Unit 4 Review Problems: Momentum; Work, Power, and Energy
？ Momentum Conceptual Problems
1. Can a bullet have the same momentum as a truck? Explain.
2. Two identical objects have the exact same momentum. Do the velocities of these objects necessarily have
a. the same directions?
b. the same magnitudes (size)? Give your reasoning in each case.
3. Thinking of the impulse-momentum theorem, explain why cars are made with
a. bumpers that can be pushed in during a crash?
b. Air bags?
4. Thinking of the impulse-momentum theorem, if you are sitting at a baseball game and a foul ball comes in your
direction, which of the following scenarios will enable you to catch it barehanded so the pain (force) to your hand is
the smallest: Should you move your hands toward the ball thereby decreasing the time of the ball’s momentum
change, hold them still, or move them in the same direction as the ball is moving to increase the time the of the ball’s
momentum change? Explain.
5. Is it possible for an object to obtain a larger impulse from a smaller force than it does from a larger force? Explain.
6. A white cue ball moves across a pool table at 3m/s and collides head-on with a stationary 8-ball. The two balls have
equal mass. After the collision the white cue ball is at rest. What must be true of the linear speed of the 8-ball?
7. During a "space walk", the tether connecting an astronaut to the space capsule breaks. Using a pistol that ejects gas
particles (matter moving very fast), the astronaut manages to get back to the capsule. Using the conservation of
momentum, explain how she does this.
8. In movies, Superman hovers in midair, holding a villain by the neck, and throws him forward. Superman, however,
remains stationary. Using the conservation of momentum, explain what is wrong with this scene. 9. A satellite explodes in outer space, far from any other body, sending thousands of pieces in all directions. How does
the total momentum of the satellite before the explosion compare with the total momentum of all the pieces together
after the explosion? Account for your answer using the conservation of momentum.
10. An iceboat is coasting along on a frozen lake. Friction between the ice and the boat is negligible, and so is air
resistance. Nothing is propelling the boat. From a bridge someone jumps straight down (the person has no horizontal
component to his velocity) and lands on the boat which continues to coast straight ahead.
a. Does the forward momentum of the boat change? Explain.
b. Does the speed of the boat increase, decrease, or remain the same? Explain your answers using the
conservation of momentum.
11. On a distant asteroid, a large catapult is used to “throw” chunks of stone into space. Could such a device be used as a
propulsion system to move the asteroid further from the earth? Explain using the conservation of momentum.
12. When driving a golf ball, a good “follow-through” helps to increase the distance of the drive. A good follow-through
means that the club head is kept in contact with the ball as long as possible. Using the impulse-momentum theorem,
explain why this technique allows you to hit the ball farther.
？ Work, Power, and Energy Conceptual Problems
13. Two people of the same mass climb the same flight of stairs. The first person climbs the stairs in 25 s; the second
person takes 35 s.
a. Which person does more work? Explain your answer.
b. Which person produces more power? Explain your answer.
14. A sailboat is moving at a constant velocity.
a. Is there a net amount of work being done by a net force acting on the boat? Explain.
b. If the only forces that are acting on the boat are the wind propelling the boat forward and the friction
provided by the water, how does the work done by the wind’s force compare to the work done by the water’s
15. A ball is moving forward with a speed of 15 m/s. Only one force acts on the ball. After this force acts, the speed of
the ball is only 7 m/s. Has the force done positive or negative work on the ball? Explain.
16. Is it correct to conclude that someone is doing twice the work of another just because they are generating twice the
power? Explain, taking into account the time the work is being completed in.
17. Chris, walking forward with a constant velocity, carries a 10N bag of groceries along a horizontal level hallway to the
kitchen (a distance of 3.50 m). He carries the bag by applying a force straight up on the handle. How much work did
that particular force that Chris applied to the handle do on the bag?
18. How much work does a 10N centripetal force do in one revolution on an object that is in uniform circular motion? 19. Explain how energy and work are related.
20. Can a baseball have potential energy and kinetic energy at the same time? Explain.
21. Can a single object have kinetic energy but no momentum? Explain.
Unit 4 AP Review Problems: Momentum, Work, Power, and Energy 1
22. A net force acts on a particle. Is this enough information to conclude that
a. the velocity of the particle changes?
b. the kinetic energy of the particle changes?
c. The momentum of the particle changes? Give your reasoning for each case.
23. Is it possible to exert a net force and yet not cause a change in kinetic energy? Explain.
24. If two identical bowling balls are raised to the same height, one on Earth and the other on the moon, which has the
larger potential energy relative to the surface of the planets (I’m classifying the moon as a planet here…)?
