Deck 8: Potential Energy and Conservation of Energy

Question 1

A 0.200-kg mass attached to the end of a spring causes it to stretch 5.0 cm. If another 0.200-kg mass is added to the spring, the potential energy of the spring will be

A) the same.
B) one-half as much.
C) twice as much.
D) 3 times as much.
E) 4 times as much.

Answer 1

4 times as much.

Question 2

Non-conservative forces can change the mechanical energy of a system.

Answer 2

True

Question 3

The sum of the kinetic and potential energies of an object is conserved only when the object is under the influence of conservative forces.

Answer 3

True

Question 4

You throw a ball straight up. Compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down.

A) Work is + on the way up and + on the way down.
B) Work is + on the way up and - on the way down.
C) Work is - on the way up and + on the way down.
D) Work is - on the way up and - on the way down.

Question 5

The frictional force is a conservative force.

Question 6

State the Conservation of Mechanical Energy

Question 7

Describe a conservative force.

Question 8

Any location can be chosen for potential energy equal to zero.

Question 9

Potential energy may be positive or negative.

Question 10

Kinetic energy may be positive or negative.

Question 11

The gravitational force is a conservative force.

Question 12

Two identical vertical springs S₁ and S₂ have masses m₁ = 400 g and m₂ = 800 g attached to them. If m₁ causes spring S₁ to stretch by 4 cm, what is the ratio of the potential energy of S₁ and S₂? Use g = 10 m/s².

A) 2:1
B) 1:2
C) 1:3
D) 4:1
E) 1:4

Question 13

FIGURE 8-1
You need to load a crate of mass m onto the bed of a truck. One possibility is to lift the crate straight up over a height h, equal to height of the truck's bed. The work done in this case is W₁. The other possibility is to slide the crate up the frictionless ramp of length L as shown in Figure 8-1. In this case you perform work W₂. What statement is true?

A) W₁ < W₂
B) W₁ = W₂
C) W₁ > W₂
D) No simple relationship exists between W₁ and W₂.

Question 14

The force acting on an object is said to be conservative if the work done by this force on the object is independent of the path chosen.

Question 15

An object is released from rest a height h above the ground. A second object with four times the mass of the first is released from the same height. The potential energy of the second object compared to the first is

A) one-fourth as much.
B) one-half as much.
C) twice as much.
D) four times as much.
E) eight times as much.

Question 16

What distinguishes a conservative force from a non-conservative force?

Question 17

Non-conservative forces convert mechanical energy into other forms of energy, or convert other forms of energy into mechanical energy.

Question 18

A block of mass m slides without friction on a table with speed v. It hits and compresses a spring of force constant k by a distance l. The spring then expands again ejecting the block in the opposite direction as it was originally traveling. Neglecting the mass of the spring, what is the speed of the object after it is ejected by the spring?

A) v/2
B) 2v
C) v
D) 4v
E) v - l

Question 19

You and your friend want to go to the top of the Eiffel Tower. Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy (U) of you and your friend, after you both reach the top.

A) It is impossible to tell, since the times are unknown.
B) It is impossible to tell, since the distances are unknown.
C) Your friend's U is greater than your U, because she got to the top faster.
D) Both of you have the same amount of potential energy.
E) Your U is greater than your friend's U, because you traveled a greater distance in getting to the top.

Question 20

If work is done on a system by non-conservative forces, the total mechanical energy of a system stays constant.

Question 21

FIGURE 8-3 A mass is attached to one end of a string. The other end of the string is attached to a rigid support. The mass is released at A and swings in a vertical arc to points B, C, and D, as shown in Figure 8-3. Neglect air resistance and use g = 10 m/ .
Refer to Figure 8-3. At what point does the mass have the most kinetic energy?

A) A
B) B
C) C
D) D
E) none of the given points

Question 22

A golfer misjudges a putt and leaves her ball way short, the ball going only one-third of the way to the hole. If the speed of the ball leaving the putter in the first case was v₀ and the force of resistance due to the grass remains the same, what speed should she have given to the ball to make the original putt?

A) v₀
B) 2 v₀
C) v₀
D) 3 v₀
E) 4 v₀

Question 23

An acorn falls from a tree. Compare its kinetic energy K, to its potential energy U.

A) K increases and U decreases.
B) K decreases and U decreases.
C) K increases and U increases.
D) K decreases and U increases.
E) Cannot be determined without knowing the initial height of the acorn.

Question 24

A ball falls from the top of a building, through the air (air friction is present), to the ground below. How does the kinetic energy (K) just before striking the ground compare to the potential energy (U) at the top of the building?

