Question 1

Two objects,one of mass m and the other of mass 2m,are dropped from the top of a building.Assuming 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

The kinetic energy (KE) of an object is given by the formula KE = 1/2 m v^2, where m is the mass and v is the velocity. When dropped from the same height without air resistance, both objects will reach the ground with the same velocity due to gravity. Therefore, the kinetic energy of the heavier object (2m) will be twice that of the lighter object (m), because KE is directly proportional to mass when velocity is constant.

Question 2

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

The work done on an object is related to the change in its kinetic energy, which is given by the formula $ \frac{1}{2}mv^2 $, where $ m $ is the mass of the object and $ v $ is its velocity. When comparing the change in kinetic energy for the two scenarios, the increase from 50 mph to 60 mph requires more work because the kinetic energy change is based on the square of the velocity. The change from a higher velocity (50 to 60 mph) results in a greater increase in kinetic energy than from a lower velocity (0 to 30 mph), even though the difference in speed is the same (10 mph) in both cases.

Question 3

When you throw a pebble straight up with initial speed V,it reaches a maximum height H assuming there is 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 potential energy at the maximum height is proportional to the square of the initial speed. To reach twice the height, the potential energy must double, which requires the initial speed to increase by a factor of $\sqrt{2}$, making the correct answer $\sqrt{2}V$.

Question 4

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

Both person X and person Y are pushing against a stationary object, so there is no displacement and no work is being done. Therefore, both do zero work.

Question 5

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 force applied to an object times the distance that the object moves in the direction of the force. Since the car does not move, the distance is zero, and therefore, the work done by both Joel and Jerry is zero, regardless of the time they spent pushing.

Question 6

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-Earth system compared to that of the first stone-Earth system 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

The gravitational potential energy (U) is given by U = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above the ground. Since the second stone has four times the mass of the first stone and both are at the same height, the gravitational potential energy of the second stone-Earth system is four times as much as that of the first stone-Earth system.

Question 7

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 (KE) formula is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity. Given the truck has four times the mass ($4m$) and twice the speed ($2v$) of the car, the truck's kinetic energy is $KE_{truck} = \frac{1}{2} \times 4m \times (2v)^2 = 16 \times \frac{1}{2}mv^2$, which is 16 times the kinetic energy of the car ($KE_{car}$).

Question 8

When you drop a pebble from height H,it reaches the ground with speed V assuming 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 when it hits the ground is given by:

V = sqrt(2gh)

where g is the acceleration due to gravity and h is the initial height of the pebble. We want to find the new initial height, h', such that the pebble will reach the ground with twice the speed, or 2V:

2V = sqrt(2gh')

Solving for h', we get:

h' = 8h

Therefore, the pebble must be dropped from a height that is 8 times the original height in order to reach the ground with twice the speed. The only answer choice that matches this is C) 4H, since 4H x 8 = 32H, which is the new height of the pebble.

Question 9

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 during a panic stop on a level road, under constant friction, is proportional to the square of the initial speed. Therefore, if the initial speed is doubled, the skidding distance becomes four times as far.

Question 10

If the force exerted 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 can be positive if the object moves in the opposite direction (against 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 11

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

Accepted Answer

The gravitational force exerted by Earth on the object does not do any work since it acts perpendicular to the direction of motion of the object. Therefore, the work done by the gravitational force on the bucket is 0 J.

Question 12

You throw a baseball straight up.Compare the sign of the work done by the gravitational force exerted by Earth on the object while the ball goes up with the sign of the work done by the same force 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

The work done by gravity is negative on the way up because the force of gravity and the displacement of the ball are in opposite directions. On the way down, the work is positive because the force of gravity and the displacement of the ball are in the same direction.

Question 13

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, where m is the mass and v is the velocity. 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.

Question 14

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 compression is identical. The lighter dart moves faster due to having less mass for the same amount of kinetic energy. Both darts had the same initial elastic potential energy because this energy is determined by the compression of the spring, not by the mass of the dart.

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 distance each car travels when skidding to a stop depends on the coefficient of kinetic friction and the initial speed, both of which are identical for all cars. Mass does not affect the stopping distance under these conditions, so all cars travel the same distance to stop.

Question 16

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.The same stopping force is exerted on both objects and both objects 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

Since the same stopping force is exerted on both objects, the distance traveled before stopping depends only on their initial velocities. Since the 1.0 kg object has a higher initial velocity, it will travel a greater distance before coming to a stop. However, the mass of the object does not factor into the calculation of distance traveled before stopping. Therefore, both objects travel the same distance.

Question 17

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 amount of work done by friction is given by the formula W = Fd, where W is work, F is force, and d is distance. Since all three cars have the same speed, they all have the same kinetic energy. When they slam on their brakes, this energy is dissipated by friction between the tires and the road surface. Since the tires of all three cars have identical coefficients of kinetic friction with the road surface, the force of friction acting on each car will be proportional to its mass. Therefore, the more massive car L will experience a greater force of friction than car M or car N. Since all three cars are stopping from the same initial speed, they will all travel the same distance while stopping. Therefore, the work done by friction, which is proportional to both force and distance, will be greatest for car L.

Question 18

When you drop a pebble from height H,it reaches the ground with kinetic energy K assuming 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 pebble must be dropped from twice the original height, 2H.

Question 19

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

Hooke's law states that the force exerted by a spring is directly proportional to the displacement or change in length of the spring. This means that the graph of force (y-axis) against displacement (x-axis) should be a straight line passing through the origin. Graph B shows a linear relationship between force and displacement, which indicates that the spring obeys Hooke's law.

Question 20

You and your friend,who has the same mass 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 the system you-Earth and your friend-Earth,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)The friend-Earth system's gravitational potential energy is greater than the you-Earth system's gravitational potential energy, because he got to the top faster.
D)Both systems have the same amount of gravitational potential energy at the top.
E)The you-Earth system's gravitational potential energy is greater than the friend-Earth system, because you traveled a greater distance in getting to the top.

Accepted Answer

The gravitational potential energy of an object depends only on its height and mass, and is independent of the time taken to get there. Both you and your friend are at the same height at the top of the Eiffel Tower and have the same mass, so both systems have the same amount of gravitational potential energy at the top. The method of getting there (taking the elevator or walking up the stairway) does not affect the gravitational potential energy.

Quiz 7: Work and Energy

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

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

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

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.

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-Earth system compared to that of the first stone-Earth system is

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

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

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?

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

A 35-N bucket of water is lifted vertically 3.0 m and then returned to its original position.How much work did the gravitational force exerted by Earth on the object do on the bucket during this process?

You throw a baseball straight up.Compare the sign of the work done by the gravitational force exerted by Earth on the object while the ball goes up with the sign of the work done by the same force while it goes down.

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 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 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.The same stopping force is exerted on both objects and both objects are brought to rest.Which object travels the greater distance before stopping?

When you drop a pebble from height H,it reaches the ground with kinetic energy K assuming 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)

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