P = mv (kg•m/s) impulse: j = F
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- Navigate this page:
- Collision Lab
- B. Forms of Energy
- Human Power Lab
- C. Conservation of Energy
- Air Resistance Lab
- Ballistic Pendulum Lab
- Practice Multiple Choice (No calculator)
A. Linear Momentum Questions 1-15 Briefly explain your answer. 1. An open cart rolls along a frictionless track while it is raining. As it rolls, what happens to the speed of the cart as the rain collects in it? (A) increase (B) the same (C) decrease
2. A small car and a large truck collide head-on and stick together. Which one has larger momentum change? (A) car (B) truck (C) tie
Questions 3-4 Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each for 1 s. 3. Which box has more momentum after the force acts? (A) light (B) heavy (C) tie
4. Which box has the greater velocity after the force acts? (A) light (B) heavy (C) tie
Questions 5-6 You drive around a curve in a narrow one-way street at 30 mph when you see an identical car heading straight toward you at 30 mph. You have two options hit the car head-on or hit a massive concrete wall head-on. 5. Which option should you take? (A) hit the car (B) hit the wall (C) doesn't matter
6. Instead of the identical car, a large truck is heading toward you. Which option should you take? (A) hit the truck (B) hit the wall (C) doesn't matter
7. A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. The both have the same mass. Which would hurt more if it hit you on the head? (A) beanbag (B) rubber ball (C) doesn't matter
8. A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest? (A) bowling (B) ping-pong (C) tie
9. You tee up a golf ball and drive it down the fairway. Assume that the collision is elastic. When the ball leaves the tee, how does its speed compare to the speed of the golf club before the collision? (A) faster (B) the same (C) slow
10. A box slides with initial velocity 10 m/s on a frictionless surface and collides inelastically with a stationary identical box. What is the final velocity of the combined boxes? (A) 0 m/s (B) 5 m/s (C) 10 m/s (D) 20 m/s
Questions 11-12 A uranium nucleus (at rest) undergoes fission and splits into two fragments, one heavy and the other light. 11. Which fragment has the greater momentum? (A) heavier one (B) lighter one (C) tie
12. Which fragment has the greater speed? (A) heavier one (B) lighter one (C) tie
13. Alice (100 lbs) and Bill (150 lbs) are standing on slippery ice and push off of each other. If Alice slides at 6 m/s, what speed does Bill have? (A) 2 m/s (B) 3 m/s (C) 4 m/s (D) 6 m/s
14. A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired at a speed of 50 m/s, what is the recoil speed of the flatcar? (A) 0 m/s (B) 0.5 m/s (C) 10 m/s (D) 50 m/s
15. If all three collisions below are totally inelastic, which one(s) will bring the box on the left to a complete halt? anchored brick wall I II III mmm2m ½m v v ½v v 2v (A) I only (B) II only (C) III only (D) all three
16. What is the momentum of a 0.5-kg ball traveling at 18 m/s?
17. What force is generated by a racket, which strikes a 0.06-kg tennis ball that reaches a speed of 65 m/s in 0.03 s?
18. A 25-kg child in a stationary 55-kg boat with a 5-kg package throws the package out horizontally at 8 m/s. What is the boat and child's resultant velocity?
19. An 85-kg safety running at 5 m/s tackles a 95-kg fullback traveling at 4 m/s from behind. What is their mutual speed just after the tackle?
20. A 0.45-kg ice puck, moving east with a speed of 3.0 m/s, has a head-on elastic collision with a 0.9-kg puck initially at rest. What are the resulting speeds and directions?
21. A 1.0-kg block traveling at 5.0 m/s in the direction of 30o south of east collides and sticks with a 2.0-kg block traveling north at 3.0 m/s. Determine a. The x-component of the resulting velocity, vx'.
b. The y-component of the resulting velocity, vy'.
c. The resultant speed.
d. The resultant direction.
Collision Lab 22. Observe an elastic collision between a swinging 200-g weight and a golf ball, and compare the actual post-collision velocities with the theoretical velocities. a. Collect the following data.
b. Calculate the following from the data.
c. Calculate the following theoretical values.
d. Calculate the percent differences.
