on the infor- 5. A student throws a baseball vertically upward and mation below. then catches it. If vertically upward is considered to be the positive direction, which graph best represents A car on a straight road starts from rest and accelerates the relationship between velocity and time for the at 1.0 meter per second2 for 10 seconds. Then the car baseball? [Neglect friction.] continues to travel at constant speed for an additional 20 seconds. 2. Determine the speed of the car at the end of the first 10 seconds. 3. On the grid at below, use a ruler or straightedge to construct a graph of the car’s speed as a function of time for the entire 30-second interval. 6. The graph below represents the displacement of an object moving in a straight line as a function of time. 4. Calculate the distance the car travels in the first 10 What was the total distance traveled by the object seconds. [Show all work, including the equation and during the 10-second time interval? substitution with units.] 1. 0 m 2. 8 m 3. 16 m 4. 24 m APlusPhysics: Kinematics-Motion Graphs VEL.C1, ACC.B1 Page 13

Name: Period: Kinematics-Motion Graphs 7. Which graph best represents the relationship between the acceleration of an object falling freely near the surface of Earth and the time that it falls? 8. Which pair of graphs represent the same motion of an object? 9. The graph below represents the velocity of an object 10. Which graph best represents the motion of a block traveling in a straight line as a function of time. accelerating uniformly down an inclined plane? Determine the magnitude of the total displacement of the object at the end of the first 6 seconds. Page 14 VEL.C1, ACC.B1 APlusPhysics: Kinematics-Motion Graphs

Name: Period: Kinematics-Motion Graphs Base your answers to questions 11 and 12 on the graph 14. The graph below shows the relationship between the below, which represents the motion of a car during a speed and elapsed time for an object falling freely 6-second time interval. from rest near the surface of a planet. 11. What is the acceleration of the car at t=5.0 seconds? What is the total distance the object falls during the 1. 0.0 m/s2 first 3 seconds? 2. 2.0 m/s2 1. 12 m 3. 2.5 m/s2 2. 24 m 4. 10 m/s2 3. 44 m 4. 72 m 12. What is the total distance traveled by the car during this 6-second interval? 15. The graph below represents the relationship between 1. 10 m speed and time for an object moving along a straight 2. 20 m line. 3. 40 m 4. 60 m 13. Which graph best represents the relationship between the velocity of an object thrown straight upward from Earth’s surface and the time that elapses while it is in the air? [Neglect friction.] What is the total distance traveled by the object dur- ing the first 4 seconds? 1. 5 m 2. 20 m 3. 40 m 4. 80 m APlusPhysics: Kinematics-Motion Graphs VEL.C1, ACC.B1 Page 15

Name: Period: Kinematics-Motion Graphs Base your answers to questions 16 and 17 on the graph 18. Determine the magnitude of the average velocity of below, which shows the relationship between speed and the car from t=6.0 seconds to t=10.0 seconds. elapsed time for a car moving in a straight line. 19. Determine the magnitude of the car’s acceleration during the first 6.0 seconds. 20. Identify the physical quantity represented by the shaded area on the graph. 16. Determine the magnitude of the acceleration of the car. 17. Calculate the total distance the car traveled during the time interval 4.0 seconds to 8.0 seconds. [Show all work, including the equation and substitution with units.] Base your answers to questions 18 through 20 on the graph below, which represents the relationship between velocity and time for a car moving along a straight line, and your knowledge of physics. Page 16 VEL.C1, ACC.B1 APlusPhysics: Kinematics-Motion Graphs

Name: Period: Kinematics-Horizontal Kinematics Base your answers to questions 1 and 2 on the information below. A 747 jet, traveling at a velocity of 70 meters per second north, touches down on a runway. The jet slows to rest at the rate of 2.0 meters per second2. 1. Calculate the total distance the jet travels on the runway as it is brought to rest. [Show all work, including the equation and substitution with units.] 2. On the diagram below, point P represents the position of the jet on the runway. Beginning at point P, draw a vec- tor to represent the magnitude and direction of the acceleration of the jet as it comes to rest. Use a scale of 1.0 centimeter = 0.50 meter/second2. 3. An observer recorded the following data for the mo- 4. A car traveling on a straight road at 15 meters per tion of a car undergoing constant acceleration. second accelerates uniformly to a speed of 21 meters per second in 12 seconds. The total distance traveled by the car in this 12-second time interval is 1. 36 m 2. 180 m 3. 216 m 4. 252 m What was the magnitude of the acceleration of the 5. A race car starting from rest accelerates uniformly at car? 4.9 m/s2. What is the car’s speed after it has traveled 1. 1.3 m/s2 200 meters? 2. 2.0 m/s2 1. 1960 m/s 3. 1.5 m/s2 2. 62.6 m/s 4. 4.5 m/s2 3. 44.3 m/s 4. 31.3 m/s APlusPhysics: Kinematics-Horizontal Kinematics VEL.B1, ACC.C1 Page 17

Name: Period: Kinematics-Horizontal Kinematics Base your answers to questions 6 through 9 on the information and diagram below. A spark timer is used to record the position of a lab cart accelerating uniformly from rest. Each 0.10 second, the timer marks a dot on a recording tape to indicate the position of the cart at that instant, as shown. 6. Using a metric ruler, measure the distance the cart traveled during the interval t=0 second to t=0.30 second. Record your answer to the nearest tenth of a centimeter. 7. Calculate the magnitude of the acceleration of the cart during the time interval t=0 second to t=0.30 second. [Show all work, including the equation and substitution with units.] 8. Calculate the average speed of the cart during the time interval t=0 second to t=0.30 second. [Show all work, in- cluding the equation and substitution with units.] 9. On the diagram below, mark at least four dots to indicate the position of a cart traveling at constant velocity. 10. A car initially traveling at a speed of 16 meters per 11. An object accelerates uniformly from 3 meters per second accelerates uniformly to a speed of 20 meters second east to 8 meters per second east in 2.0 sec- per second over a distance of 36 meters. What is the onds. What is the magnitude of the acceleration of magnitude of the car’s acceleration? the object? 1. 0.11 m/s2 1. 2.5 m/s2 2. 2.0 m/s2 2. 5.0 m/s2 3. 0.22 m/s2 3. 5.5 m/s2 4. 9.0 m/s2 4. 11 m/s2 Page 18 VEL.B1, ACC.C1 APlusPhysics: Kinematics-Horizontal Kinematics

Name: Period: Kinematics-Horizontal Kinematics Base your answers to questions 12 and 13 on the informa- Base your answers to questions 17 and 18 on the infor- tion below. mation below. A physics class is to design an experiment to determine A car traveling at a speed of 13 meters the acceleration of a student on inline skates coasting per second accelerates uniformly to a straight down a gentle incline. The incline has a constant speed of 25 meters per second in 5.0 slope. The students have tape measures, traffic cones, and seconds. stopwatches. 17. Calculate the magnitude of the acceleration of the 12. Describe a procedure to obtain the measurements car during this 5.0-second time interval. [Show all necessary for this experiment. work, including the equation and substitution with units.] 13. Indicate which equation(s) they should use to deter- mine the student’s acceleration. 18. A truck traveling at a constant speed covers the same total distance as the car in the same 5.0-second time interval. Determine the speed of the truck. 14. A car increases its speed from 9.6 meters per second 19. If a car accelerates uniformly from rest to 15 meters to 11.2 meters per second in 4.0 seconds. The average per second over a distance of 100 meters, the magni- acceleration of the car during this 4-second interval is tude of the car’s acceleration is 1. 0.40 m/s2 1. 0.15 m/s2 2. 2.4 m/s2 2. 1.1 m/s2 3. 2.8 m/s2 3. 2.3 m/s2 4. 5.2 m/s2 4. 6.7 m/s2 15. As a car is driven south in a straight line with decreas- 20. The speed of a wagon increases from 2.5 meters per ing speed, the acceleration of the car must be second to 9.0 meters per second in 3.0 seconds as it 1. directed northward accelerates uniformly down a hill. What is the mag- 2. directed southward nitude of the acceleration of the wagon during this 3. zero 3.0-second interval? 4. constant, but not zero 1. 0.83 m/s2 2. 2.2 m/s2 16. The speed of an object undergoing constant accel- 3. 3.0 m/s2 eration increases from 8.0 meters per second to 16.0 4. 3.8 m/s2 meters per second in 10 seconds. How far does the object travel during the 10 seconds? 1. 3.6 × 102 m 2. 1.6 × 102 m 3. 1.2 × 102 m 4. 8.0 × 101 m APlusPhysics: Kinematics-Horizontal Kinematics VEL.B1, ACC.C1 Page 19

