Question 1

A stone is held at a height h above the ground. A second stone with four times the mass of the first one is held at the same height. The gravitational potential energy of the second stone compared to that of the first stone is
A) one-fourth as much.
B) one-half as much.
C) twice as much.
D) four times as much.
E) the same.

Accepted Answer

Gravitational potential energy is directly proportional to both mass and height. Since the second stone has four times the mass of the first stone, its gravitational potential energy is four times as much. Therefore, the answer is D, four times as much.

Question 2

Person X pushes twice as hard against a stationary brick wall as person Y. Which one of the following statements is correct?
A) Both do positive work, but person X does four times the work of person Y.
B) Both do positive work, but person X does twice the work of person Y.
C) Both do the same amount of positive work.
D) Both do zero work.
E) Both do positive work, but person X does one-half the work of person Y.

Accepted Answer

When pushing against a stationary object, no work is being done because the object is not moving. Therefore, both person X and person Y do zero work.

Question 3

Two men, Joel and Jerry, push against a car that has stalled, trying unsuccessfully to get it moving. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do on the car.
A) Joel does 75% more work than Jerry.
B) Joel does 50% more work than Jerry.
C) Jerry does 50% more work than Joel.
D) Joel does 25% more work than Jerry.
E) Neither of them does any work.

Accepted Answer

Work is defined as the product of force and displacement in the direction of the force. Since the car does not move, there is no displacement, and therefore, neither Joel nor Jerry does any work on the car, regardless of the time spent pushing.

Question 4

When you throw a pebble straight up with initial speed V, it reaches a maximum height H with no air resistance. At what speed should you throw it up vertically so it will go twice as high?
A) 16V
B) 8V
C) 4V
D) 2V
E) $\sqrt { 2 }$ V

Accepted Answer

The maximum height reached by a projectile is proportional to the square of its initial velocity. To reach twice the height, the initial speed must be multiplied by the square root of 2.

Question 5

Three cars (car L, car M, and car N) are moving with the same speed and slam on their brakes. The most massive car is car L, and the least massive is car N. If the tires of all three cars have identical coefficients of kinetic friction with the road surface, for which car is the amount of work done by friction in stopping it the greatest?
A) The amount of work done by friction is the same for all cars.
B) Car L
C) Car M
D) Car N

Accepted Answer

The work done by friction is equal to the frictional force times the distance over which it acts. The frictional force is the product of the coefficient of friction and the normal force, which is equal to the weight of the car (mass times gravity). Therefore, the most massive car (car L) will have the greatest frictional force and thus the greatest work done by friction.

Question 6

If the force on an object is in the negative direction, the work it does on the object must be
A) negative.
B) positive.
C) The work could be either positive or negative, depending on the direction the object moves.

Accepted Answer

The work done on an object is defined as the force applied to the object times the distance the object moves in the direction of the force. If the force is in the negative direction, the work done can be positive if the object moves in the opposite direction to the force, or negative if the object moves in the same direction as the force. Therefore, the work could be either positive or negative, depending on the direction of the object's movement relative to the direction of the force.

Question 7

Which requires more work, increasing a car's speed from 0 mph to 30 mph or from 50 mph to 60 mph?
A) 0 mph to 30 mph
B) 50 mph to 60 mph
C) It is the same in both cases.

Accepted Answer

Increasing a car's speed from 0 mph to 30 mph requires a great deal of work as the car has to overcome inertia and gain momentum from a stationary position. On the other hand, increasing the speed from 50 mph to 60 mph does not require as much work as the car is already in motion and only needs to accelerate by an additional 10 mph. Therefore, option B which is increasing from 50 mph to 60 mph requires less work.

Question 8

Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. If there is no air resistance, when they hit the ground
A) both will have the same kinetic energy.
B) the heavier one will have twice the kinetic energy of the lighter one.
C) the heavier one will have four times the kinetic energy of the lighter one.
D) the heavier one will have half the kinetic energy of the lighter one.
E) the heavier one will have one-fourth the kinetic energy of the lighter one.

Accepted Answer

Both objects will experience the same acceleration due to gravity, so they will have the same final velocity when they hit the ground. The kinetic energy of an object is given by 1/2 mv^2, so the object with mass 2m will have 2 times the mass and the same velocity, resulting in 2*1/2mv^2 = mv^2, which is twice the kinetic energy of the object with mass m. Therefore, the correct choice is B.