23. A 0.50-kg softball is traveling at 40 m/s. A bat makes contact with the ball for 0.025 s, after which, the ball's velocity is 35 m/s in the opposite direction (v = -75 m/s). a. Determine the change in the ball's momentum.
b. Determine the average force exerted by the bat.
24. Consider two masses, mA = 1 kg and mB = 3 kg, which can move on a frictionless surface. a. Mass A, moving east with a speed of 2 m/s, has a head-on inelastic collision with mass B, moving west with a speed of 1 m/s. What is the resulting speed and direction of the combined masses?
b. Mass A, moving east with a speed of 2 m/s, has a head-on elastic collision with mass B initially at rest. What are the resulting speeds and directions?
c. Mass A, moving 53o north of east at 5 m/s collides and sticks to mass B moving north at 3 m/s. What is the resulting speed and direction of the combined masses?
d. A spring (k = 600 N/m) compressed 0.1 m is placed between the two stationary masses and then released. Mass A has a velocity of 12 m/s west. What is the speed and direction of Mass B?
B. Forms of Energy Questions 25-50 Briefly explain your answer. Questions 25-30 Use the following options (A) W > 0 (B) W = 0 (C) W < 0 25. Work done to hold a 10-kg bowling ball in your arms.
26. Work done to pull a 10-kg box across a rough floor at constant speed.
27. Work done by a pitcher to throw a 90-mph fast ball.
28. Work done by a catcher to stop a 90-mph fast ball.
29. Work done to whirl a ball in a circle at the end of a string.
30. You lift a 10-kg box a distance of 2 m. a. Work done by you.
b. Work done by gravity.
c. Total work done.
31. A box is being pulled up a rough incline by a rope. How many forces are doing work on the box? (A) 1 (B) 2 (C) 3 (D) 4
32. Which contributes more to the cost of your electric bill each month, a 1500-Watt hair dryer or a 600-Watt microwave oven? (A) hair drier (B) microwave oven (C) both contribute equally (D) depends upon how long each one is on
Questions 33-34 Alice applied 10 N of force over 3 m in 10 s. Bill applies the same force over the same distance in 20 s. 33. Who did more work? (A) Alice (B) Bill (C) They did the same
34. Who produced the greater power? (A) Alice (B) Bill (C) They did the same
35. Car A has twice the mass of car B, but they both have the same kinetic energy. How do their speeds compare? (A) 2vA = vB (B) 2vA = vB (C) 4vA = vB
36. A system of particles has total kinetic energy of zero. What can you say about the total momentum of the system? (A) p > 0 (B) p = 0 (C) p < 0
37. A system of particles has total momentum of zero. Does it necessarily follow that the total kinetic energy is zero? (A) yes (B) no
38. Two objects have the same momentum. Do these two objects also have the same kinetic energy? (A) yes (B) no
Question 39-40 Stone A has twice the mass as stone B. They are dropped from a cliff and reach a point just above ground. 39. What is the speed of stone A compared to stone B? (A) vA = vB (B) vA = ½vB (C) vA = 2vB (D) vA = 4vB
40. What is the kinetic energy of stone A compared to stone B? (A) KA = KB (B) KA = ½KB (C) KA = 2KB (D) KA = 4KB
41. If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? (A) 20 m (B) 40 m (C) 80 m (D) 160 m
42. A car starts from rest and accelerates to 30 mph. Later, it gets on a highway and accelerates to 60 mph. Which takes more energy, the 0 30 mph or the 30 60 mph? (A) 0 30 mph (B) 30 60 mph (C) both the same
43. The work Wo accelerates a car for 0 to v. How much work is needed to accelerate the car from v to 3v? (A) 2Wo (B) 3Wo (C) 8Wo (D) 9Wo
44. Blocks A and B of mass mA and mB (mA > mB) slide on a frictionless floor and have the same kinetic energy when they hit a long rough stretch ( > 0), which slows them down to a stop. Which one goes farther (A) A (B) B (C) both the same
45. A golfer making a putt gives the ball an initial velocity of vo, but he has misjudged the putt, and the ball only travels one-quarter of the distance to the hole. What speed should he have given the ball? (A) 2vo (B) 3vo (C) 4vo (D) 8vo
46. Which can never be negative? (A) W (B) K (C) U
47. You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen different levels for h = 0 in this problem. Which of the quantities will you and your friend agree on? I. Ug II. Ug III. K (A) I only (B) II only (C) III only (D) II and III
48. Two paths lead to the top of a big hill. A is steep and direct, while the B is twice as long but less steep. The change in potential energy on path A compared to path B is (A) UA < UB (B) UA = UB (C) UA > UB
49. How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? (A) W2 = W1 (B) W2 = 2W1 (C) W2 = 4W1 (D) W2 = 8W1
50. A mass attached to a vertical spring causes the spring to stretch and the mass to move downward. Which is true about the sign for Us and Ug? (A) +Us, +Ug (B) +Us, –Ug (C) –Us, +Ug (D) –Us, –Ug
