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Energy
Freedman
1. The diagram below shows block A, having mass 2m and
speed v, and block B having mass m and speed 2v.
6. Which graph best represents the relationship between the
kinetic energy, KE, and the velocity of an object accelerating
in a straight line?
A)
Compared to the kinetic energy of block A, the kinetic
energy of block B is
A) the same
C) one-half as great
B) twice as great
D) four times as great
B)
2. If the direction of a moving car changes and its speed
remains constant, which quantity must remain the same?
A) velocity
C) displacement
B) momentum
D) kinetic energy
C)
3. A 60.0-kilogram runner has 1920 joules of kinetic energy.
At what speed is she running?
A) 5.66 m/s
C) 32.0 m/s
B) 8.00 m/s
D) 64.0 m/s
D)
4. A 45.0-kilogram boy is riding a 15.0-kilogram bicycle with
a speed of 8.00 meters per second. What is the combined
kinetic energy of the boy and the bicycle?
A) 240. J
C) 1440 J
B) 480. J
D) 1920 J
5. If the speed of a car is doubled, the kinetic energy of the car
is
A) quadrupled
C) doubled
B) quartered
D) halved
7. A 1.0-kilogram rubber ball traveling east at 4.0 meters per
second hits a wall and bounces back toward the west at 2.0
meters per second. Compared to the kinetic energy of the
ball before it hits the wall, the kinetic energy of the ball
after it bounces off the wall is
A) one-fourth as great
C) the same
B) one-half as great
D) four times as great
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8. A 1.0-kilogram book resting on the ground is moved 1.0
meter at various angles relative to the horizontal. In which
direction does the 1.0-meter displacement produce the
greatest increase in the book’s gravitational potential
energy?
A)
B)
C)
D)
9. What is the gravitational potential energy with respect to the
surface of the water of a 75.0 kilogram diver located 3.00
meters above the water?
A) 2.17
C) 2.25
104 J
102 J
B) 2.21
D) 2.29
103 J
101 J
10. An object weighing 15 Newtons is lifted from the ground
to a height of 0.22 meter. The increase in the object’s
gravitational potential energy is approximately
A) 310 J B) 32 J
C) 3.3 J
D) 0.34 J
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11. Which graph best represents the relationship between the gravitational potential energy of a freely falling object
and the object’s height above the ground near the surface of Earth?
A)
B)
C)
D)
12. Two weightlifters, one 1.5 meters tall and one 2.0 meters
tall, raise identical 50.-kilogram masses above their heads.
Compared to the work done by the weightlifter who is 1.5
meters tall, the work done by the weightlifter who is 2.0
meters tall is
A) less
C) the same
B) greater
13. A student does 60. joules of work pushing a 3.0-kilogram
box up the full length of a ramp that is 5.0 meters long.
What is the magnitude of the force applied to the box to do
this work?
A) 20. N B) 15 N
14. The diagram below shows a 50.-kilogram crate on a
frictionless plane at angle to the horizontal. The crate is
pushed at constant speed up the incline from point A to
point B by force F.
C) 12 N
D) 4.0 N
If angle were increased, what would be the effect on the
magnitude of force F and the total work W done on the
crate as it is moved from A to B?
A) W would remain the same and the magnitude of F
would decrease.
B) W would remain the same and the magnitude of F
would increase.
C) W would increase and the magnitude of F would
decrease.
D) W would increase and the magnitude of F would
increase.
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15. The diagram below shows points A, B, and C at or near
Earth's surface. As a mass is moved from A to B, 100.
joules of work are done against gravity.
20. A 40.-kilogram student runs up a staircase to a floor that is
5.0 meters higher than her starting point in 7.0 seconds.
The student’s power output is
A) 29 W
C) 1.4 × 103 W
B) 280 W
D) 1.4 × 104 W
21. The graph below represents the relationship between the
work done by a student running up a flight of stairs and the
time of ascent.
What is the amount of work done against gravity as an
identical mass is moved from A to C?
A) 100. J B) 200. J C) 173 J
D) 273 J
16. A constant force of 1900 Newtons is required to keep an
automobile having a mass of 1.0 × 103 kilograms moving
at a constant speed of 20. meters per second. The work
done in moving the automobile a distance of 2.0 × 103
meters is
A) 2.0 × 104J
C) 2.0 × 106 J
B) 3.8 × 104J
D) 3.8 × 106 J
17. Which combination of units can be used to express work?
A) newton • second
meter
B) newton • meter
second
C) newton/meter
D) newton • meter
What does the slope of this graph represent?