Name: Period: Kinematics-Horizontal Kinematics 21. A skater increases her speed uniformly from 2.0 me- 25. A car traveling west in a straight line on a highway ters per second to 7.0 meters per second over a dis- decreases its speed from 30.0 meters per second to tance of 12 meters. The magnitude of her acceleration 23.0 meters per second in 2.00 seconds. The car’s av- as she travels this 12 meters is erage acceleration during this time interval is 1. 1.9 m/s2 1. 3.5 m/s2 east 2. 2.2 m/s2 2. 3.5 m/s2 west 3. 2.4 m/s2 3. 13 m/s2 east 4. 3.8 m/s2 4. 13 m/s2 west 22. During a 5.0-second interval, an object’s velocity 26. In a race, a runner traveled 12 meters in 4.0 seconds as changes from 25 meters per second east to 15 meters she accelerated uniformly from rest. The magnitude per second east. Determine the magnitude and direc- of the acceleration of the runner was tion of the object’s acceleration. 1. 0.25 m/s2 2. 1.5 m/s2 3. 3.0 m/s2 4. 48 m/s2 27. What is the final speed of an object that starts from rest and accelerates uniformly at 4.0 meters per sec- ond2 over a distance of 8.0 meters? 1. 8.0 m/s 2. 16 m/s 3. 32 m/s 4. 64 m/s 23. A car, initially traveling east with a speed of 5 me- 28. A truck, initially traveling at a speed of 22 meters per ters per second, is accelerated uniformly at 2 meters second, increases speed at a constant rate of 2.4 me- per second2 east for 10 seconds along a straight line. ters per second2 for 3.2 seconds. What is the total During this 10-second interval, the car travels a total distance traveled by the truck during this 3.2-second distance of time interval? 1. 50 m 1. 12 m 2. 60 m 2. 58 m 3. 1.0 × 102 m 3. 70 m 4. 1.5 × 102 m 4. 83 m 24. A child riding a bicycle at 15 meters per second ac- 29. A car is moving with a constant speed of 20 meters celerates at -3.0 meters per second2 for 4.0 seconds. per second. What total distance does the car travel in What is the child’s speed at the end of this 4.0-sec- 2 minutes? ond interval? 1. 10 m 1. 12 m/s 2. 40 m 2. 27 m/s 3. 1200 m 3. 3.0 m/s 4. 2400 m 4. 7.0 m/s Page 20 VEL.B1, ACC.C1 APlusPhysics: Kinematics-Horizontal Kinematics

Name: Period: Kinematics-Horizontal Kinematics 30. A car, initially traveling at 15 m/s north, accelerates to 25 m/s north in 4 seconds. The magnitude of the average acceleration is 1. 2.5 m/s2 2. 6.3 m/s2 3. 10 m/s2 4. 20 m/s2 APlusPhysics: Kinematics-Horizontal Kinematics VEL.B1, ACC.C1 Page 21

Name: Period: Kinematics-Free Fall Base your answers to questions 1 through 4 on the information and data table provided. A 1.00-kilogram mass was dropped from rest from a height of 25 meters above Earth’s surface. The speed of the mass was determined at 5-meter intervals and recorded in the data table. Using the information in the data table, construct a graph on the grid, following the directions below. 1. Mark an appropriate scale on the axis labeled “Height Above Earth’s Sur- face (m).” 2. Plot the data points for speed versus height above Earth’s surface. 3. Draw the line or curve of best fit. 4. Using your graph, determine the speed of the mass after it has fallen a vertical distance of 12.5 meters. 5. A rock is dropped from a bridge. What happens to 7. A ball is thrown straight downward with a speed of the magnitude of the acceleration and the speed of 0.50 meter per second from a height of 4.0 meters. the rock as it falls? What is the speed of the ball 0.70 second after it is 1. Both acceleration and speed increase. released? [Neglect friction.] 2. Both acceleration and speed remain the same. 1. 0.50 m/s 3. Acceleration increases and speed decreases. 2. 7.4 m/s 4. Acceleration remains the same and speed increas- 3. 9.8 m/s es. 4. 15 m/s 6. A rock falls from rest a vertical distance of 0.72 meter 8. An astronaut drops a hammer from 2.0 meters above to the surface of a planet in 0.63 second. The magni- the surface of the moon. If the acceleration due to tude of the acceleration due to gravity on the planet is gravity on the moon is 1.62 m/s2, how long will it take 1. 1.1 m/s2 for the hammer to fall to the Moon’s surface? 2. 2.3 m/s2 1. 0.62 s 3. 3.6 m/s2 2. 1.2 s 4. 9.8 m/s2 3. 1.6 s 4. 2.5 s Page 22 VEL.B1, ACC.C1 APlusPhysics: Kinematics-Free Fall

Name: Period: Kinematics-Free Fall 9. An object is dropped from rest and falls freely 20 me- 15. A 25-newton weight falls freely from rest from the ters to Earth. When is the speed of the object 9.8 roof of a building. What is the total distance the meters per second? weight falls in the first 1.0 second? 1. during the entire first second of its fall 1. 19.6 m 2. at the end of its first second of fall 2. 9.8 m 3. during its entire time of fall 3. 4.9 m 4. after it had fallen 9.8 meters 4. 2.5 m 10. A ball is thrown vertically upward with an initial ve- 16. A basketball player jumped straight up to locity of 29.4 meters per second. What is the maxi- grab a rebound. If she was in the air for mum height reached by the ball? [Neglect friction.] 0.80 second, how high did she jump? 1. 14.7 m 1. 0.50 m 2. 29.4 m 2. 0.78 m 3. 44.1 m 3. 1.2 m 4. 88.1 m 4. 3.1 m 11. A soccer ball kicked on a level field has an initial verti- 17. How far will a brick starting from rest fall freely in cal velocity component of 15 meters per second. As- 3.0 seconds? suming the ball lands at the same height from which 1. 15 m it was kicked, what is the total time the ball is in the 2. 29 m air? [Neglect friction.] 3. 44 m 1. 0.654 s 4. 88 m 2. 1.53 s 3. 3.06 s 18. A ball thrown vertically upward reaches a maximum 4. 6.12 s height of 30 meters above the surface of Earth. At its maximum height, the speed of the ball is 12. What is the speed of a 2.5-kilogram mass after it has 1. 0.0 m/s fallen freely from rest through a distance of 12 me- 2. 3.1 m/s ters? 3. 9.8 m/s 1. 4.8 m/s 4. 24 m/s 2. 15 m/s 3. 30 m/s 19. A rocket initially at rest on the ground lifts off verti- 4. 43 m/s cally with a constant acceleration of 2.0 × 101 meters per second2. How long will it take the rocket to reach 13. A baseball dropped from the roof of a tall building an altitude of 9.0 × 103 meters? takes 3.1 seconds to hit the ground. How tall is the 1. 3.0 × 101 s building? [Neglect friction.] 2. 4.3 × 101 s 1. 15 m 3. 4.5 × 102 s 2. 30 m 4. 9.0 × 102 s 3. 47 m 4. 94 m 20. Objects in free fall near the surface of Earth acceler- ate downward at 9.81 meters per second2. Explain 14. A ball dropped from rest falls freely until it hits the why a feather does not accelerate at this rate when ground with a speed of 20 m/s. The time during dropped near the surface of Earth. which the ball is in free fall is approximately 1. 1 s 2. 2 s 3. 0.5 s 4. 10 s APlusPhysics: Kinematics-Free Fall VEL.B1, ACC.C1 Page 23