25. Suppose the total energy “KE + PE” of an object is conserved (the sum is constant). g
a. If the kinetic energy decreases, what must be true about the potential energy?
b. If the potential energy decreases, what must be true about the kinetic energy?
c. If the kinetic energy does not change, what must be true about the potential energy?
Solve all Problems using the ideas of Momentum, Work, Power, and Energy
？ Momentum Problems
26. Two men pushing a stalled car apply a net force of +680 N for 7.2 s. What is the final momentum of the car? (4.90
27. A 62-kg person, standing on a diving board, dives straight down into the water. Just before striking the water, her
speed is 5.5 m/s. At a time of 1.65 s after entering the water, her speed is reduced to 1.1 m/s. What is the average net
force (magnitude and direction) that acts on her when she is in the water? (165.33N, up)
28. Hannah is standing on the ice. Another player fires a puck (m= 0.17 kg) at her with a velocity of +65 m/s. -3a. If she catches the puck with her glove and brings it to rest in a time of 5 x 10s, what is the average force
(magnitude and direction) exerted on the puck by her glove? (2.21 E3 N, opp the dxn of motion for puck)
b. Instead of catching the puck, she slaps it with her stick and returns the puck straight back to the player with a -3velocity of –65 m/s. The puck and stick are in contact for a time of 5 x 10s. Now, what is the average force
exerted on her by the puck? (4.42 E3N)
29. A basketball (m= 0.6 kg) is dropped from rest. Just before striking the floor, the magnitude of the basketball’s
momentum is 3.1 kg？m/s. At what height was the basketball dropped? (1.36m above the ground)
30. A 0.15 kg projectile is fired with a velocity of 715 m/s at a 2 kg wooden block that rests on a frictionless table. The
velocity of the block, immediately after the projectile passes through it, is 40 m/s. Find the velocity with which the
projectile exits the block. (181.67 m/s)
31. Kevin has a mass of 87 kg and is skating with in-line skates. He sees his 22 kg younger brother up ahead standing on
the sidewalk with his back turned. Coming up from behind, he grabs his brother and rolls off with him at a speed of
2.4 m/s. Ignoring friction, find Kevin’s speed just before he grabbed his brother. (3.01 m/s)
32. Batman (mass = 91 kg) jumps straight down from a bridge into a boat (mass = 510 kg) in which a criminal is fleeing.
The forward velocity of the boat is initially +11 m/s. What is the velocity of the boat after Batman lands in it?
33. The lead female character in a movie is standing on the edge of an offshore oil rig. As she fires a gun, she is driven
back over the edge and into the sea. Suppose the mass of a bullet is .01 kg and its velocity is +720 m/s. Her mass
(including the gun) is 51 kg.
a. What recoil velocity does she acquire in response to a single shot from a stationary position, assuming that no
external force keeps her in place? (-0.14m/s)
b. Under the same assumption, what would be her recoil velocity if, instead, she shoots a blank cartridge that -4ejects a mass of 5 x 10 kg at a velocity of +720 m/s? (-7.06 E-3 m/s)
34. A 3 kg block of wood rests on the muzzle opening of a vertically oriented rifle, the stock of the rifle being firmly 2planted on the ground. The rifle fires an 8 g bullet at 8 x 10 m/s straight upward and it becomes completely
embedded in the block.
a. Using conservation of momentum, find the velocity of the block/bullet system immediately after the collision.
b. Ignoring air resistance, determine how high the block/bullet system rises above the muzzle opening of the
rifle. (0.23 m)
35. A 60 kg person, running horizontally with a velocity of +3.8 m/s, jumps onto a 12 kg sled that is initially at rest.
a. Ignoring the effects of friction during the collision, find the velocity of the sled and person as they move
away. (3.17 m/s)
b. The sled and the person coast 30 m on level snow before coming to rest. What is the coefficient of kinetic
friction between the sled and the snow? (0.017)
Unit 4 AP Review Problems: Momentum, Work, Power, and Energy 2
36. An automobile has a mass of 2300 kg and a velocity of +16 m/s. It makes a rear-end collision with a stationary car
whose mass is 1800 kg. The cars lock bumpers and skid off together with the wheels locked.