A) impulse
C) speed
B) momentum
D) power
22. In raising an object vertically at a constant speed of 2.0
meters per second, 10. watts of power is developed. The
weight of the object is
A) 5.0 N B) 20. N C) 40. N D) 50. N
18. In the diagram below, a 20.0-newton force is used to push
a 2.00-kilogram cart a distance of 5.00 meters.
23. A 2000-watt motor working at full capacity can vertically
lift a 400-newton weight at a constant speed of
A) 2 × 103 m/s
C) 5 m/s
B) 50 m/s
D) 0.2 m/s
The work done on the cart is
A) 100. J B) 200. J C) 150. J D) 40.0 J
19. A student applies a 20.-newton force to move a crate at a
constant speed of 4.0 meters per second across a rough
floor. How much work is done by the student on the crate
in 6.0 seconds?
A) 80. J
B) 120 J
C) 240 J
24. A boat weighing 9.0 × 102 Newtons requires a horizontal
force of 6.0 × 102 Newtons to move it across the water at
1.5 × 101 meters per second. The boat’s engine must
provide energy at the rate of
A) 2.5 × 10–2 J
C) 7.5 × 103 J
B) 4.0 × 101 W
D) 9.0 × 103 W
D) 480 J
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25. A 95-kilogram student climbs 4.0 meters up a rope in 3.0
seconds. What is the power output of the student?
A) 1.3 × 102 W
C) 1.2 × 103 W
B) 3.8 × 102 W
D) 3.7 × 103 W
31. The diagram below shows a moving, 5.00-kilogram cart at
the foot of a hill 10.0 meters high. For the cart to reach the
top of the hill, what is the minimum kinetic energy of the
cart in the position shown? [Neglect energy loss due to
friction.]
26. A motor used 120. watts of power to raise a 15-newton
object in 5.0 seconds. Through what vertical distance was
the object raised?
A) 1.6 m B) 8.0 m C) 40. m D) 360 m
27. A 3.0-kilogram block is initially at rest on a frictionless,
horizontal surface. The block is moved 8.0 meters in 2.0
seconds by the application of a 12-newton horizontal
force, as shown in the diagram below.
A) 4.91 J B) 50.0 J C) 250. J D) 491 J
32. A 1-kilogram rock is dropped from a cliff 90 meters high.
After falling 20 meters, the kinetic energy of the rock is
approximately
A) 20 J
B) 200 J C) 700 J
D) 900 J
33. As a ball falls freely (without friction) toward the ground,
its total mechanical energy
What is the average power developed while moving the
block?
A) decreases
C) remains the same
B) increases
A) 24 W B) 32 W C) 48 W D) 96 W
34. As an object falls freely, the kinetic energy of the object
28. A motor having a power rating of 500. watts is used to lift
an object weighing 100. Newtons. How much time does
the motor take to lift the object a vertical distance of 10.0
meters?
A) 0.500 s
C) 5.00 s
B) 2.00 s
D) 50.0 s
29. What is the maximum height to which a 1200-watt motor
could lift an object weighing 200. Newtons in 4.0 seconds?
A) 0.67 m
C) 6.0 m
B) 1.5 m
D) 24 m
A) decreases
C) remains the same
B) increases
35. Which device transforms mechanical energy into electrical
energy?
A) generator
C) transformer
B) motor
D) mass spectrometer
36. As shown in the diagram below, a student exerts an
average force of 600. newtons on a rope to lift a
50.0-kilogram crate a vertical distance of 3.00 meters.
30. A 0.50-kilogram ball is thrown vertically upward with an
initial kinetic energy of 25 joules. Approximately how
high will the ball rise? [Neglect air resistance.]
A) 2.6 m B) 5.1 m C) 13 m
D) 25 m
Compared to the work done by the student, the
gravitational potential energy gained by the crate is
A) exactly the same
C) 330 J more
B) 330 J less
D) 150 J more
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37. When a force moves an object over a rough, horizontal
surface at a constant velocity, the work done against
friction produces an increase in the object’s
A) weight
C) potential energy
40. In the diagram below, 400. joules of work is done raising a
72-newton weight a vertical distance of 5.0 meters.
