Physics: Work and Energy

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?

(Square root of 2)V

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?

0 J

A force produces power P by doing work W in a time T. What power will be produced by a force that does six times as much work in half as much time?

12P

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?

2H

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?

4H

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

50 mph to 60 mph

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

The 500-kg object

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. -A,B,E

A heavy sled and a light sled, both moving horizontally with the same speed, suddenly slide onto a rough patch of snow and eventually come to a stop. The coefficient of kinetic friction between the sleds and the rough snow is the same for both of them. Which of the following statements about these sleds are correct? (There could be more than one correct choice.) A) Both sleds will slide the same distance on the rough snow before stopping. B) The heavy sled will slide farther on the rough snow than the light sled. C) The light sled will slide farther on the rough snow than the heavy sled. D) The friction from the snow will do more negative work on the heavy sled than on the light sled. E) The friction from the snow will do the same amount of work on both sleds.

A, D

A heavy stone and a light stone are released from rest in such away that they both have the same amount of gravitational potential energy just as they are released. Air resistance is negligibly small. Which of the following statements about these stones are correct? (There could be more than one correct choice.) A) The initial height of the light stone is greater than the initial height of the heavy stone. B) The stones must have been released from the same height. C) The stones both have the same speed just as they reach the ground. D) Just as it reaches the ground, the light stone is traveling faster than the heavy stone. E) The stones both have the same kinetic energy just as they reach the ground.

A,D,E

A 1-kg ball is released from a height of 6 m, and a 2-kg ball is released from a height of 3 m. Air resistance is negligible as they fall. Which of the following statements about these balls are correct? (There could be more than one correct choice.) A) As they reach the ground, the 1-kg ball will have more kinetic energy than the 2-kg ball because it was dropped from a greater height. B) As they reach the ground, the 1-kg ball will be moving faster than the 2-kg ball. C) Both balls will reach the ground with the same speed. D) Both balls will reach the ground with the same kinetic energy. E) Both balls will take the same time to reach the ground.

B, D

A heavy dart and a light dart are launched vertically by identical ideal springs. Both springs were initially compressed by the same amount. There is no significant air resistance. Which of the following statements about these darts are correct? (There could be more than one correct choice.) A) The heavy dart goes higher than the light dart. B) The light dart goes higher than the heavy dart. C) Both darts reach the same maximum height. D) At the maximum height, both darts have the same gravitational potential energy. E) Both darts began moving upward with the same initial speed.

B, D

A heavy rock and a light rock are dropped from the same height and experience no significant air resistance as they fall. Which of the following statements about these rocks are correct? (There could be more than one correct choice.) A) Both rocks have the same kinetic energy when they reach the ground. B) Both rocks have the same speed when they reach the ground. C) The heavier rock reaches the ground before the lighter rock. D) Just as they were released, both rocks had the same amount of gravitational potential energy. E) When they reach the ground, the heavier rock has more kinetic energy than the lighter rock.

B,E

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

Both do zero work

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?

Both objects travel the same distance

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.

Both of you have the same amount of gravitational potential energy at top

Two frisky otters slide down frictionless hillsides of the same height but different slopes. The slope of the hill of otter 1 is 30°, while the slope of the hill of otter 2 is 60°. If both start from rest, which otter is moving faster when she reaches the bottom of her hill?

Both otters have the same speed at the bottom

A heavy sled and a light sled, both moving horizontally with the same kinetic energy, suddenly slide onto a rough patch of snow and eventually come to a stop. The coefficient of kinetic friction between the sleds and the rough snow is the same for both of them. Which of the following statements about these sleds are correct? (There could be more than one correct choice.) A) Both sleds will slide the same distance on the rough snow before stopping. B) The heavy sled will slide farther on the rough snow than the light sled. C) The light sled will slide farther on the rough snow than the heavy sled. D) On the rough snow, the change in kinetic energy will be the same for both sleds. E) The friction from the snow will do the same amount of work on both sleds.

C,D,E

Two identical grasshoppers jump into the air with the same initial speed and experience no air resistance. Grasshopper A goes straight up, but grasshopper B goes up at a 66° angle above the horizontal. Which of the following statements about these grasshoppers are correct? (There could be more than one correct choice.) A) At their highest point, both of them have the same amount of gravitational potential energy. B) At their highest point, both of them have the same amount of kinetic energy. C) At their highest point, both of them have the same amount of mechanical energy. D) At their highest point, grasshopper B is moving faster than grasshopper A. E) At their highest point, grasshopper A has more gravitational potential energy than grasshopper B.

C,D,E

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?

Car L

A heavy frog and a light frog jump straight up into the air. They push off in such away that they both have the same kinetic energy just as they leave the ground. Air resistance is negligible. Which of the following statements about these frogs are correct? (There could be more than one correct choice.) A) Just as they leave the ground, the heavier frog is moving faster than the lighter frog. B) Just as they leave the ground, the lighter frog is moving faster than the heavier frog. C) They both leave the ground with the same speed. D) The lighter frog goes higher than the heavier frog. E) The heavier frog goes higher than the lighter frog. F) Both frogs reach the same maximum height.

F only

If a stone is dropped with an initial gravitational potential energy of 100 J but reaches the ground with a kinetic energy of only 75 J, this is a violation of the principle of conservation of energy.

False

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

Four times as much

Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. If there is no air resistance, the maximum height of Joe's ball will be

Four times that of Bill's ball

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?

Graph B

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?

It would have skidded 4 times farther

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

Kt=16Kc

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.

Neither of them does any work

If the units of your answer are kg ∙ m2/s3, which of the following types of quantities could your answer be?

Power

Two cyclists who weigh the same and have identical bicycles ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that has a lower grade. Joe gets to the top before Bob. Ignoring friction and wind resistance, which one of the following statements is true?

The amount of work done by Joe is equal to the amount of work done by Bob, but the average power exerted by Joe is greater than that of Bob.

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

The heavier one will have twice the kinetic energy of the lighter one

A stone can slide down one of four different frictionless ramps, as shown in the figure. For which ramp will the speed of the ball be the greatest at the bottom?

The speed of the ball will be the same for all ramps

A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case. Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45° above horizontal. Case D: Thrown straight out horizontally.

The speed will be the same in all cases

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

The work could be either positive or negative, depending on the direction the object moves

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.

The work is negative on the way up and positive on the way down.

A person stands on the edge of a cliff. She throws three identical rocks with the same speed. Rock X is thrown vertically upward, rock Y is thrown horizontally, and rock Z is thrown vertically downward. If the ground at the base of the cliff is level, which rock hits the ground with the greatest speed if there is no air resistance?

They all hit the ground with the same speed

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?

They all travel the same distance in stopping.

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 with no air resistance. Which object rises to a greater height?

They both slide to exactly the same height

Swimmers at a water park have a choice of two frictionless water slides, as shown in the figure. 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 bottom of slide 1 compare with v2, the speed of a swimmer reaching the end of slide 2?

V1=V2

Jill does twice as much work as Jack does and in half the time. Jill's power output is

four times Jack's power output