Name: Period: Kinematics-Free Fall 21. A 1.0-kilogram ball is dropped from the roof of a 27. Which diagram best represents the position of a ball, building 40 meters tall. What is the approximate at equal time intervals, as it falls freely from rest near time of fall? [Neglect air resistance.] Earth’s surface? 1. 2.9 s 2. 2.0 s 3. 4.1 s 4. 8.2 s 22. A 0.25-kilogram baseball is thrown upward with a speed of 30 meters per second. Neglecting friction, the maximum height reached by the baseball is ap- proximately 1. 15 m 2. 46 m 3. 74 m 4. 92 m 23. A rock falls from rest off a high cliff. How far has the rock fallen when its speed is 39.2 meters per second? [Neglect friction.] 1. 19.6 m 2. 44.1 m 3. 78.3 m 4. 123 m 24. An astronaut standing on a platform on the Moon drops a hammer. If the hammer falls 6.0 meters verti- cally in 2.7 seconds, what is its acceleration? 1. 1.6 m/s2 2. 2.2 m/s2 3. 4.4 m/s2 4. 9.8 m/s2 25. What is the time required for an object starting from rest to fall freely 500. meters near Earth’s surface? 1. 51.0 s 2. 25.5 s 3. 10.1 s 4. 7.14 s 26. A 3.00-kilogram mass is thrown vertically upward with an initial speed of 9.80 meters per second. What is the maximum height this object will reach? [Ne- glect friction.] 1. 1.00 m 2. 4.90 m 3. 9.80 m 4. 19.6 m Page 24 VEL.B1, ACC.C1 APlusPhysics: Kinematics-Free Fall

Name: Period: Kinematics-Projectiles 1. A volleyball hit into the air has an initial speed of 10 meters per second. Which vector best represents the angle above the horizontal that the ball should be hit to remain in the air for the greatest amount of time? Base your answers to questions 2 through 4 on the information below. A projectile is fired from the ground with an initial velocity of 250 meters per second at an angle of 60° above the horizontal. 2. On the diagram at right, use a protractor and ruler to draw a vector to represent the initial velocity of the projectile. Begin the vector at P, and use a scale of 1.0 centimeter = 50 meters per second. 3. Determine the horizontal component of the initial velocity. 4. Explain why the projectile has no acceleration in the horizontal direction. [Neglect friction.] 5. Two stones, A and B, are thrown horizontally from 6. The diagram below represents the path of a stunt car the top of a cliff. Stone A has an initial speed of 15 that is driven off a cliff, neglecting friction. meters per second and stone B has an initial speed of 30 meters per second. Compared to the time it takes stone A to reach the ground, the time it takes stone B to reach the ground is 1. the same 2. twice as great 3. half as great 4. four times as great Compared to the horizontal component of the car’s velocity at point A, the horizontal component of the car’s velocity at point B is 1. smaller 2. greater 3. the same APlusPhysics: Kinematics-Projectiles ACC.D1 Page 25

Name: Period: Kinematics-Projectiles Base your answers to questions 7 through 9 on the infor- 11. A golf ball is hit with an initial velocity of 15 meters mation and diagram below. per second at an angle of 35° above the horizontal. What is the vertical component of the golf ball’s ini- An object was projected horizontally from a tall cliff. The tial velocity? diagram below represents the path of the object, neglect- 1. 8.6 m/s ing friction. 2. 9.8 m/s 3. 12 m/s 4. 15 m/s 12. As shown in the diagram below, a student standing on the roof of a 50-meter-high building kicks a stone at a horizontal speed of 4 meters per second. 7. How does the magnitude of the horizontal compo- nent of the object’s velocity at A compare with the magnitude of the horizontal component of the ob- ject’s velocity at point B? 8. How does the magnitude of the vertical component How much time is required for the stone to reach of the object’s velocity at point A compare with the the level ground below? [Neglect friction.] magnitude of the vertical component of the object’s 1. 3.19 s velocity at point B? 2. 5.10 s 3. 10.2 s 4. 12.5 s 9. On the diagram above, sketch a likely path of the 13. A machine launches a tennis ball at an angle of 25° horizontally projected object, assuming that it was above the horizontal at a speed of 14 m/s. The ball subject to air resistance. returns to level ground. Which combination of changes must produce an increase in time of flight of 10. A golf ball is propelled with an initial velocity of 60 a second launch? meters per second at 37° above the horizontal. The 1. decrease the launch angle and decrease the ball’s horizontal component of the golf ball’s initial veloc- initial speed ity is 2. decrease the launch angle and increase the ball’s 1. 30 m/s initial speed 2. 36 m/s 3. increase the launch angle and decrease the ball’s 3. 40 m/s initial speed 4. 48 m/s 4. increase the launch angle and increase the ball’s initial speed Page 26 ACC.D1 APlusPhysics: Kinematics-Projectiles

Name: Period: Kinematics-Projectiles Base your answers to questions 14 through 16 on the information below. A kicked soccer ball has an initial velocity of 25 meters per second at an angle of 40° above the horizontal, level ground. [Neglect friction.] 14. Calculate the magnitude of the vertical component of the ball’s initial velocity. [Show all work, including the equation and substitution with units. 15. Calculate the maximum height the ball reaches above its initial position. [Show all work, including the equation and substitution with units.] 16. On the diagram, sketch the path of the ball’s flight from its initial position at point P until it returns to level ground. 17. Two spheres, A and B, are simultaneously projected Base your answers to questions 18 and 19 on the infor- horizontally from the top of a tower. Sphere A has mation below. a horizontal speed of 40 m/s and sphere B has a horizontal speed of 20 m/s. Which statement best An outfielder throws a baseball to second base at a speed describes the time required for the spheres to reach of 19.6 m/s and an angle of 30° above the horizontal. the ground and the horizontal distance they travel? 1. Both spheres hit the ground at the same time 18. Which pair represents the initial horizontal velocity and at the same distance from the base of the (vx) and initial vertical velocity (vy) of the baseball? tower. 1. vx = 17.0 m/s and vy = 9.80 m/s 2. Both spheres hit the ground at the same time, 2. vx = 9.80 m/s and vy = 17.0 m/s but sphere A lands twice as far as sphere B from 3. vx = 19.4 m/s and vy = 5.90 m/s the base of the tower. 4. vx = 19.6 m/s and vy = 19.6 m/s 3. Both spheres hit the ground at the same time, but sphere B lands twice as far as sphere A from 19. If the ball was caught at the same height from which the base of the tower. it was thrown, calculate the amount of time the ball 4. Sphere A hits the ground before sphere B, and was in the air, showing all work including the equa- sphere A lands twice as far as sphere B from the tion and substitution with units. base of the tower. APlusPhysics: Kinematics-Projectiles ACC.D1 Page 27