Question 9

When you drop a pebble from height H, it reaches the ground with speed V if there is no air resistance. From what height should you drop it so it will reach the ground with twice speed?
A) $\sqrt { 2 }$ H
B) 2H
C) 4H
D) 8H
E) 16H

Accepted Answer

The speed of the pebble is proportional to the square root of the height from which it is dropped. To double the speed, the height must be quadrupled, hence 4H.

Question 10

A truck has four times the mass of a car and is moving with twice the speed of the car. If K_t and K_c refer to the kinetic energies of truck and car respectively, it is correct to say that A) K_t = 16K_c. B) K_t = 4K_c. C) K_t = 2K_c. D) K_t = K_c. E) K_t = $\frac { 1 } { 2 }$ Kc.

Accepted Answer

The kinetic energy is given by $ K = \frac{1}{2}mv^2 $. If the truck has four times the mass (4m) and twice the speed (2v) of the car, then its kinetic energy is $ \frac{1}{2}(4m)(2v)^2 = 16(\frac{1}{2}mv^2) $, which is 16 times the kinetic energy of the car.

Question 11

You slam on the brakes of your car in a panic, and skid a certain distance on a straight level road. If you had been traveling twice as fast, what distance would the car have skidded, under the same conditions?
A) It would have skidded 4 times farther.
B) It would have skidded twice as far.
C) It would have skidded 1.4 times farther.
D) It would have skidded one half as far.
E) It is impossible to tell from the information given.

Accepted Answer

The distance skidded by a car under braking on a level road is proportional to the square of the speed. Therefore, if the speed is doubled, the skidding distance becomes four times as far.

Question 12

A heavy dart and a light dart are launched horizontally on a frictionless table by identical ideal springs. Both springs were initially compressed by the same amount. Which of the following statements about these darts are correct? (There could be more than one correct choice.)
A) The darts both have the same kinetic energy just as they move free of the spring.
B) The lighter dart leaves the spring moving faster than the heavy dart.
C) The heavy dart had more initial elastic potential energy than the light dart.
D) Both darts move free of the spring with the same speed.
E) Both darts had the same initial elastic potential energy.

Accepted Answer

The kinetic energy imparted to both darts is the same because it depends on the energy stored in the spring, which is the same for both as the springs were compressed by the same amount (A). Since kinetic energy is given by $ \frac{1}{2}mv^2 $, for the same amount of kinetic energy, the lighter dart must have a higher velocity to compensate for its lower mass, making (B) correct. The initial elastic potential energy in the spring is solely a function of how much the spring is compressed, not on the mass of the dart, so both darts had the same initial elastic potential energy, making (E) correct.

Question 13

When you drop a pebble from height H, it reaches the ground with kinetic energy K if there is no air resistance. From what height should you drop it so it will reach the ground with twice as much kinetic energy?
A) $\sqrt { 2 }$ H
B) 2H
C) 4H
D) 8H
E) 16H

Accepted Answer

The kinetic energy of the pebble is proportional to the height from which it is dropped. To double the kinetic energy, the height must be doubled.

Question 14

The graphs shown show the magnitude F of the force exerted by a spring as a function of the distance x the spring has been stretched. For which one of the graphs does the spring obey Hooke's law? 
a)

b)

c)

d)

e)

A) Graph a
B) Graph b
C) Graph c
D) Graph d
E) Graph e

Accepted Answer

The spring in graph b demonstrates a linear relationship between the amount it is stretched and the force exerted, suggesting that it follows Hooke's law where the force is directly proportional to the displacement. The other graphs do not show a linear relationship and therefore do not obey Hooke's law.

Question 15

Three cars (car F, car G, and car H) are moving with the same speed and slam on their brakes. The most massive car is car F, and the least massive is car H. If the tires of all three cars have identical coefficients of kinetic friction with the road surface, which car travels the longest distance to skid to a stop?
A) They all travel the same distance in stopping.
B) Car F
C) Car G
D) Car H

Accepted Answer

The stopping distance depends on the initial speed and the coefficient of kinetic friction, not on the mass of the car. Since all cars have the same speed and friction coefficient, they all travel the same distance to stop.

Question 16

You throw a baseball 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) The work is positive on the way up and positive on the way down.
B) The work is positive on the way up and negative on the way down.
C) The work is negative on the way up and positive on the way down.
D) The work is negative on the way up and on the way down because gravity is always downward.

Accepted Answer

Work done by gravity is negative on the way up because the force of gravity (downward) is opposite to the direction of motion (upward). On the way down, the work is positive because the force of gravity and the direction of motion (downward) are in the same direction.