A) K is equal to U.
B) K is greater than U.
C) K is less than U.
D) It is impossible to tell.

Question 25

Two identical balls are thrown from the top of a building with the same speed. Ball 1 is thrown horizontally, while ball 2 is thrown at an angle θ above the horizontal. Neglecting air resistance, which ball will have the greatest speed when hitting the ground below?

A) Ball 1
B) Ball 2
C) Both balls reach the ground with the same speed.
D) Cannot be determined without knowing the height of the building.
E) Cannot be determined without knowing the time each ball is in the air.

Question 26

A ball drops some distance and loses 30 J of gravitational potential energy. Do not ignore air resistance. How much kinetic energy did the ball gain?

A) more than 30 J
B) exactly 30 J
C) less than 30 J
D) Cannot be determined from the information given.

Question 27

Describe the energy of a car driving up a hill.

A) entirely kinetic
B) entirely potential
C) both kinetic and potential
D) gravitational
E) elastic

Question 28

Two inclined planes A and B have the same height but different angles of inclination with the horizontal. An object is released at rest from the top of each of the inclined planes. How does the speed of the object at the bottom of inclined plane A compare with that of the speed at the bottom of inclined plane B?

A) It is directly proportional to the angle.
B) It is inversely proportional to the angle.
C) It is same for both planes.
D) There is not enough information to answer the question.

Question 29

FIGURE 8-3 A mass is attached to one end of a string. The other end of the string is attached to a rigid support. The mass is released at A and swings in a vertical arc to points B, C, and D, as shown in Figure 8-3. Neglect air resistance and use g = 10 m/ .
Refer to Figure 8-3. At what point does the mass have its highest speed?

A) A
B) B
C) C
D) D
E) none of the given points

Question 30

An object of mass m is held at a vertical height h from ground level. It is then released and falls under the influence of gravity. Which of the following statements is true in this situation? (Neglect air resistance.)

A) The total energy of the object is decreasing.
B) The kinetic energy of the object is decreasing.
C) The potential energy of the object is increasing.
D) The total energy of the object is increasing.
E) The potential energy of the object is decreasing and the kinetic energy is increasing.

Question 31

A ball is tied to the end of an 80.0-cm string and swings in a vertical circle about a fixed center under the influence of gravity. The speed of the mass at the bottom of the swing is 6.00 m/s. Which of the following statements is true?

A) The ball does not have enough energy to reach the top of the circle.
B) The ball has enough energy to reach the top of the circle but the string becomes slack before it can reach that point.
C) The ball has enough energy to continue revolving in a complete vertical circle.
D) This question cannot be answered without knowing the mass of the ball.
E) This question cannot be answered without knowing the tension in the string.

Question 32

A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill. Which rises to a greater height?

A) The heavy object, because it has greater kinetic energy.
B) The light object, because it has smaller kinetic energy.
C) The lightweight object, because it weighs less.
D) The heavy object, because it weighs more.
E) They both slide to the same height.

Question 33

Two blocks of masses m₁ and m₂ are released from the top of two frictionless inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. Which of the blocks is going faster when it reaches the bottom of its respective incline?

A) We must know the actual masses of the blocks to answer.
B) Both blocks have the same speed at the bottom.
C) Block 1 is faster.
D) Block 2 is faster.
E) There is not enough information to answer the question.

Question 34

Neglecting air resistance, when you toss a stone straight up in the air from Earth's surface, which of the following statements is true for the upward motion of the stone.

A) The stone's total energy increases.
B) The stone's kinetic and gravitational potential energies increase simultaneously.
C) The stone's kinetic and gravitational potential energies decrease simultaneously.
D) The stone's kinetic energy decreases while its gravitational potential energy increases.
E) The stone's kinetic energy increases while its gravitational potential energy decreases.

Question 35

FIGURE 8-2
Swimmers at a water park have a choice of two frictionless water slides (see Figure 8-2). Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v₁ of a swimmer reaching the end of slide 1 compares with v₂, the speed of a swimmer reaching the end of slide 2?

A) v₁ > v₂
B) v₁ < v₂
C) v₁ = v₂
D) No simple relationship exists between v₁ and v₂.

Question 36

Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

A) We must know the actual masses of the blocks to answer.
B) Both blocks have the same speed at the bottom.
C) Block 1 is faster.
D) Block 2 is faster.
E) There is not enough information to answer the question.

Question 37

A ball drops some distance and gains 30 J of kinetic energy. Do not ignore air resistance. How much gravitational potential energy did the ball lose?

A) more than 30 J
B) exactly 30 J
C) less than 30 J
D) Cannot be determined from the information given.