51. How much work is done to move a 50-kg crate horizontally 10 m against a 150-N force of friction?
52. How much work is done to pull a 100-kg crate horizontally 10 m using a force of 100 N at 30o?
53. How much work is done to carry a 100-kg crate 10 m up a 30o ramp?
54. Why is work not needed to keep the earth orbiting the sun?
55. How much power is needed to change the speed of a 1500-kg car from 10 m/s to 20 m/s in 5 s?
56. How much power does a 75-kg person generate when climbing 50 steps (rise of 25 cm per step) in 12 s? a. in Watts
b. in horse power (1hp = 746 W)
57. How much power is needed to maintain a speed of 25 m/s against a total friction force of 200 N?
58. How long will it take a 1750-W motor to lift a 285-kg piano to a sixth-story window 16 m above?
59. A 1000-kg car travels at 30 m/s against 600-N of friction. a. How much power does the car engine deliver?
b. The car accelerates at 2 m/s2. How much power does the car engine deliver now?
c. The car goes up a 10o incline at 30 m/s. How much power does the car engine deliver now?
60. What is the kinetic energy of a 2-kg block moving at 9 m/s?
61. What is the gravitational potential energy of a 2-kg block that is 6 m above zero potential energy?
62. What is the gravitational potential energy of the earth-moon system? (MEarth = 5.97 x 1024 kg, Mmoon = 7.35 x 1022 kg, distance between Earth and moon, r = 3.84 x 108 m)
63. Consider the following spring (k = 100 N/m). a. Calculate the force (F = kx) needed to stretch a spring from 0.0 m to 0.5 m.
b. Graph the data
c. Calculate the area under the graph.
d. How much potential energy is stored in the stretched spring?
Human Power Lab 64. Run up a flight of stairs at the football stadium and calculate the power that you generated. a. Collect the following data.
b. Calculate the following from the data.
c. Calculate the power in horse power (1 hp = 746 W).
C. Conservation of Energy Questions 65-73 Briefly explain your answer. 65. Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greatest speed at the bottom of the ramp?  