B) momentum
D) internal energy
38. A constant force is used to keep a block sliding at constant
velocity along a rough horizontal track. As the block
slides, there could be an increase in its
A)
B)
C)
D)
gravitational potential energy, only
internal energy, only
gravitational potential energy and kinetic energy
internal energy and kinetic energy
39. A block weighing 15 Newtons is pulled to the top of an
incline that is 0.20 meter above the ground, as shown
below.
If 4.0 joules of work are needed to pull the block the full
length of the incline, how much work is done against
friction?
A) 1.0 J
B) 0.0 J
C) 3.0 J
How much work is done to overcome friction as the
weight is raised?
A) 40. J
B) 360 J
C) 400. J D) 760 J
D) 7.0 J
41. The diagram below shows a 5.0-kilogram mass sliding 9.0
meters down an incline from a height of 2.0 meters in 3.0
seconds. The object gains 90. joules of kinetic energy
while sliding.
How much work is done against friction as the mass slides
the 9.0 meters?
A) 0 J
B) 8 J
C) 45 J
D) 90. J
42. When a 1.53-kilogram mass is placed on a spring with a
spring constant of 30.0 newtons per meter, the spring is
compressed 0.500 meter. How much energy is stored in
the spring?
A) 3.75 J B) 7.50 J C) 15.0 J D) 30.0 J
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43. The spring in a scale in the produce department of a
supermarket stretches 0.025 meter when a watermelon
weighing 1.0 × 102 newtons is placed on the scale. The
spring constant for this spring is
A) 3.2 × 105 N/m
C) 2.5 N/m
46. The graph below shows elongation as a function of the
applied force for two springs, A and B.
B) 4.0 × 103 N/m
D) 3.1 × 10–2 N/m
44. As shown in the diagram below, a 0.50-meter-long spring
is stretched from its equilibrium position to a length of
1.00 meter by a weight.
Compared to the spring constant for spring A, the spring
constant for spring B is
A) smaller
C) the same
B) larger
If 15 joules of energy are stored in the stretched spring,
what is the value of the spring constant?
A) 30. N/m
C) 120 N/m
B) 60. N/m
D) 240 N/m
45. A 5-newton force causes a spring to stretch 0.2 meter.
What is the potential energy stored in the stretched spring?
A) 1 J
B) 0.5 J
C) 0.2 J
D) 0.1 J
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47. Which graph best represents the elastic potential energy stored in a spring (PEs) as a function of its elongation, x?
A)
B)
C)
D)
48. The graph below shows the relationship between the
elongation of a spring and the force applied to the spring
causing it to stretch.
50. In the diagram below, a student compresses the spring in a
pop-up toy 0.020 meter.
If the spring has a spring constant of 340 newtons per
meter, how much energy is being stored in the spring?
A) 0.068 J
C) 3.4 J
B) 0.14 J
D) 6.8 J
What is the spring constant for this spring?
A) 0.020 N/m
C) 25 N/m
B) 2.0 N/m
D) 50. N/m
51. The diagram below shows a 0.1-kilogram apple attached to
a branch of a tree 2 meters above a spring on the ground
below.
49. A spring has a spring constant of 120 newtons per meter.
How much potential energy is stored in the spring as it is
stretched 0.20 meter?
A) 2.4 J
B) 4.8 J
C) 12 J
D) 24 J
The apple falls and hits the spring, compressing it 0.1
meter from its rest position. If all of the gravitational
potential energy of the apple on the tree is transferred to
the spring when it is compressed, what is the spring
constant of this spring?
A) 10 N/m
C) 100 N/m
B) 40 N/m
D) 400 N/m
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52. The spring of a toy car is wound by pushing the car
backward with an average force of 15 Newtons through a
distance of 0.50 meter. How much elastic potential energy
is stored in the car’s spring during this process?
A) 1.9 J
B) 7.5 J
C) 30. J
D) 56 J
53. A catapult with a spring constant of 1.0 × 104 newtons per
meter is required to launch an airplane from the deck of an
aircraft carrier. The plane is released when it has been
displaced 0.50 meter from its equilibrium position by the
catapult. The energy acquired by the airplane from the
catapult during takeoff is approximately
A) 1.3 × 103 J
C) 2.5 × 103 J
B) 2.0 × 104 J
D) 1.0 × 104 J
54. A 0.10-kilogram ball dropped vertically from a height of
l.00 meter above the floor bounces back to a height of 0.80
meter. The mechanical energy lost by the ball as it
bounces is
A) 0.080 J
C) 0.30 J
B) 0.20 J
D) 0.78 J
55. The diagram below shows three positions, A, B, and C, in
the swing of a pendulum, released from rest at point A.