Question 38

The total mechanical energy of a system

A) is equally divided between kinetic energy and potential energy.
B) is either all kinetic energy or all potential energy, at any one instant.
C) can never be negative.
D) is constant, only if conservative forces act.
E) is not uniquely determined for most naturally occurring systems.

Question 39

King Kong falls from the top of the Empire State Building, through the air (air friction is present), to the ground below. How does his kinetic energy (K) just before striking the ground compare to his potential energy (U) at the top of the building?

A) K is equal to U.
B) K is less than U.
C) K is greater than U.
D) It is impossible to tell.

Question 40

FIGURE 8-3 A mass is attached to one end of a string. The other end of the string is attached to a rigid support. The mass is released at A and swings in a vertical arc to points B, C, and D, as shown in Figure 8-3. Neglect air resistance and use g = 10 m/ .
Refer to Figure 8-3. At what point does the mass have the most potential energy?

A) A
B) B
C) C
D) D
E) none of the given points

Question 41

An object of mass 20.0 kg is lifted vertically through 1.00 m by a 400 N force. How much work is done by the net force in lifting this object? Use g = 10.0 m/s².

A) 20.0 J
B) 40.0 J
C) 100 J
D) 200 J
E) 400 J

Question 42

A person drops a brick from the top of a building. The height of the building is 400 m and the mass of the brick is 2.00 kg. What will be the speed of the brick right before it touches the ground? Use g = 10.0 m/s².

A) 10.0 m/s
B) 13.2 m/s
C) 89.4 m/s
D) 59.4 m/s
E) 63.2 m/s

Question 43

FIGURE 8-4 An object of mass 2 kg is held at the top of a triangular wedge as shown in Figure 8-4, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10 m/s².
Refer to Figure 8-4. What is the kinetic energy of the object at the top of the wedge?

A) 30 J
B) 40 J
C) 0 J
D) 60 J
E) 80 J

Question 44

An object of mass 4 kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s². What is the kinetic energy of the object as it reaches its maximum height?

A) 800 J
B) 400 J
C) 200 J
D) 0 J
E) 80 J

Question 45

A mass of 1.0 kg is pushed against a spring with a spring constant of 25 N/m. As a result, the spring is compressed by 20 cm. The mass is then released. What is the amount of work required to compress the spring?

Question 46

A force of 4.0 N applied to a spring compresses it by 8.0 cm. What is the amount of work done to compress the spring by an additional amount of 5.0 cm?

A) 20 J
B) 0.26 J
C) 0.50 J
D) 2.0 J
E) 50 N/m

Question 47

An object of mass 2.00 kg is held at a position A, a vertical height of 20.0 m above the ground. Point B is 8.00 m directly below A. Neglect air resistance and use g = 10.0 m/s².
(a) What is the speed of the object at position B when it falls from position A?
(b) What is the speed of the object just before it touches the ground?
(c) What is the ratio of the total energy of the object at position A to position B?

Question 48

A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope. When the skier reaches the bottom of the hill, her speed is 30.0 m/s.
(a) How much work is done by friction as the skier comes down the hill?
(b) What is the magnitude of the friction force if the skier travels directly down the hill?

Question 49

FIGURE 8-4 An object of mass 2 kg is held at the top of a triangular wedge as shown in Figure 8-4, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10 m/s².
Refer to Figure 8-4. What is the speed of the object just before it reaches the bottom of the wedge?

A) 6 m/s
B) 8 m/s
C) 0 m/s
D) 10 m/s
E) 2 m/s

Question 50

FIGURE 8-4 An object of mass 2 kg is held at the top of a triangular wedge as shown in Figure 8-4, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10 m/s².
Refer to Figure 8-4. What is the amount of work done by the gravitational force as the object comes to the bottom of the wedge?

A) 60 J
B) 10 J
C) 0 J
D) 40 J
E) 80 J

Question 51

An object of mass 20 kg is raised vertically through a distance of 8.0 m above ground level. Using g = 10 m/s² what is the potential energy of this object at this position?

A) 1.6 J
B) 16 J
C) 160 J
D) 1600 J
E) 16000 J

Question 52

As an object of mass 60 kg approaches the bottom of a ramp, point A, its speed is 20 m/s. It goes up the frictionless plane and turns around at point B. What is the potential energy of this object at point B? Use g = 10 m/s².

A) 0 J
B) 6.0 × 10³ J
C) 9 × 10³ J
D) 12 × 10³ J
E) 18 × 10³ J

Question 53

(a) A force of 15 N applied to a spring compresses it by 4 cm. What is the potential energy of the spring in the compressed position?
(b) A force of 15 N applied to a spring stretches it by 4 cm. What is the potential energy of the spring in the stretched position?