A B C
(A) A (B) B (C) C (D) All the same
66. A stationary block slides down a frictionless ramp and attains a speed of 2 m/s. To achieve a speed of 4 m/s, how many times higher must the ball start from? (A) 2 times (B) 4 times (C) 8 times
67. A box sliding on a frictionless flat surface runs into a fixed spring, which compresses a distance x to stop the box. If the initial speed of the box is doubled, how much would the spring compress? (A) ½x (B) x (C) 2x (D) 4x
Questions 68-69 Alice and Bill start from rest at the same time on frictionless water slides with different shapes. Alice 68. At the bottom whose velocity is greater? (A) Alice (B) Bill (C) tie
69. Who makes it to the bottom first? (A) Alice (B) Bill (C) both are the same
70. A cart starting from rest rolls down a hill and at the bottom has a speed of 4 m/s. If the cart were given a push, so its initial speed at the top of the hill was 3 m/s, what would be its speed at the bottom? (A) 4 m/s (B) 5 m/s (C) 6 m/s (D) 7 m/s
71. You see a leaf falling to the ground with constant speed. When you first notice it, the leaf has initial total mechanical energy Ei. You watch the leaf until just before it hits the ground, at which point it has final total mechanical energy Ef. How do these total energies compare? (A) Ei < Ef (B) Ei = Ef (C) Ei > Ef
72. You throw a ball straight up into the air. In addition to gravity, the ball feels a force due to air resistance. Compared to the time it takes the ball to go up, the time to come back down is (A) less (B) equal (C) greater
73. When a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly, but you can hold the gun while it is fired? (A) the bullet is much sharper than the gun (B) the bullet is smaller and can penetrate the body (C) the bullet has more kinetic energy than the gun (D) the bullet goes a longer distance and gains speed
74. A rock is dropped from 20 m. What is the final velocity? a. Use kinematics to solve this problem.
b. Use conservation of energy to solve this problem.
75. A pendulum bob reaches a maximum height of 0.6 m above the lowest point in the swing, what is its fastest speed?
76. How far must a 1 kg ball fall in order to compress a spring 0.1 m? (k = 1000 N/m)
77. A 10-kg box is initially at the top of a 5-m long ramp set at 53o. The box slides down to the bottom of the ramp. The force of friction is 31 N. Determine the a. potential energy at the top of the ramp.
b. work done by friction during the slide.
c. velocity of the box at the bottom of the ramp.
78. A spring (k = 500 N/m) is attached to the wall. A 5-kg block on a horizontal surface ( = 0.25) is pushed against the spring so that the spring is compressed 0.2 m. The block is released and propelled across the surface. a. Determine the potential energy of the spring.
b. Determine the distance that the block travels.
79. A 15-g bullet penetrates a 1.1-kg block of wood. As a result, the block slides along a surface ( = 0.85) for 9.5 m. a. How much work is done by friction?
b. What is the velocity of the system just after the impact?
c. What is the velocity of the bullet just before the impact?
80. An 18-g bullet traveling at 230 m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m long string. a. Determine for the bullet/pendulum just after impact. (1) velocity
(2) kinetic energy
b. How high does the pendulum rise?
Air Resistance Lab 81. Measure how far a cart rolls down a ramp and across a straight away with and without a sail. a. Collect the following data.
b. Calculate the following from the data.
c. Engineers estimate the force of air resistance with the formula, Fair Av2, where A is sail area and v is velocity. Discuss whether the data supports this formula or not.
d. For a human body in free fall, Fair = 0.22v2. What is the maximum speed attained by a falling person?
82. Andre hits a 0.06-kg tennis ball straight up into the air with a 300-N force. The ball remains on the racket for 0.25 m. a. Using dynamics and kinematics, determine (1) The acceleration.
(2) The initial velocity.
(3) The maximum height reached by the tennis ball.
b. Use conservation of energy to determine the maximum height reached by the tennis ball.
83. How much power is used to lift 100 kg a distance of 2 m in 4 s?
84. A 1,000-kg car maintains a constant speed of 30 m/s against a combined friction and air resistance force of 550 N. a. How much power is needed to cruise at 30 m/s?
b. How steep an incline can the car climb if the engine can generate 50,000 W of power?
85. A 1-kg block is pushed down against a spring (k = 500 N/m), which is compressed 0.1 m. The block is released and propelled vertically. a. Determine the potential energy of the spring.
b. Determine the maximum height reached by the block.
86. A 10-kg box is initially at the top of a 5-m long ramp set at 30o. The box slides down to the bottom of the ramp. The force of friction is 26 N. Determine the a. potential energy at the top of the ramp.
b. work done by friction during the slide.
c. velocity of the box at the bottom of the ramp.
87. A 0.050-kg bullet traveling at 1,000 m/s penetrates a 10-kg block of wood. a. What is the velocity of the block after impact?
b. How far does the block travel along a rough surface ( = 0.25) before stopping?
c. How high does the block rise if it were suspended from a long string?