[Neglect friction.]
Which statement is true about this swinging pendulum?
A) The potential energy at A equals the kinetic energy at
C.
B) The speed of the pendulum at A equals the speed of
the pendulum at B.
C) The potential energy at B equals the potential energy
at C.
D) The potential energy at A equals the kinetic
energy at B.
Page 9
Base your answers to questions 56 and 57 on the information and diagram below.
A
-kilogram car is initially at rest at point A on a roller coaster track. The car carries a
passenger and is
meters above the ground at point . [Neglect friction.]
-kilogram
56. Calculate the total gravitational potential energy, relative to the ground, of the car and the passenger at point
[Show all work, including the equation and substitution with units.]
57. Calculate the speed of the car and passenger at point
with units.]
.
. [Show all work, including the equation and substitution
Base your answers to questions 58 through 60 on the information and diagram below.
A 1000.-kilogram empty cart moving with a speed of 6.0 meters per second is about to collide with a
stationary loaded cart having a total mass of 5000. kilograms, as shown. After the collision, the carts lock
and move together. [Assume friction is negligible.]
58. Calculate the speed of the combined carts after the collision.
59. Calculate the kinetic energy of the combined carts after the collision.
60. How does the kinetic energy of the combined carts after the collision compare to the kinetic energy of the carts
before the collision?
Page 10
Base your answers to questions 61 through 63 on the
information below.
The driver of a car made an emergency stop on a
straight horizontal road. The wheels locked and the
car skidded to a stop. The marks made by the rubber
tires on the dry asphalt are 16 meters long, and the
car’s mass is 1200 kilograms.
Base your answers to questions 65 through 67 on the
information and diagram below.
A mass, M, is hung from a spring and reaches
equilibrium at position B. The mass is then raised to
position A and released. The mass oscillates between
positions A and C. [Neglect friction.]
61. Calculate the magnitude of the frictional force the road
applied to the car in stopping it.
62. Calculate the work done by the frictional force in stopping
the car.
63. Assuming that energy is conserved, calculate the speed of
the car before the brakes were applied.
64. Base your answer to the following question on the
information below.
A proton starts from rest and gains
joule of kinetic energy as it accelerates between points
A and B in an electric field.
65. At which position, A, B, or C, is mass M located when the
kinetic energy of the system is at a maximum? Explain
your choice.
What is the final speed of the proton?
A) 7.07 × 106 m/s
C) 4.28 × 108 m/s
B) 1.00 × 107 m/s
D) 5.00 × 1013 m/s
66. At which position, A, B, or C, is mass M located when the
gravitational potential energy of the system is at a
maximum? Explain your choice.
67. At which position, A, B, or C, is mass M located when the
elastic potential energy of the system is at a maximum?
Explain your choice.
Page 11
Base your answers to questions 68 and 69 on the
information and diagram below.
A 160.-newton box sits on a 10.-meter-long
frictionless plane inclined at an angle of 30.° to the
horizontal as shown. Force (F) applied to a rope
attached to the box causes the box to move with a
constant speed up the incline.
68. On the diagram above, construct a vector to represent the
weight of the box. Use a metric ruler and a scale of 1.0
centimeter = 40. newtons. Begin the vector at point B and
label its magnitude in newtons.
69. Calculate the amount of work done in moving the box
from the bottom to the top of the inclined plane. [Show all
work, including the equation and substitution with units.]
Page 12
Base your answers to questions 70 and 71 on the information and diagram below.
A block of mass m starts from rest at height h on a frictionless incline. The block slides down the
incline across a frictionless level surface and comes to rest by compressing a spring through
distance x, as shown in the diagram below.
70. Name the forms of mechanical energy possessed by the system when the block is in position A and in position B.
71. Determine the spring constant, k, in terms of g, h, m, and x. [Show all work including formulas and an algebraic
solution for k.]
Base your answers to questions 72 and 73 on the information below.
A student conducted a series of experiments to investigate the effect of mass, length, and
amplitude (angle of release) on a simple pendulum. The table below shows the initial conditions
for a series of trials.
72. Which three trials should the student use to test the effect of mass on the period of the pendulum?
73. Which three trials should the student use to test the effect of length on the period of the pendulum?
Page 13
Base your answers to questions 74 and 75 on the information below.