Name: Period: Kinematics-Projectiles 20. Four projectiles, A, B, C, and D, were launched from, and returned to, level ground. The data table below shows the initial horizontal speed, initial vertical speed, and time of flight for each projectile. Which projectile traveled the greatest horizontal distance? [Neglect friction.] 1. A 2. B 3. C 4. D 21. Four identical projectiles are launched with the same initial speed, v, but at various angles above the level ground. Which diagram represents the initial velocity of the projectile that will have the largest total horizontal displace- ment? [Neglect air resistance.] Base your answers to questions 22 and 23 on the information and diagram below. A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of 35° with the horizontal, as shown. The ball has an initial vertical velocity of 4.9 meters per second and a total time of flight of 1.0 second. [Neglect air resistance.] 22. What is the horizontal component of the ball’s initial velocity? 23. Find the maximum height reached by the ball. Page 28 ACC.D1 APlusPhysics: Kinematics-Projectiles

Name: Period: Kinematics-Projectiles Base your answers to questions 24 through 26 on the information below. The path of a stunt car driven horizontally off a cliff is represented in the diagram at right. After leaving the cliff, the car falls freely to point A in 0.50 second and to point B in 1.00 second. 24. Determine the magnitude of the horizontal component of the velocity of the car at point B. [Neglect friction.] 25. Determine the magnitude of the vertical velocity of the car at point A. 26. Calculate the magnitude of the vertical displacement, dy, of the car from point A to point B. [Neglect friction. Show all work, including the equation and substitution with units.] Base your answers to questions 27 through 29 on the information and diagram below. A projectile is launched into the air with an initial speed of vi at a launch angle of 30° above the horizontal. The projectile lands on the ground 2.0 seconds later. 27. On the diagram, sketch the ideal path of the projectile. 28. How does the maximum altitude of the projectile change as the launch angle is increased from 30° to 45° above the horizontal? [Assume the same initial speed, vi.] 29. How does the total horizontal distance traveled by the projectile change as the launch angle is increased from 30° to 45° above the horizontal? [Assume the same initial speed, vi.] APlusPhysics: Kinematics-Projectiles ACC.D1 Page 29

Name: Period: Kinematics-Projectiles Base your answers to questions 30 through 32 on the information and graph below. A machine fired several projectiles at the same angle, θ, above the horizontal. Each projectile was fired with a different initial velocity, vi. The graph below represents the relationship between the magnitude of the initial vertical velocity, viy, and the magni- tude of the corresponding initial velocity, vi, of these projectiles. 30. Determine the magnitude of the initial vertical velocity of the projectile, viy, when the magnitude of its initial velocity, vi, was 40 meters per second. 31. Determine the angle, θ, above the horizontal at which the projectiles were fired. 32. Calculate the magnitude of the initial horizontal velocity of the projectile, vix, when the magnitude of its initial velocity, vi, was 40 meters per second. [Show all work, including the equation and substitution with units.] 33. A plane flying horizontally above Earth’s surface 35. A 0.2-kilogram red ball is thrown horizontally at at 100 meters per second drops a crate. The crate a speed of 4 meters per second from a height of 3 strikes the ground 30 seconds later. What is the meters. A 0.4-kilogram green ball is thrown hori- magnitude of the horizontal component of the zontally from the same height at a speed of 8 meters crate’s velocity just before it strikes the ground? per second. Compared to the time it takes the red [Neglect friction.] ball to reach the ground, the time it takes the green 1. 0 m/s ball to reach the ground is 2. 100 m/s 1. one-half as great 3. 294 m/s 2. twice as great 4. 394 m/s 3. the same 4. four times as great 34. The diagram below represents the path of an object after it was thrown. 36. A ball is thrown at an angle of 38° to the horizontal. What happens to the magnitude of the ball’s vertical What happens to the object’s acceleration as it trav- acceleration during the total time interval that the els from A to B? ball is in the air? 1. It decreases. 1. It decreases, then increases. 2. It increases. 2. It decreases, then remains the same. 3. It remains the same. 3. It increases, then decreases. 4. It remains the same. Page 30 ACC.D1 APlusPhysics: Kinematics-Projectiles

Name: Period: Kinematics-Projectiles Base your answers to questions 37 through 39 on the 40. A ball is thrown horizontally at a speed of 24 meters information and diagram below. per second from the top of a cliff. If the ball hits the ground 4.0 seconds later, approximately how high is A projectile is launched horizontally at a speed of 30 the cliff ? meters per second from a platform located a vertical 1. 6.0 m distance h above the ground. The projectile strikes the 2. 39 m ground after time t at horizontal distance d from the 3. 78 m base of the platform. [Neglect friction.] 4. 96 m 41. A golf ball is given an initial speed of 20 meters per second and returns to level ground. Which launch angle above level ground results in the ball traveling the greatest horizontal distance? [Neglect friction.] 1. 60° 2. 45° 3. 30° 4. 15° 37. On the diagram above, sketch the theoretical path of 42. A golf ball is hit at an angle of 45° above the hori- the projectile. zontal. What is the acceleration of the golf ball at the highest point in its trajectory? [Neglect friction.] 38. Calculate the horizontal distance, d, if the projectile’s 1. 9.8 m/s2 upward time of flight is 2.5 seconds. [Show all work, includ- 2. 9.8 m/s2 downward ing the equation and substitution with units.] 3. 6.9 m/s2 horizontal 4. 0.0 m/s2 43. A soccer player kicks a ball with an initial velocity of 10 meters per second at an angle of 30° above the horizontal. The magnitude of the horizontal compo- nent of the ball’s initial velocity is 1. 5.0 m/s 2. 8.7 m/s 3. 9.8 m/s 4. 10 m/s 39. Express the projectile’s total time of flight, t, in terms 44. A vector makes an angle, θ, with the horizontal. The of the vertical distance, h, and the acceleration due to horizontal and vertical components of the vector will gravity, g. [Write an appropriate equation and solve be equal in magnitude if angle θ is it for t.] 1. 30° 2. 45° 3. 60° 4. 90° APlusPhysics: Kinematics-Projectiles ACC.D1 Page 31

Name: Period: Kinematics-Projectiles 45. The diagram below represents a setup for demonstrating motion. When the lever is released, the support rod withdraws from ball B, allowing it to fall. At the same instant, the rod contacts ball A, propelling it horizontally to the left. Which statement describes the motion that is observed after the lever is released and the balls fall? [Neglect friction.] 1. Ball A travels at constant velocity. 2. Ball A hits the tabletop at the same time as ball B. 3. Ball B hits the tabletop before ball A. 4. Ball B travels with an increasing acceleration. 46. A projectile launched at an angle of 45° above the 49. A toy rocket is launched twice into the air from horizontal travels through the air. Compared to the level ground and returns to level ground. The rocket projectile’s theoretical path with no air friction, the is first launched with initial speed v at an angle of actual trajectory of the projectile with air friction is 45° above the horizontal. It is launched the sec- 1. lower and shorter ond time with the same initial speed, but with the 2. lower and longer launch angle increased to 60° above the horizontal. 3. higher and shorter Describe how both the total horizontal distance the 4. higher and longer rocket travels and the time in the air are affected by the increase in launch angle. [Neglect friction.] 47. A projectile is fired with an initial velocity of 120 meters per second at an angle, θ, above the horizon- 50. A projectile is launched at an angle above the tal. If the projectile’s initial horizontal speed is 55 ground. The horizontal component of the projectile’s meters per second, then angle θ measures approxi- velocity, vx, is initially 40 meters per second. The mately vertical component of the projectile’s velocity, vy, is 1. 13° initially 30 meters per second. What are the compo- 2. 27° nents of the projectile’s velocity after 2.0 seconds of 3. 63° flight? [Neglect friction.] 4. 75° 1. vx=40 m/s and vy=10 m/s 2. vx=40 m/s and vy=30 m/s 48. A baseball is thrown at an angle of 40° above the 3. vx=20 m/s and vy=10 m/s horizontal. The horizontal component of the base- 4. vx=20 m/s and vy=30 m/s ball’s initial velocity is 12 meters per second. What is the magnitude of the ball’s initial velocity? 1. 7.71 m/s 2. 9.20 m/s 3. 15.7 m/s 4. 18.7 m/s Page 32 ACC.D1 APlusPhysics: Kinematics-Projectiles