Ballistic Pendulum Lab 88. Measure the velocity of a projectile using pendulum data, kinematic data and the velocimeter, and comparing the three values. a. Collect the following data.
b. Calculate the following from the data.
c. Calculate the percent differences with the velocimeter.
Practice Multiple Choice (No calculator) Briefly explain why the answer is correct in the space provided.
1. Two pucks, where mI = 3mII, are attached by a stretched spring and are initially held at rest on a frictionless surface. 
The pucks are released simultaneously. Which is the same for both pucks as they move toward each other? (A) Speed (B) Velocity (C) Acceleration (D) Magnitude of momentum
2. A 2,000-kg railroad car rolls to the right at 10 m/s and collides and stick to a 3,000-kg car that is rolling to the left at 5 m/s. What is their speed after the collision? (A) 1 m/s (B) 2.5 m/s (C) 5 m/s (D) 7 m/s
3. A 5-kg block with momentum = 30 kg•m/s, sliding east across a horizontal, frictionless surface, strikes an obstacle. The obstacle exerts all impulse of 10 N•s to the west on the block. The speed of the block after the collision is (A) 4 m/s (B) 8 m/s (C) 10 m/s (D) 20 m/s
4. In the diagram, a block of mass M initially at rest on a frictionless horizontal surface is struck by a bullet of mass m moving with horizontal velocity v. 
What is the velocity of the bullet-block system after the bullet embeds itself in the block? (A) (M + v)m/M (B) (m + v)m/M (C) (m + M)v/M (D) mv/(m + M)
5. A disc of mass m is moving to the right with speed v when it collides and sticks to a second disc of mass 2m. The second disc was moving to the right with speed v/2. 
The speed of the composite body after the collision is (A) v/3 (B) v/2 (C) 2v/3 (D) 3v/2
6. An object of mass m is moving with speed vo to the right on a horizontal frictionless surface when it explodes into two pieces. Subsequently, one piece of mass 2/5m moves with a speed ½vo to the left. The speed of the other piece of the object is (A) vo/2 (B) vo/3 (C) 7vo/5 (D) 2 vo
7  . Two objects of mass 0.2 kg and 0.1 kg, respectively, move parallel to the x-axis. The 0.2 kg object overtakes and collides with the 0.1 kg object. Immediately after the collision, the y-component of the velocity of the 0.2 kg object is 1 m/s upward.
What is the y-component of the velocity of the 0.1 kg object immediately after the collision? (A) 2 m/s downward (B) 0.5 m/s downward (C) 0 m/s (D) 0.5 m/s upward
8  . Two particles of equal mass mo
moving with equal speeds vo along paths inclined at 60° to the x-axis, collide and stick together. Their velocity after the collision has magnitude (A) vo/4 (B) vo/2 (C) vo/2 (D) 3vo/2
9. Student A lifts a 50-N box to a height of 0.4 m in 2.0 s. Student B lifts a 40-N box to a height of 0.50 m in 1.0 s. Compared to student A, student B does (A) the same work but develops more power (B) the same work but develops less power (C) more work but develops less power (D) less work but develops more power
10. What is the change in gravitational potential energy for a 50-kg snowboarder raised a vertical distance of 400 m? (A) 50 J (B) 200 J (C) 20,000 J (D) 200,000 J
11. How high is a 50-N object moved if 250 J of work is done against the force of gravity? (A) 2.5 m (B) 10 m (C) 5 m (D) 25 m
12. What is the spring potential energy when a spring (k = 80 N/m) is stretched 0.3 m from its equilibrium length? (A) 3.6 J (B) 12 J (C) 7.2 J (D) 24 J
13. What is the kinetic energy of a 5-kg block that slides down an incline at 6 m/s? (A) 20 J (B) 90 J (C) 120 J (D) 240 J
Questions 14-15 A weight lifter lifts a mass m at constant speed to a height h in time t. 14. How much work is done by the weight lifter? (A) mg (B) mh (C) mgh (D) mght
15. What is the average power output of the weight lifter? (A) mg (B) mh (C) mgh (D) mgh/t
16. The graphs show the position d versus time t of three objects that move along a straight, level path. 
has no change in kinetic energy? (A) II only (B) III only (C) I and II (D) I and III
17. Which is a scalar quantity that is always positive or zero? (A) Power (B) Work (C) Kinetic energy (D) Potential Energy
Questions 18-19 A constant force of 900 N pushes a 100 kg mass up the inclined plane at a uniform speed of 4 m/s. 