Question 17

A 35-N bucket of water is lifted vertically 3.0 m and then returned to its original position. How much work did gravity do on the bucket during this process?
A) 180 J
B) 90 J
C) 45 J
D) 0 J
E) 900 J

Accepted Answer

Gravity did not do any work on the bucket during the process because the displacement of the bucket was zero (it returned to its original position). Work is equal to force multiplied by displacement; since displacement is zero, the work done by gravity is also zero.

Question 18

You and your friend, who weighs the same as you, 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 of you and your friend, after you both reach the top.
A) It is impossible to tell, since the times you both took are unknown.
B) It is impossible to tell, since the distances you both traveled are unknown.
C) Your friend's gravitational potential energy is greater than yours, because he got to the top faster.
D) Both of you have the same amount of gravitational potential energy at the top.
E) Your gravitational potential energy is greater than that of your friend, because you traveled a greater distance in getting to the top.

Accepted Answer

The gravitational potential energy of an object only depends on its mass and height above the ground. Since you and your friend weigh the same and reached the same height at the top of the Eiffel Tower, your gravitational potential energies are the same. The time it took or the distance traveled does not affect gravitational potential energy.

Question 19

A 4.0 kg object is moving with speed 2.0 m/s. A 1.0 kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping?
A) the 4.0 kg object
B) the 1.0 kg object
C) Both objects travel the same distance.
D) It cannot be determined from the information given.

Accepted Answer

Both objects experience the same force and reach the same final velocity (0 m/s), so the distance traveled before stopping is determined solely by their initial velocities. Since the 1.0 kg object has a higher initial velocity, it travels a greater distance before coming to a stop.

Question 20

Which one has larger kinetic energy: a 500-kg object moving at 40 m/s or a 1000-kg object moving at 20 m/s?
A) The 500-kg object
B) The 1000-kg object
C) Both have the same kinetic energy.

Accepted Answer

The kinetic energy (KE) is given by the formula KE = 1/2 mv^2. For the 500-kg object moving at 40 m/s, KE = 1/2 * 500 * (40)^2 = 400,000 Joules. For the 1000-kg object moving at 20 m/s, KE = 1/2 * 1000 * (20)^2 = 200,000 Joules. Therefore, the 500-kg object has a larger kinetic energy.

Quiz 10: Energy and Work

A stone is held at a height h above the ground. A second stone with four times the mass of the first one is held at the same height. The gravitational potential energy of the second stone compared to that of the first stone is

Person X pushes twice as hard against a stationary brick wall as person Y. Which one of the following statements is correct?

Two men, Joel and Jerry, push against a car that has stalled, trying unsuccessfully to get it moving. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do on the car.

When you throw a pebble straight up with initial speed V, it reaches a maximum height H with no air resistance. At what speed should you throw it up vertically so it will go twice as high?

If the force on an object is in the negative direction, the work it does on the object must be

Which requires more work, increasing a car's speed from 0 mph to 30 mph or from 50 mph to 60 mph?

Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. If there is no air resistance, when they hit the ground

When you drop a pebble from height H, it reaches the ground with speed V if there is no air resistance. From what height should you drop it so it will reach the ground with twice speed?

A truck has four times the mass of a car and is moving with twice the speed of the car. If Kt and Kc refer to the kinetic energies of truck and car respectively, it is correct to say that

You slam on the brakes of your car in a panic, and skid a certain distance on a straight level road. If you had been traveling twice as fast, what distance would the car have skidded, under the same conditions?

A heavy dart and a light dart are launched horizontally on a frictionless table by identical ideal springs. Both springs were initially compressed by the same amount. Which of the following statements about these darts are correct? (There could be more than one correct choice.)

When you drop a pebble from height H, it reaches the ground with kinetic energy K if there is no air resistance. From what height should you drop it so it will reach the ground with twice as much kinetic energy?

The graphs shown show the magnitude F of the force exerted by a spring as a function of the distance x the spring has been stretched. For which one of the graphs does the spring obey Hooke's law? a) b) c) d) e)

You throw a baseball 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 35-N bucket of water is lifted vertically 3.0 m and then returned to its original position. How much work did gravity do on the bucket during this process?

You and your friend, who weighs the same as you, 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 of you and your friend, after you both reach the top.

A 4.0 kg object is moving with speed 2.0 m/s. A 1.0 kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping?

Which one has larger kinetic energy: a 500-kg object moving at 40 m/s or a 1000-kg object moving at 20 m/s?

A truck has four times the mass of a car and is moving with twice the speed of the car. If K_t and K_c refer to the kinetic energies of truck and car respectively, it is correct to say that