Name: Period: Kinematics-Projectiles 51. A ball is thrown with an initial speed of 10 meters Base your answers to questions 55 and 56 on the per second. At what angle above the horizontal information below and on your knowledge of physics. should the ball be thrown to reach the greatest height? A football is thrown at an angle of 30° above the 1. 0° horizontal. The magnitude of the horizontal component 2. 30° of the ball’s initial velocity is 13.0 meters per second. The 3. 45° magnitude of the vertical component of the ball’s initial 4. 90° velocity is 7.5 meters per second. [Neglect friction.] 52. The components of a 15-meters-per-second velocity 55. On the axes below, draw a graph representing the at an angle of 60° above the horizontal are relationship between the horizontal displacement of 1. 7.5 m/s vertical and 13 m/s horizontal the football and the time the football is in the air. 2. 13 m/s vertical and 7.5 m/s horizontal 3. 6.0 m/s vertical and 9.0 m/s horizontal 4. 9.0 m/s vertical and 6.0 m/s horizontal 53. Which combination of initial horizontal velocity, (vH) and initial vertical velocity, (vV) results in the greatest horizontal range for a projectile over level ground? [Neglect friction.] 56. The football is caught at the same height from which it is thrown. Calculate the total time the football was in the air. [Show all work, including the equa- tion and substitution with units.] 54. Without air resistance, a kicked ball would reach a maximum height of 6.7 meters and land 38 meters away. With air resistance, the ball would travel 1. 6.7 m vertically and more than 38 m horizontally 2. 38 m horizontally and less than 6.7 m vertically 3. more than 6.7 m vertically and less than 38 m horizontally 4. less than 38 m horizontally and less than 6.7 m vertically APlusPhysics: Kinematics-Projectiles ACC.D1 Page 33

Name: Period: Dynamics-Newton's 1st Law 1. As shown in the diagram, an open box and its contents have a com- bined mass of 5.0 kilograms. A horizontal force of 15 newtons is required to push the box at a constant speed of 1.5 meters per second across a level surface. The inertia of the box and its contents increases if there is an increase in the 1. speed of the box 2. mass of the contents of the box 3. magnitude of the horizontal force applied to the box 4. coefficient of kinetic friction between the box and the level surface 2. Which unit is equivalent to a newton per kilogram? 7. The data table below lists the mass and speed of four 1. m/s2 different objects 2. W/m 3. J∙s 4. kg∙m/s 3. Which object has the most inertia? Which object has the greatest inertia? 1. A 0.001-kilogram bumblebee traveling at 2 1. A meters per second 2. B 2. A 0.1-kilogram baseball traveling at 20 meters 3. C per second 4. D 3. A 5-kilogram bowling ball traveling at 3 meters per second 8. A 0.50-kilogram cart is rolling at a speed of 0.40 4. A 10-kilogram sled at rest meter per second. If the speed of the cart is doubled, the inertia of the cart is 4. If the sum of all the forces acting on a moving object 1. halved is zero, the object will 2. doubled 1. slow down and stop 3. quadrupled 2. change the direction of its motion 4. unchanged 3. accelerate uniformly 4. continue moving with constant velocity 9. Which person has the greatest inertia? 1. A 110-kg wrestler resting on a mat 5. The mass of a high school football player is approxi- 2. A 90-kg man walking at 2 m/s mately 3. A 70-kg long-distance runner traveling 5 m/s 1. 100 kg 4. A 50-kg girl sprinting at 10 m/s 2. 101 kg 3. 102 kg 10. Which object has the greatest inertia? 4. 103 kg 1. a falling leaf 2. a softball in flight 6. Which object has the greatest inertia? 3. a seated high school student 1. A 5-kg mass moving at 10 m/s 4. a rising helium-filled toy balloon 2. A 10-kg mass moving at 1 m/s 3. A 15-kg mass moving at 10 m/s 4. A 20-kg mass moving at 1 m/s Page 34 DYN.A1 APlusPhysics: Dynamics-Newton's 1st Law

Name: Period: Dynamics-Newton's 1st Law 11. A lab cart is loaded with different masses and moved at various velocities. Which diagram shows the cart-mass system with the greatest inertia? 12. Which object has the greatest inertia? 18. A 15-kilogram cart is at rest on a horizontal surface. 1. A 5-kg object moving at 5 m/s A 5-kilogram box is placed in the cart. Compared to 2. A 10-kg object moving at 3 m/s the mass and inertia of the cart, the cart-box system 3. A 15-kg object moving at 1 m/s has 4. A 20-kg object at rest 1. more mass and more inertia 2. more mass and the same inertia 13. A force of 1 newton is equivalent to 1 3. the same mass and more inertia 1. kg∙m/s2 4. less mass and more inertia 2. kg∙m/s 3. kg∙m2/s2 19. A different force is applied to each of four different 4. kg2∙m2/s2 blocks on a frictionless, horizontal surface. In which diagram does the block have the greatest inertia 2.0 14. Which object has the greatest inertia? seconds after starting from rest? 1. a 1-kg object moving at 15 m/s 2. a 5-kg object at rest 3. a 10-kg object moving at 2 m/s 4. a 15-kg object at rest 15. Which cart has the greatest inertia? 1. a 1-kg cart traveling at 4 m/s 2. a 2-kg cart traveling at 3 m/s 3. a 3-kg cart traveling at 2 m/s 4. a 4-kg cart traveling at 1 m/s 16. Which object has the greatest inertia? 1. a 15-kg mass traveling at 5 m/s 2. a 10-kg mass traveling at 10 m/s 3. a 10-kg mass traveling at 5 m/s 4. a 5-kg mass traveling at 15 m/s 17. Which object has the greatest inertia? 1. a 0.010-kg bullet traveling at 90 m/s 2. a 30-kg child traveling at 10 m/s on her bike 3. a 490-kg elephant walking with a speed of 1 m/s 4. a 1500-kg car at rest in a parking lot APlusPhysics: Dynamics-Newton's 1st Law DYN.A1 Page 35

Name: Period: Dynamics-Newton's 2nd Law 1. A constant unbalanced force is applied to an object for a period of time. Which graph best represents the ac- celeration of the object as a function of elapsed time? 2. The diagram below shows a horizontal 12-newton Base your answers to questions 5 and 6 on the diagram force being applied to two blocks, A and B, initially below, which shows a 1-newton metal disk resting on an at rest on a horizontal, frictionless surface. Block A index card that is balanced on top of a glass. has a mass of 1 kilogram and block B has a mass of 2 kilograms. The magnitude of the acceleration of block B is 5. What is the net force acting on the disk? 1. 6.0 m/s2 1. 1.0 N 2. 2.0 m/s2 2. 2.0 N 3. 3.0 m/s2 3. 0 N 4. 4.0 m/s2 4. 9.8 N 3. Which body is in equilibrium? 6. When the index card is quickly pulled away from the 1. a satellite moving around Earth in a circular orbit glass in a horizontal direction, the disk falls straight 2. a cart rolling down a frictionless incline down into the glass. This action is a result of the disk’s 3. an apple falling freely toward the surface of Earth 1. inertia 4. a block sliding at constant velocity across a table- 2. charge top 3. shape 4. temperature 4. The weight of a typical high school physics student is closest to 7. A student is standing in an elevator that is accelerat- 1. 1500 N ing downward. The force that the student exerts on 2. 600 N the floor of the elevator must be 3. 120 N 1. less than the weight of the student when at rest 4. 60 N 2. greater than the weight of the student when at rest 3. less than the force of the floor on the student 4. greater than the force of the floor on the student Page 36 DYN.B2 APlusPhysics: Dynamics-Newton's 2nd Law