Question 54

FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s².
Refer to Figure 8-5. What is the kinetic energy of the bead at point A?

A) 2.0 x 10^-2 J
B) 16 x 10^-3 J
C) 0.40 J
D) 0 J
E) There is not enough information to solve this problem.

Question 55

A 20-kg object is resting at the top of a table 1.6 m above ground level. The object is then picked up and moved to a height of 8.7 m above ground level. What is the change in the gravitational potential energy of this object? Use g = 10 m/s².

A) 71 J
B) 140 J
C) 1740 J
D) 320 J
E) 1420 J

Question 56

A simple pendulum of length 2.00 m is made with a mass of 2.00 kg. The mass has a speed of 3.00 m/s when the pendulum is 30.0° above its lowest position.
(a) What is the maximum angle away from the lowest position the pendulum will reach?
(b) What is the speed of the mass when the pendulum is 45° above its lowest position?

Question 57

What should the height of a slide in a park be so that a child will reach the bottom of the slide with a speed of 15.0 m/s? Use g = 10.0 m/s².

A) 22.5 m
B) 15.1 m
C) 11.3 m
D) 10.5 m
E) 0.75 m

Question 58

An object of mass 4.00 kg is sitting at the top of an inclined plane of height h and angle θ with the horizontal. The object slides down the inclined plane and right before it reaches the bottom of the plane, it has speed of 16.0 m/s. Neglect friction and use g = 10.0 m/s².
(a) What is the height of the inclined plane?
(b) If the height of the inclined plane is raised to 15.0 m, what is the speed of the object right before it reaches the bottom of the inclined plane?

Question 59

FIGURE 8-4 An object of mass 2 kg is held at the top of a triangular wedge as shown in Figure 8-4, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10 m/s².
Refer to Figure 8-4. What is the gravitational potential energy of the object at the top of the wedge?

A) 30 J
B) 40 J
C) 100 J
D) 60 J
E) 80 J

Question 60

A mass of 1.0 kg is pushed against a spring with a spring constant of 25 N/m. As a result, the spring is compressed by 20 cm. The mass is then released.
(a) What is the amount of potential energy acquired by the spring when it is compressed?
(b) What is the kinetic energy of the mass after the mass is released and it is no longer in contact with the spring?

Question 61

FIGURE 8-6 A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in Figure 8-6. The vertical height at position A above ground level is 200 m. Neglect friction and use g = 10.0 m/s².
What is the speed of the roller coaster at point C?

A) 0 m/s
B) 34.6 m/s
C) 69.2 m/s
D) 20.0 m/s
E) There is not enough information to solve this problem.

Question 62

FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s².
Refer to Figure 8-5. What is the speed of the bead at point B?

A) 10 m/s
B) 4.9 m/s
C) 0 m/s
D) 4.5 m/s
E) There is not enough information to solve this problem.

Question 63

An 8 kg object moving with an initial velocity of 4 m/s comes to rest due to friction after it travels a horizontal distance of 10 m. If the initial speed of the object is doubled, what distance will it travel before coming to rest? Use g = 10 m/s².

A) 10 m
B) 20 m
C) 30 m
D) 40 m
E) 80 m

Question 64

FIGURE 8-8
6 J of work is needed to push an object of mass 2 kg from point A to point B of the inclined plane as shown in Figure 8-8. If the angle of inclination is 30°, the height of the plane is h, what is the length of the inclined plane? Use g = 10 m/s².

A) 0.6 m
B) 0.3 m
C) 10 m
D) 6 m
E) 3 m

Question 65

FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s².
Refer to Figure 8-5. What is the kinetic energy of the bead at point B?

A) 0 J
B) 2.0 x 10^-2 J
C) 16 x 10^-3 J
D) 0.40 J
E) There is not enough information to solve this problem.

Question 66

A snowboarder coasts on a smooth track that rises from one level to another. If the snowboarder's initial speed is 4 m/s, the snowboarder just makes it to the upper level and comes to rest. With a slightly greater initial speed of 5 m/s, the snowboarder is still moving to the right on the upper level. What is the snowboarder's final speed in this case?

A) 1 m/s
B) 2 m/s
C) 3 m/s
D) 4 m/s
E) 5 m/s

Question 67

FIGURE 8-8
An object of mass 2.00 kg starts at rest from the top of a rough inclined plane of height 20.0 m as shown in Figure 8-8. If the work done by the force of friction is -150 J, what is the speed of the object as it reaches the bottom of the inclined plane? Use g = 10.0 m/s².