a. What is the velocity of the two cars just after the collision? (8.98 m/s)
b. Find the impulse (magnitude and direction) that acts on the skidding cars from just after the collision until
they come to a halt. (3.68 E4 kgm/s, opposite the dxn of motion)
c. If the coefficient of friction between the wheels of the cars and the pavement is ;= 0.8, determine how far the
cars skid before coming to rest. (5.12m)
？ Work, Power, and Energy Problems
37. A student removes a 10.5 kg stereo amplifier from a shelf that is 1.82 m high and lowers it at a constant speed to a
height of 0.75 m. What is the work done by
a. the person? (-110.10 J)
b. the gravitational force that acts on the amplifier? (+110.10 J)
38. A cable lifts a 1200 kg elevator up at a constant velocity for a distance of 35 m. What is the work done on the elevator
a. the tension in the cable? (4.12 E5 J)
b. the elevator’s weight? (-4.12 E5 J)
39. In 2 minutes, the free-fall ride at 6-Flags can lift four insane thrill-seekers at constant speed straight up to a height of
140 m. The average mass of each kid is 65 Kg and the lift is 500Kg. What is the average power provided by the
tension in the cable pulling the lift? (8.69 E3 W) 340. The brakes of a truck cause it to slow down by applying a net force of 3 x 10 N to the truck over a distance of 850 m.
What is the work done by this force on the truck? (-2.55 E6 J)
41. Rocket man has a propulsion unit strapped to his back. He starts from rest on the ground, fires the unit, and is
propelled straight upward. At a height of 16 m, his speed is 5 m/s. His mass, including the propulsion unit, is 136 kg.
Find the work done by just the non-conservative force generated by the propulsion unit. (2.30 E4 J)
42. If an object at rest initially has 500J of PE and it slides 10m down an incline where there exists a friction force of g
20N, how much KE does the object have when it reaches the bottom of the incline? (300 J)
43. A person pulls a sled for a distance of 35 m along the snow with a rope directed 25； above the snow. The tension in
the rope is 94 N.
a. How much work is done on the sled by the tension force in the rope? (2.98 E3 J)
b. How much work is done on the sled if the same tension is directed parallel to the snow? (3.29 E3 J) 344. Suppose that +1.1 x 10 J of work is done by a pulling force on a piece of luggage with a 30 N force directed along the
handle at some angle to the ground to move it a distance of 50 m. At what angle is the handle oriented with respect to 0the ground? (42.83)
45. A person pushes on the handle of a 16 kg shopping cart moving it at a constant velocity for a distance of 22 m. The
handle is 29； to the horizontal. A 48 N frictional force opposes the motion of the cart.
a. What is the magnitude of the force that the shopper exerts on the handle? (54.88N)
b. Determine the work done by
？ the pushing force. (1.06 E3 J)
？ the frictional force. (-1.06 E3 J)
？ the gravitational force. (0 J) 246. A 2.4 x 10 N force is pulling an 85 kg refrigerator across a horizontal surface. The force acts at an angle of 20；
above the surface. The coefficient of friction is 0.2, and the refrigerator moves a distance of 8 m. Find
a. the work done by the pulling force. (1.80 E3 J)
b. the work done by the frictional force. (-1.20 E3 J)
47. A husband and wife take turns pulling their child in a wagon along a horizontal sidewalk. Each exerts a constant force
and pulls the wagon through the same displacement. They do the same amount of work, but the husband’s pulling
force is directed 58； above the horizontal, while the wife’s pulling force is directed 38； above the horizontal. The
husband pulls with a force whose magnitude is 67 N. What is the magnitude of the pulling force exerted by his wife?
48. A 100 kg crate is being pulled across a horizontal floor by a force that makes an angle of 30； above the horizontal.
The coefficient of friction is 0.20. How large should the pulling force in the handle be so that the net work done on it
is zero? (Hint: This will take a lot of manipulating things around before plugging any numbers into an equation…but
you’ll feel smart when you get it….). (202.89 N)
49. A 1200 kg box is being pushed up a 15； hill. The frictional force has a magnitude of 524N. A force is applied to the
box to propel it forward. The length of the hill is 290 m. What should be the magnitude of the applied force so that
the net work done by all the forces acting on the box is +150 KJ? (4.08 E3 N)
Unit 4 AP Review Problems: Momentum, Work, Power, and Energy 3
2 50. A 3 x 10kg piano is being lifted at a constant speed from ground level straight up to an apartment 10 m above the 2ground. The crane that is doing the lifting produces a steady power of 4 x 10 W. How much time does it take to lift
the piano? (73.50 s)
51. The poodle, one of the fastest (and meanest) of all wild animals, can accelerate from rest to 27 m/s (about 60 mi/h) in
4 s. If its mass is 110 kg, determine the power developed by the poodle during the acceleration phase of its motion.