Name: Period: Dynamics-Newton's 2nd Law 8. The diagram below represents two concurrent forces. Which vector below represents the force that will produce equilibrium with these two forces? 9. In the diagram below, a 20-newton force due north Base your answers to questions 12 and 13 on the infor- and a 20-newton force due east act concurrently on mation and diagram below. an object, as shown in the diagram below. A soccer ball is kicked from point Pi at an angle above a horizontal field. The ball follows an ideal path before landing on the field at point Pf. The additional force necessary to bring the object into 12. On the diagram below, draw an arrow to represent a state of equilibrium is the direction of the net force on the ball when it is at 1. 20 N, northeast position X. Label the arrow Fnet. [Neglect friction.] 2. 20 N, southwest 3. 28 N, northeast 4. 28 N, southwest 10. A man standing on a scale in an elevator notices that the scale reads 30 newtons greater than his normal weight. Which type of movement of the elevator could cause this greater-than-normal reading? 1. accelerating upward 2. accelerating downward 3. moving upward at constant speed 4. moving downward at constant speed 11. Two forces, F1 and F2, are applied to a block on a fric- 13. On the diagram above, draw an arrow to represent the tionless, horizontal surface as shown below. direction of the acceleration of the ball at position Y. Label the arrow a. [Neglect friction.] If the magnitude of the block’s acceleration is 2 m/s2, 14. A 5-newton force could have perpendicular compo- what is the mass of the block? nents of 1. 1 kg 1. 1 N and 4 N 2. 5 kg 2. 2 N and 3 N 3. 6 kg 3. 3 N and 4 N 4. 7 kg 4. 5 N and 5 N APlusPhysics: Dynamics-Newton's 2nd Law DYN.B2 Page 37

Name: Period: Dynamics-Newton's 2nd Law 15. Which graph best represents the motion of an object in equilibrium? 16. Which diagram represents a box in equilibrium? 17. The diagram below shows a 5-kilogram block at rest Base your answers to questions 18 and 19 on the infor- on a horizontal, frictionless table. mation below. The instant before a batter hits a 0.14-kilogram baseball, the velocity of the ball is 45 meters per second west. The instant after the batter hits the ball, the ball’s velocity is 35 meters per second east. The bat and ball are in con- tact for 1.0 × 10-2 second. Which diagram best represents the force exerted on 18. Determine the magnitude and direction of the aver- the block by the table? age acceleration of the baseball while it is in contact with the bat. 19. Calculate the magnitude of the average force the bat exerts on the ball while they are in contact. [Show all work, including the equation and substitution with units.] Page 38 DYN.B2 APlusPhysics: Dynamics-Newton's 2nd Law

Name: Period: Dynamics-Newton's 2nd Law 20. The vector diagram below represents two forces, F1 and F2, simultaneously acting on an object. Which vector best represents the resultant of the two forces? 21. Two forces act concurrently on an object on a hori- Base your answers to questions 24 through 26 on the zontal, frictionless surface, as shown in the diagram information and diagram below. below. Force A with a magnitude of 5.6 newtons and force B with a magnitude of 9.4 newtons act concurrently on point P. What additional force, when applied to the object, will establish equilibrium? 1. 16 N toward the right 2. 16 N toward the left 3. 4 N toward the right 4. 4 N toward the left 22. A 3-newton force and a 4-newton force are act- 24. Determine the scale used in the diagram. ing concurrently on a point. Which force could not produce equilibrium with these two forces? 1 cm = ______ N 1. 1 N 2. 7 N 3. 9 N 4. 4 N 23. The diagram shows a worker using a rope to pull a cart. The worker’s pull on the handle of the 25. On the diagram, use a ruler and protractor to con- cart can best be described as struct a vector representing the resultant of forces A a force having and B. 1. magnitude, only 2. direction, only 26. Determine the magnitude of the resultant force. 3. both magnitude and direction 4. neither magnitude nor direction APlusPhysics: Dynamics-Newton's 2nd Law DYN.B2 Page 39

Name: Period: Dynamics-Newton's 2nd Law 27. Two 30-newton forces act concurrently on an object. In which diagram would the forces produce a resultant with a magnitude of 30 newtons? Base your answers to questions 28 through 30 on the 31. The diagram below shows a force of magnitude F ap- information and diagram below. plied to a mass at an angle θ relative to a horizontal frictionless surface. In the scaled diagram, two forces, F1 and F2, act on a 4.0-kilogram block at point P. Force F1 has a magnitude of 12 newtons, and is directed toward the right. As angle θ is increased, the horizontal acceleration of the mass 1. decreases 2. increases 3. remains the same 28. Using a ruler and the scaled diagram, determine the 32. Forces A and B have a resultant R. Force A and magnitude of F2 in newtons. resultant R are represented in the diagram below. 29. Determine the magnitude of the net force acting on the block. Which vector best represents force B? 30. Calculate the magnitude of the acceleration of the block. [Show all work, including the equation and substitution with units.] Page 40 DYN.B2 APlusPhysics: Dynamics-Newton's 2nd Law

Name: Period: Dynamics-Newton's 2nd Law Base your answers to questions 33 and 34 on the 37. A 0.50-kilogram frog is at rest on the bank sur- information below. rounding a pond of water. As the frog leaps from the bank, the magnitude of the ac- A soccer player accelerates a 0.50-kilogram celeration of the frog is 3.0 meters soccer ball by kicking it with a net force of 5 per second2. Calculate the magni- newtons. tude of the net force exerted on the frog as it leaps. [Show 33. Calculate the magnitude of the accel- all work, including the equa- eration of the ball. [Show all work, tion and substitution with units.] including the equation and substitu- tion with units.] 34. What is the magnitude of the force of the soccer ball 38. Which graph best represents the motion of an object on the player’s foot? that is not in equilibrium as it travels along a straight line? 35. The vector diagram below represents the horizontal component, FH, and the vertical component, FV, of a 24-newton force acting at 35° above the horizontal. What are the magnitudes of the horizontal and 39. The diagram below represents a 5-newton force and vertical components? a 12-newton force acting on point P. 1. FH = 3.5 N and FV = 4.9 N 2. FH = 4.9 N and FV = 3.5 N The resultant of the two forces has a magnitude of 3. FH = 14 N and FV = 20 N 1. 5 N 4. FH = 20 N and FV = 14 N 2. 7 N 3. 12 N 36. Two forces act concurrently on an object. Their 4. 13 N resultant force has the largest magnitude when the angle between the forces is DYN.B2 Page 41 1. 0° 2. 30° 3. 90° 4. 180° APlusPhysics: Dynamics-Newton's 2nd Law