A 680-newton student runs up a flight of stairs 3.5 meters high in 11.4 seconds. The student takes 8.5
seconds to run up the same flight of stairs during a second trial.
74. Determine the power developed by the student during the 11.4 -second climb.
75. Using one or more complete sentences, compare the power developed by the student climbing the stairs in 11.4
seconds to the power developed during the 8.5-second trial.
Base your answers to questions 76 through 78 on the information and the diagram below, which is drawn to a
scale of 1.0 centimeter = 3.0 meters.
A 650-kilogram roller coaster car starts from rest at the top of the first hill of its track and glides freely.
[Neglect friction.]
76. Using a metric ruler and the scale of 1.0 cm = 3.0 m, determine the height of the first hill.
77. Determine the gravitational potential energy of the car at the top of the first hill. [Show all calculations, including
the equation and substitution with units.]
Page 14
78. Using one or more complete sentences, compare the kinetic energy of the car at the top of the second hill to its
kinetic energy at the top of the third hill.
Base your answers to questions 79 through 81 on the information and diagram below.
A 20.-kilogram block is placed at the top of a 10.-meter-long inclined plane. The block starts
from rest and slides without friction down the length of the incline.
79. Determine the gravitational potential energy of the block at the top of the incline. [Show all calculations,
including the equation and substitution with units.]
80. Determine the kinetic energy of the block just as it reaches the bottom of the incline.
81. On the axes provided above, sketch a graph of the gravitational potential energy of the block as a function of its
kinetic energy for the complete slide. Label your graph with appropriate values and units.
Page 15
Page 16
Answer Key
2015-16 Energy
1.
B
38.
B
60.
70.
The KE of the
combined carts
after the collision is
less than the KE of
the carts before the
collision.
2.
D
39.
A
3.
B
40.
A
4.
D
41.
B
5.
A
42.
A
6.
D
43.
B
61.
7.
A
44.
C
Ff = 8,000 N or
8,040 N
8.
D
45.
B
62.
W = 1.3 × 10 5 J or
128,000 J
9.
B
46.
B
10.
C
47.
D
63.
11.
A
48.
D
v = 15 m/s or v i =
14.6 m/s
12.
B
49.
A
64.
13.
C
50.
A
65.
14.
D
51.
D
15.
A
52.
B
16.
D
53.
A
17.
D
54.
B
18.
A
55.
D
19.
D
56.
20.
B
21.
D
22.
A
23.
C
24.
D
25.
C
26.
C
27.
C
28.
B
29.
D
30.
B
31.
D
32.
B
58.
v f = 1.0 m/s
33.
C
59.
KE = 3.0 x 10 3 J
34.
B
35.
A
36.
B
37.
D
B
B, because the mass
has the greatest
speed or
B, because the total
71.
potential energy is
least or
B, the speed at A
and C is zero
66.
A, because it is the
highest point of
travel
67.
C, because the
spring is stretched
the maximum
amount or
C, because the KE
and gravitational
PE are a minimum
57.
68.
69.
Credit for
indicating kinetic
energy when the
block is in position
A and credit for
indicating potential
energy when the
block is in position
B. Appropriate
responses include,
but are not limited
to:
Position A: kinetic
or KE, or energy of
motion
Position B: elastic
or potential, or
energy of position
PE = mg h
PE s
2
= kx
kx 2 = mg h
k
= 2mg h / x 2
72.
Credit for R, U, Y
73.
Credit for W, X, Z
74.
P = W/ t; P =
(680 N ×
3.5m)/11.4s; P =
208.8 J/s
w = Fd sin
w = (160. N)(10.
m)(sin 30.°)
w = 800 J
Page 17
Answer Key
2015-16 Energy
75.
– The power
developed during
the 11.4 -second
trial is less.
– The power
developed during
the 11.4 -second
trial is less than the
power developed
during the 8.5
-second trial.
76.
24 m
77.
PE = 152,880
kg•m 2/s2 or PE =
1.5 × 10 5 J
78.
The kinetic energy
of the car at the top
of the second hill is
less than the kinetic
energy of the car at
the top of the third
hill.
or The car's KE is
less.
79.
Acceptable
responses: PE =
mg h; PE =
(20. kg)(9.8 m/s 2
)(5.0 m); PE =
980 J; or PE =
9.8 × 102 kg•m 2/s2
80.
980 J; Allow credit
for an answer that
is consistent with
the student’s
answer to the
previous question.
1m
81.
Page 18