(1.00 E4 W)
52. A 0.6 kg hot dog is dropped out of a window that is 6.1 m above the ground. The pup is caught by a butcher whose
hands are 1.5 m above the ground.
a. How much work is done on the dog by gravity as it falls to the final height? (+27.05 J)
b. What is the gravitational potential energy of the pup, relative to the ground, when it is
？ released? (35.87 J)
？ caught? (8.82 J)
c. How is the change in the pup’s gravitational potential energy related to the work done on it by gravity?
(they’re the same magnitude----- 27.05 J lost in PE vs. 27.05 J done by work)
d. How much kinetic energy does it gain as it falls? (+27.05 J)
53. A 0.075 kg arrow is fired horizontally. The bowstring exerts a net force of 65 N on the arrow over a distance of 0.9m
while in the bow.
a. With what kinetic energy does the arrow leave the bow? (58.50 J)
b. If the arrow is initially 1 m off the ground, what is its total energy the moment it leaves the bow? (59.24 J) 754. The aircraft carrier Nimitz has a fully loaded mass of 8.35 x 10 kg. It travels a distance of 208 km in 3.5 hours with a
constant velocity. What is the average kinetic energy of the Nimitz? (1.14 E10 J)
55. Two cars, A and B, are traveling with the same speed of 40 m/s, each having started from rest. Car A has a mass of 331.2 x 10 kg, and car B has a mass of 2 x 10 kg. Compared to the work required to bring car A up to speed, how
much additional work is required to bring car B up to speed? Ignore friction. (6.40 E5 J more)
56. When a 0.045 kg golf ball takes off after being hit, its speed is 41 m/s.
a. How much work is done on the ball by the club? (37.82 J)
b. Assume that the force of the golf club acts parallel to the motion of the ball and that the club is in contact
with the ball for a distance of 0.01 m. Ignore the weight of the ball and determine the net force applied to the
ball by the club. (3.78 E3 N) 457. A 5 x 10 kg space probe is traveling at a speed of 11,000 m/s through deep space. Retrorockets are fired along the 5line of motion to reduce the probe’s speed. The retrorockets generate a non-conservative force of 4 x 10 N over a
distance of 2500 km. What is the final speed of the probe? (9.0 E3 m/s)
58. A 2 kg rock is released from rest at a height of 20 m. Ignore air resistance and determine the kinetic energy,
gravitational potential energy, and total mechanical energy at each of the following heights: 20, 10, and 0 m.
PE KE Total Energy
392 J 0 J 392 J 20m
196 J 196 J 392 J 10m
0 J 392 J 392 J 0m
59. A 75 kg skier rides a 2830 m long lift to the top of a mountain. The lift makes an angle of 14.6； with the horizontal.
What is the change in the skier’s gravitational potential energy? (5.24 E5 J)
60. The height of the upper falls of Yellowstone Falls is 33.2 m. When the water reaches the bottom of the falls, its speed
is 25.8 m/s. Neglecting the air resistance, what is the speed of the water at the top of the falls? (3.86 m/s)
61. A cyclist approaches the bottom of a set of gradual hills at a speed of 11 m/s. The first hill is 5 m high, and the cyclist
estimates that she is going fast enough to coast up and over it without pedaling. Ignoring air resistance and friction,
a. the speed at which the cyclist crests (reaches the top of) the first hill. (4.80 m/s)
b. the maximum height she can attain on the next hill if she continues coasting. (6.17 m)
62. A rescue helicopter lifts a 79 kg bunny straight up by means of a cable. The rabbit has an upward acceleration of 0.7 2m/s and is lifted from rest through a distance of 11 m.
a. What is the tension in the cable? (829.50 N)
b. How much work is done by the tension in the cable? (9.12 E3 J)
c. Use the work-energy theorem and find his final velocity. (3.90m/s)
Additional AP Problems that are a mish-mash of all Physics concepts
63. A gymnast is swinging on a high bar. The distance between his waist and the bar is 0.9 m. At the top of the swing his
speed is momentarily zero. Ignoring friction, find the speed he is moving at the bottom of the swing. (5.94 m/s)
Unit 4 AP Review Problems: Momentum, Work, Power, and Energy 4
64. A water skier is pulled up a jump ramp that makes some random angle to the horizontal. At the top of the ramp when
the skier is moving at a speed of 15 m/s she lets go of the tow-rope. At the highest point in her path, she has a total
speed of 12 m/s. Ignoring air resistance, determine the skier’s height above the top of the ramp at her highest point.