Name: Period: Dynamics-Newton's 2nd Law 40. Which pair of forces acting concurrently on an object 46. The weight of a chicken egg is most nearly equal will produce the resultant of greatest magnitude? to 1. 10-3 N 2. 10-2 N 3. 100 N 4. 102 N 41. A 5-newton force and a 7-newton force act concur- 47. A 1.5-kilogram lab cart is accelerated uniformly from rently on a point. As the angle between the forces is rest to a speed of 2.0 meters per second in 0.50 sec- increased from 0° to 180°, the magnitude of the resul- ond. What is the magnitude of the force producing tant of the two forces changes from this acceleration? 1. 0 N to 12 N 1. 0.70 N 2. 2 N to 12 N 2. 1.5 N 3. 12 N to 2 N 3. 3.0 N 4. 12 N to 0 N 4. 6.0 N 42. A force of 25 newtons east and a force of 25 newtons 48. Which body is in equilibrium? west act concurrently on a 5-kilogram cart. What is 1. a satellite orbiting Earth in a circular orbit the acceleration of the cart? 2. a ball falling freely toward the surface of Earth 1. 1.0 m/s2 west 3. a car moving with a constant speed along a 2. 0.20 m/s2 east straight, level road 3. 5.0 m/s2 east 4. a projectile at the highest point in its trajectory 4. 0 m/s2 49. The diagram below represents a force vector, A, and a resultant vector, R. 43. A high school physics student is sitting in a seat read- Which force vector B below could be added to force ing this question. The magnitude of the force with vector A to produce resultant vector R? which the seat is pushing up on the student to sup- port him is closest to 1. 0 N 2. 60 N 3. 600 N 4. 6,000 N 44. As the angle between two concurrent forces decreases, 50. A 25-newton horizontal force northward and a the magnitude of the force required to produce equi- 35-newton horizontal force southward act concur- librium rently on a 15-kilogram object on a frictionless sur- 1. decreases face. What is the magnitude of the object’s accelera- 2. increases tion? 3. remains the same 1. 0.67 m/s2 2. 1.7 m/s2 45. A 60-kg skydiver is falling at a constant speed near 3. 2.3 m/s2 the surface of Earth. The magnitude of the force of 4. 4.0 m/s2 air friction acting on the skydiver is approximately 1. 0 N 2. 6 N 3. 60 N 4. 600 N Page 42 DYN.B2 APlusPhysics: Dynamics-Newton's 2nd Law

Name: Period: Dynamics-Newton's 2nd Law 51. A woman is standing on a bathroom scale 57. A number of 1-newton horizontal forces are ex- in an elevator car. If the scale reads a value erted on a block on a frictionless, horizontal surface. greater than the weight of the woman at rest, Which top-view diagram shows the forces producing the elevator car could be moving the greatest magnitude of acceleration of the block? 1. downward at constant speed 2. upward at constant speed 3. downward at increasing speed 4. upward at increasing speed 52. A net force of 10 newtons accelerates an object at 5.0 meters per second2. What net force would be required to accelerate the same object at 1.0 meter per second2? 1. 1.0 N 2. 2.0 N 3. 5.0 N 4. 50 N 53. A 6.0-newton force and an 8.0-newton force act 58. A rock is thrown straight up into the air. At the high- concurrently on a point. As the angle between these est point of the rock’s path, the magnitude of the net forces increases from 0° to 90°, the magnitude of their force acting on the rock is resultant 1. less than the magnitude of the rock’s weight, but 1. decreases greater than zero 2. increases 2. greater than the magnitude of the rock’s weight 3. remains the same 3. the same as the magnitude of the rock’s weight 4. zero 54. Which situation describes an object that has no un- balanced force acting on it? 59. Four forces act concurrently on a block on a horizon- 1. an apple in free fall tal surface as shown in the diagram below. 2. a satellite orbiting Earth 3. a hockey puck moving at constant velocity across ice 4. a laboratory cart moving down a frictionless 30° incline 55. Two 20-newton forces act concurrently on an object. What angle between these forces will produce a resul- tant force with the greatest magnitude? 1. 0° 2. 45° 3. 90° 4. 180° 56. Which situation represents a person in equilibrium? As a result of these forces, the block 1. a child gaining speed while sliding down a slide 1. moves at constant speed to the right 2. a woman accelerating upward in an elevator 2. moves at a constant speed to the left 3. a man standing still on a bathroom scale 3. accelerates to the right 4. a teenager driving around a corner in his car 4. accelerates to the left APlusPhysics: Dynamics-Newton's 2nd Law DYN.B2 Page 43

Name: Period: Dynamics-Newton's 2nd Law Base your answers to questions 60 through 63 on the information below and diagram at right as well as your knowledge of physics. Two forces, a 60-newton force east and an 80-newton force north, act concurrently on an object located at point P, as shown. 60. Using a ruler, determine the scale used in the vector diagram. 61. Draw the resultant force vector to scale on the diagram. Label the vector “R.” 62. Determine the magnitude of the resultant force, R. 63. Determine the measure of the angle, in degrees, between north and the resultant force, R. 64. A 4.0-kilogram object is accelerated at 3.0 meters 67. A student throws a 5.0-newton ball straight up. What per second2 north by an unbalanced force. The same is the net force on the ball at its maximum height? unbalanced force acting on a 2.0-kilogram object will 1. 0.0 N accelerate this object toward the north at 2. 5.0 N, up 1. 12 m/s2 3. 5.0 N, down 2. 6.0 m/s2 4. 9.8 N, down 3. 3.0 m/s2 4. 1.5 m/s2 68. An object is in equilibrium. Which force vector diagram could represent the force(s) acting on the 65. A 750-newton person stands in an elevator that is object? accelerating downward. The upward force of the elevator floor on the person must be 1. equal to 0 N 2. less than 750 N 3. equal to 750 N 4. greater than 750 N 66. A 160-kilogram space vehicle is traveling along a straight line at a constant speed of 800 meters per second. The magnitude of the net force on the space vehicle is 1. 0 N 2. 1.60 × 102 N 3. 8.00 × 102 N 4. 1.28 × 105 N Page 44 DYN.B2 APlusPhysics: Dynamics-Newton's 2nd Law

Name: Period: Dynamics-Newton's 3rd Law 1. A student pulls a 60-newton sled with 6. When a child squeezes the nozzle of a garden hose, water a force having a magnitude of 20 shoots out of the hose toward the east. What is the newtons. What is the magnitude of compass direction of the force being exerted on the child the force that the sled exerts on the by the nozzle? student? 1. 20 N 7. A 100-kg boy and a 50-kg girl, each holding a spring 2. 40 N scale, pull against each other as shown in the diagram 3. 60 N below. 4. 80 N 2. If a 65-kilogram astronaut exerts a force with a The graph below shows the relationship between the magnitude of 50 newtons on a satellite that she is magnitude of the force that the boy applies on his spring repairing, the magnitude of the force that the satel- scale and time. lite exerts on her is 1. 0 N 2. 50 N less than her weight 3. 50 N more than her weight 4. 50 N 3. A 400-newton girl standing on a dock exerts a force Which graph best represents the relationship between the of 100 newtons on a 10,000-newton sailboat as she magnitude of the force that the girl applies on her spring pushes it away from the dock. How much force does scale and time? the sailboat exert on the girl? 1. 25 N 2. 100 N 3. 400 N 4. 10,000 N 4. A carpenter hits a nail with a hammer. Compared to the magnitude of the force the hammer exerts on the nail, the magnitude of the force the nail exerts on the hammer during contact is 1. less 2. greater 3. the same 5. A woman is pushing a baby stroller. Compared to the magnitude of the force exerted on the stroller by the woman, the magnitude of the force exerted on the woman by the stroller is 1. zero 2. smaller, but greater than zero 3. larger 4. the same APlusPhysics: Dynamics-Newton's 3rd Law DYN.C1 Page 45