A) 15.8 m/s
B) 150 m/s
C) 10.0 m/s
D) 20.0 m/s
E) 200 m/s

Question 68

An object of mass m moving with a certain speed has a kinetic energy of 0.0124 J. The object collides with a horizontal spring and compresses it by 0.800 m before it is brought to rest. What is the spring constant of this spring?

A) 0.315 N/m
B) 0.150 N/m
C) 0.194 N/m
D) 0.0235 N/m
E) 0.0388 N/m

Question 69

An object moving along a horizontal surface approaches the bottom of a ramp. At the very bottom of the ramp, point A, its speed is 40 m/s. The object goes up the ramp and reverses direction at point B. What is the height of point B above point A? The angle of inclination is 30°. Neglect friction and use g = 10 m/s².

A) 50 m
B) 60 m
C) 70 m
D) 80 m
E) 90 m

Question 70

An object of mass 4.0 kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s². How high did the object go?

A) 20 m
B) 4.5 m
C) 15 m
D) 80 m
E) None of the other choices is correct.

Question 71

FIGURE 8-7 Two masses M₁ = 2.0 kg and M₂ = 4.0 kg are attached by a string as shown in Figure 8-7. M₁ falls vertically down and M₂ moves on a frictionless surface. Initially the system is at rest. Use g = 10 m/s².
Refer to Figure 8-7. What is the speed of mass M₁ just before it touches the ground?

A) 2.3 m/s
B) 2.9 m/s
C) 3.8 m/s
D) 4.6 m/s
E) 5.8 m/s

Question 72

FIGURE 8-6 A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in Figure 8-6. The vertical height at position A above ground level is 200 m. Neglect friction and use g = 10.0 m/s².
What is the total energy of the roller coaster at point A?

A) 16.0 × 10³ J
B) 20.2 × 10³ J
C) 16.0 × 10⁴ J
D) 17.6 × 10⁴ J
E) There is not enough information to solve this problem.

Question 73

FIGURE 8-8
An object of mass 4 kg starts at rest from the top of a rough inclined plane of height 10 m as shown in Figure 8-8. If the speed of the object at the bottom of the inclined plane is 10 m/s, how much work is done by the force of friction? Use g = 10 m/s².

A) -100 J
B) 100 J
C) 0
D) -200 J
E) 200 J

Question 74

An object approaches the bottom of a ramp, point A. It goes up the ramp and turns around at point B, which is 40.0 m above A. The ramp makes an angle of 30.0° with the horizontal. What is the speed of the object at point A? Neglect friction and use g = 10.0 m/s².

A) 23.8 m/s
B) 28.3 m/s
C) 10.0 m/s
D) 11.6 m/s
E) 15.3 m/s

Question 75

FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s².
Refer to Figure 8-5. What is the potential energy of the bead at point A?

A) 2.0 x 10^-2 J
B) 16 x 10^-3 J
C) 0.40 J
D) 0 J
E) There is not enough information to solve this problem.

Question 76

FIGURE 8-7 Two masses M₁ = 2.0 kg and M₂ = 4.0 kg are attached by a string as shown in Figure 8-7. M₁ falls vertically down and M₂ moves on a frictionless surface. Initially the system is at rest. Use g = 10 m/s².
Refer to Figure 8-7. What is the potential energy of the mass M₁ just before it touches the ground?

A) 2.3 J
B) 2.5 J
C) 0 J
D) 4 J
E) 5.2 J

Question 77

An object of mass 4 kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s². What is the kinetic energy of the object just before it hits the ground?

A) 800 J
B) 400 J
C) 0 J
D) 100 J
E) 200 J

Question 78

FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s².
Refer to Figure 8-5. What is the speed of the bead at point C?

A) 0 m/s
B) 1.0 m/s
C) 2.0 m/s
D) 4.0 m/s
E) There is not enough information to solve this problem.

Question 79

FIGURE 8-6 A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in Figure 8-6. The vertical height at position A above ground level is 200 m. Neglect friction and use g = 10.0 m/s².
What is the total energy of the roller coaster at point B?

A) 16.4 × 10³ J
B) 20.2 × 10³ J
C) 17.6 × 10⁴ J
D) 16.4 × 10⁴ J
E) There is not enough information to solve this problem.

Question 80

FIGURE 8-6 A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in Figure 8-6. The vertical height at position A above ground level is 200 m. Neglect friction and use g = 10.0 m/s².
What is the speed of the roller coaster at point B?

A) 66.3 m/s
B) 20.0 m/s
C) 46.9 m/s
D) 17.6 m/s
E) There is not enough information to solve this problem.