18. The power developed by the 900-N force is (A) 400 W (B) 800 W (C) 900 W (D) 3600 W
19. The gain in potential energy when the mass goes from the bottom of the ramp to the top. (A) 100 J (B) 500 J (C) 1000 J (D) 2000 J
20. What is the maximum height that a 0.1-kg stone rises if 40 J of work is used to shoot it straight up in the air? (A) 0.4 m (B) 4 m (C) 40 m (D) 400 m
2  1. A 40-N block is released from rest on an incline 8 m above the horizontal.
What is the kinetic energy of the block at the bottom of the incline if 50 J of energy is lost due to friction? (A) 50 J (B) 270 J (C) 320 J (D) 3100 J
22. A 50-kg diver falls freely from a diving platform that is 3 m above the surface of the water. What is her kinetic energy at 1 m above the water? (A) 0 (B) 500 J (C) 750 J (D) 1000 J
23. A 1000 W electric motor lifts a 100 kg safe at constant velocity. The vertical distance through which the motor can raise the safe in 10 s is most nearly (A) 1 m (B) 3 m (C) 10 m (D) 32 m
Questions 24-27 The vertical height versus gravitational potential energy for an object near earth's surface is graphed below. Ug (J)
24. What is Ug when the object is 2.25 m above the surface? (A) 50 J (B) 45 J (C) 60 J (D) 55 J
25. What is the mass of the object? (A) 1.5 kg (B) 2.0 kg (C) 2.5 kg (D) 3.0 kg
26. What does the slope of the graph represent? (A) mass of the object (B) gravitational force on the object (C) kinetic energy of the object (D) potential energy of the object
27. If an object with greater mass was graphed instead of the object graphed above, how would the slope of the graph differ from the above graph? (A) more positive (B) less positive (C) equal but negative (D) be the same
28. Which is the graph of the spring potential energy of a spring versus elongation from equilibrium? (   A) (B) (C) (D)
29. Which is the graph of the gravitational potential energy of an object versus height? (Assume height << earth's radius) (A) (B) (C) (D) 
30. An object falls freely near earth's surface. Which graph best represents the relationship between the object's kinetic energy and its time of fall? (A) (B) (C) (D) 
31. A system consists of two masses m1 and m2 (m1 < m2). The objects are connected by a string, hung over a pulley and then released. When the object of mass m2 has descended a distance h, the change in potential energy of the system is (A) (m1 – m2)gh (B) m2gh (C) (m1 + m2)gh (D) ½(m1 + m2)gh
32. From the top of a 70-m-high building, a 1-kg ball is thrown directly downward with an initial speed of 10 m/s. If the ball reaches the ground with a speed of 30 m/s, the energy lost to friction is most nearly (A) 50 J (B) 250 J (C) 300 J (D) 450 J
33. A block of mass M is released from rest at the top of an inclined plane of height h. If the plane is frictionless, what is the speed of the sphere at the bottom of the incline? (A) (2gh)½ (B) 2Mgh (C) 2MghR2 (D) 5gh
34. Block of mass m slides on a horizontal frictionless table with an initial speed vo. It then compresses a spring of force constant k and is brought to rest. How much is the spring compressed from its natural length? (A) vo2/2g (B) mgvo/k (C) mvo/k (D) vo(m/k)½
35. A small mass is released from rest U at a very great distance from a larger (A) stationary mass. Which graph 0 r represents the gravitational potential (B) energy U of the system of the two masses as a function of r? (C)
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