Name: Period: Dynamics-Newton's 3rd Law 8. The diagram below shows a compressed spring between two carts initially at rest on a horizontal, frictionless surface. Cart A has a mass of 2 kilo- grams and cart B has a mass of 1 kilogram. A string holds the carts together. The string is cut and the carts move apart. Com- pared to the magnitude of the force the spring exerts on cart A, the magnitude of the force the spring exerts on cart B is 1. the same 2. half as great 3. twice as great 4. four times as great 9. A baseball bat exerts a force of magnitude F on a ball. If the mass of the bat is three times the mass of the ball, the magnitude of the force of the ball on the bat is 1. F 2. 2F 3. 3F 4. F/3 10. As a 5.0 × 102-newton basketball player jumps from the floor up toward the basket, the magnitude of the force of her feet on the floor is 1.0 × 103 newtons. As she jumps, the magnitude of the force of the floor on her feet is 1. 25 N 2. 100 N 3. 500 N 4. 1,000 N Page 46 DYN.C1 APlusPhysics: Dynamics-Newton's 3rd Law

Name: Period: Dynamics-Friction 1. Which vector diagram best represents a cart slowing down as it travels to the right on a horizontal surface? Base your answers to questions 2 and 3 on the informa- Base your answers to questions 5 through 8 on the infor- tion below. mation below. A student and the waxed skis she is wearing An ice skater applies a horizontal force to a 20-kg block have a combined weight of 850 newtons. on frictionless, level ice, causing the block to accelerate The skier travels down a snow-covered hill uniformly at 1.4 m/s2 to the right. After the skater stops and then glides to the east across a snow-cov- pushing the block, it slides onto a region of ice that is ered, horizontal surface. covered with a thin layer of sand. The coefficient of ki- netic friction between the block and the sand-covered ice 2. Determine the magnitude of the normal force exerted is 0.28. by the snow on the skis as the skier glides across the horizontal surface. 5. Calculate the magnitude of the force applied to the block by the skater. 3. Calculate the magnitude of the force of friction act- 6. On the diagram below, starting at point A, draw a ing on the skis as the skier glides across the snow- vector to represent the force applied to the block by covered, horizontal surface. [Show all work, including the skater. Begin the vector at point A and use a scale the equation and substitution with units.] of 1 cm = 10 newtons. 4. The coefficient of kinetic friction between a 780-new- 7. Determine the magnitude of the normal force acting ton crate and a level warehouse floor is 0.200. Cal- on the block. culate the magnitude of the horizontal force required to move the crate across the floor at constant speed. 8. Calculate the magnitude of the force of friction act- [Show all work, including the equation and substitu- ing on the block as it slides over the sand-covered ice. tion with units.] [Show all work, including the equation and substitu- tion with units.] APlusPhysics: Dynamics-Friction DYN.D1 Page 47

Name: Period: Dynamics-Friction Base your answers to questions 9 through 13 on the in- Base your answers to questions 14 and 15 on the informa- formation below. tion and diagram below. A manufacturer’s advertisem*nt claims that their A force of 60 newtons is applied to a rope to pull a sled 1,250-kilogram (12,300-newton) sports car can acceler- across a horizontal surface at a constant velocity. The rope ate on a level road from 0 to 60 miles per hour (0 to 26.8 is at an angle of 30 degrees above the horizontal. meters per second) in 3.75 seconds. 9. Determine the acceleration, in meters per second2, of 14. Calculate the magnitude of the component of the the car according to the advertisem*nt. 60-newton force that is parallel to the horizontal sur- face. [Show all work, including the equation and sub- stitution with units.] 10. Calculate the net force required to give the car the acceleration claimed in the advertisem*nt. [Show all work, including the equation and substitution with units.] 15. Determine the magnitude of the frictional force act- ing on the sled. 11. What is the normal force exerted by the road on the 16. A child pulls a wagon at a constant velocity along car? a level sidewalk. The child does this by applying a 22-newton force to the wagon handle, which is in- 12. The coefficient of friction between the car’s tires and clined at 35° to the sidewalk as shown below. the road is 0.80. Calculate the maximum force of friction between the car’s tires and the road. [Show all work, including the equation and substitution with units.] 13. Using the values for the forces you have calculated, What is the magnitude of the force of friction on the explain whether or not the manufacturer’s claim for wagon? the car’s acceleration is possible. 1. 11 N 2. 13 N Page 48 DYN.D1 3. 18 N 4. 22 N APlusPhysics: Dynamics-Friction

Name: Period: Dynamics-Friction Base your answers to questions 17 through 21 on the in- 22. The diagram below shows a 4-kilogram object accel- formation and diagram below. erating at 10 m/s2 on a rough horizontal surface. A horizontal force of 8 newtons is used to pull a 20-new- ton wooden box moving toward the right along a hori- zontal, wood surface, as shown (not drawn to scale). 17. Starting at point P on the diagram below, use a metric What is the magnitude of the frictional force Ff act- ruler and a scale of 1 cm = 10 N to draw a vector rep- ing on the object? resenting the normal force acting on the box. Label 1. 5 N the vector FN. 2. 10 N 3. 20 N 4. 40 N 23. A car’s performance is tested on various horizontal road surfaces. The brakes are applied, causing the rubber tires of the car to slide along the road without rolling. The tires encounter the greatest force of fric- tion to stop the car on 1. dry concrete 2. dry asphalt 3. wet concrete 4. wet asphalt 18. Calculate the magnitude of the frictional force acting 24. When a 12-newton horizontal force is applied to a on the box. [Show all work, including the equation box on a horizontal tabletop, the box remains at rest. and substitution with units.] The force of static friction acting on the box is 1. 0 N 2. between 0 N and 12 N 3. 12 N 4. greater than 12 N 19. Determine the magnitude of the net force acting on 25. A box is pushed toward the right across a classroom the box. floor. The force of friction on the box is directed to- ward the 20. Determine the mass of the box. 1. left 2. right 3. ceiling 4. floor 21. Calculate the magnitude of the acceleration of the 26. A skier on waxed skis is pulled at constant speed box. [Show all work, including the equation and sub- across level snow by a horizontal force of 39 newtons. stitution with units.] Calculate the normal force exerted on the skier. APlusPhysics: Dynamics-Friction DYN.D1 Page 49

Name: Period: Dynamics-Friction Base your answers to questions 27 through 31 on the in- Base your answers to questions 32 through 34 on the in- formation below. Show all work, including the equation formation and diagram below. and substitution with units. A 10-kg box, sliding to the right across a rough horizontal A force of 10 newtons toward the right is exerted on a floor, accelerates at -2 m/s2 due to the force of friction. wooden crate initially moving to the right on a horizontal wooden floor. The crate weighs 25 newtons. 32. Calculate the magnitude of the net force acting on the box. [Show all work, including the equation and 27. Calculate the magnitude of the force of friction be- substitution with units.] tween the crate and the floor. 33. On the diagram below, draw a vector representing the 28. On the diagram below, draw and label all vertical net force acting on the box. Begin the vector at point forces acting on the crate. P and use a scale of 1 cm = 10 newtons. 34. Calculate the coefficient of kinetic friction between 29. On the diagram above, draw and label all horizontal the box and the floor. [Show all work, including the forces acting on the crate. equation and substitution with units.] 30. What is the magnitude of the net force acting on the crate? 31. Is the crate accelerating? Explain your answer. 35. A 10-kg rubber block is pulled horizontally at con- stant velocity across a sheet of ice. Calculate the magnitude of the force of friction acting on the block. [Show all work, including the equation and substitu- tion with units.] Page 50 DYN.D1 APlusPhysics: Dynamics-Friction