65. A skier starts from rest at the top of a hill of height h ABOVE the height of a second hill. The skier coasts down the
first hill and up the second hill that has a circular crest of radius of 41m. Neglecting friction and air resistance, what
must be the height of the first hill above the second hill (i.e., how much taller is the first than the second hill) so the
skier just loses contact with the snow at the crest of the second hill? (20.5 m)
66. A 5 E2 Kg hot air balloon takes off from rest at the surface of the earth. The non-conservative wind and lift forces do
+9.7 E4J of work on the balloon in the process. At what height above the surface of the earth does the balloon have a
speed of 8.0 m/s? (16.53 m)
67. A 0.75 Kg projectile is shot straight up with an initial speed of 18m/s.
a. How high would it go if there were no air friction? (16.53 m)
b. If the projectile only reaches a height of 9 m, what is the average net force due to air resistance? (-6.15 N,
neg due to opposing the motion of the object) 068. A 63 Kg skier coasts up a snow covered hill that makes an angle of 25 to the horizontal. The initial speed of the skier
is 6.6 m/s. After coasting a distance of 1.9m up the slope, the speed of the skier is only 4.4 m/s.
a. Find the work done by the kinetic friction force that acts on the skis. (-266.54 J)
b. What is the magnitude and direction of the kinetic friction force? (-140.29 N) 069. An extreme skier, starting from rest, coasts down a mountain (μ = 0.19) that makes a 27 angle to the horizontal. She
coasts for a distance of 12.2 m before coming to the edge of a cliff. Without slowing down, she skis off the edge and
lands downhill at a point that is a vertical distance of 3.5 m below the edge. How fast is she going just before she
lands (her total speed)? (11.69 m/s)
70. A toy matchbox car is given a push to give it an initial speed of 4m/s at the bottom of a loop-the-loop track (so it will
move on the inside of the circular track). What is the largest radius the circular loop can have if the toy car is to
remain in contact with the track at the highest point in the track? (Note: The car does NOT move at a constant speed
while it is inside of the track as it doesn’t have an engine and gravity is acting on it so its KE and PE will continually
change). This is a fun problem…. ignore friction. (0.33 m)
71. A dump truck is being filled with sand. The sand falls straight downward from rest from a height of 2m above the
truck bed and the mass of sand that hits the truck per second is 55 kg/s. The truck is parked on the platform of a
weight scale. By how much does the scale reading exceed the actual weight of the truck and sand? (XX N) 072. A person stands in a stationary canoe and throws a 5kg stone with a velocity of 8m/s at an angle of 30 above the
horizontal. The person, canoe, and stone have a combined mass of 105 kg. Ignoring air resistance and water friction,
find the horizontal recoil velocity of the canoe. (-0.35 m/s)
73. An automobile has a mass of 2300 kg and a velocity of +16m/s. It makes a rear-end collision with an 1800 kg
stationary car. The cars lock bumpers and skid off together with the wheels locked.
a. What is the velocity of the two car system just after the collision? (8.98 m/s)
b. Find the impulse (magnitude and direction) that acts of the skidding cars from just after the collision until
they come to a halt. (-3.68 E4 Ns)
c. If the coefficient of kinetic friction between the wheels of the cars and the pavement is 0.80, how far will the
cars skid before coming to rest? (5.14 m)
74. A 5 kg ball moving to the right at a velocity of +2m/s on a frictionless table collides head-on with a stationary 7.5 kg
ball. Find the final velocities of the balls if the collision is completely
a. Inelastic (i.e., they stick together after the collision). (0.8 m/s)
b. elastic (i.e., KE is conserved and they don’t stick together after the collision) (v’ = -0.4 m/s, v’ = +1.6 m/s) 12
75. Two 0.5 kg balls are traveling toward each other with velocities of –4.0 and +7.0 m/s and they experience an elastic
head-on collision. What are the velocities of the two balls after the collision? (v’ = +7 m/s, v’ = -4 m/s) 12076. A 1500 kg car is traveling 30 North of East at 27 m/s when it collides with a 1200 kg car traveling exactly North with
a speed of 18 m/s. The cars lock together after the collision. What is the velocity of the cars immediately after the 0collision? (20.22 m/s, 50.03 North of East)
Unit 4 AP Review Problems: Momentum, Work, Power, and Energy 5