How much kinetic energy will a 5 kg object gain if it falls from a height of 7 m above the ground, to a height of 2 m above the ground if air resistance is ignored?

A. 98 J
Incorrect. This is the gravitational potential energy at a height of 2 m.

B. 245 J
Correct! The kinetic energy gained is equal to the potential energy lost as it falls.

C. 343 J
Incorrect. This is the gravitational potential energy at a height of 7 m.

D. 62.5 J
Incorrect. You calculated one-half times the mass times the displacement squared; you need on-half times the mass times the velocity squared.

A 500 kg car is driving at 25 m/s when the driver slams on the brakes and skids to a stop. If the stopping distance is 50 meters, what is the average value of the stopping force?

A. -12500 N
Incorrect. You calculated the change in the momentum of the car; you need to find the change in kinetic energy and divide by displacement.

B. -250 N
Incorrect. You divided the change in momentum by displacement; you need to divide the change in kinetic energy by displacement.

C. -156250 N
Incorrect. You calculated the change in kinetic energy; you need to divide this result by the displacement.

D. -3125 N
Correct! The change in kinetic energy is equal to the force times the displacement.

A 10,000 kg railroad car is moving at 6 m/s when it collides and couples with a 5,000 kg railroad car that is initially at rest. What is the velocity of the two cars as they roll off together?

A. 4 m/s
Correct! The total momentum is conserved.

B. 0 m/s
Incorrect. This is the initial velocity of the 5,000 kg car.

C. 15000 m/s
Incorrect. This is the total mass of the system in kg.

D. 60000 m/s
Incorrect. This is the total momentum of the system in kgm/s.

What is the total mechanical energy of a 0.125 kg baseball thrown at 40m/s at a height of 1.2 meters above the ground?

A. 1.47 J
Incorrect. This is the gravitational potential energy, not the total mechanical energy.

B. 100.00 J
Incorrect. This is the kinetic energy, not the total mechanical energy.

C. 101.47 J
Correct! This is the potential energy added to the kinetic energy.

D. 5.00 J
Incorrect. The momentum of the ball is 5 kgm/s; you need energy.

A student is sitting next to a campfire. The heat from the fire is being transferred to the student by —

A. conduction
Incorrect. Conduction is the transfer of heat by contact.

B. induction
Incorrect. Induction is the interaction between electric and magnetic forces in a circuit.

C. convection
Incorrect. Convection is the transfer of heat by upward movement of heated air.

D. radiation
Correct! This heat that is next to the side of the fire is transferred by radiation.

What was the initial speed of a 0.05 kg box if it is brought to rest in 4 cm by a 750 N/m spring?

A. 4.9 m/s
Correct! Set the elastic potential energy equal to the initial kinetic energy.

B. 490 m/s
Incorrect. You need to convert from centimeters to meters.

C. 600 m/s
Incorrect. You calculated the acceleration of the box; you need the initial velocity.

D. 34.6 m/s
Incorrect. You calculated the force of the spring, not the energy.

A small body of water with a mass of 2000 kg cools from 25°C to 20 °C. How much heat was lost to the surroundings? (The specific heat of water is 4180 J/kg °C.)

A. 209,000,000 J
Incorrect. This was the initial energy of the water.

B. 167,200,000 J
Incorrect. This was the final energy level of the water.

C. 41,800,000 J
Correct! This is the heat loss.

D. 10,000 J
Incorrect. You forgot to multiply by the specific heat.

What is the momentum of a 10 kg model plane that is flying at 15 m/s at an altitude of 20 meters?

A. 1125 kgm/s
Incorrect. You calculated the kinetic energy.

B. 1960 kgm/s
Incorrect. You calculated the gravitational potential energy.

C. 3085 kgm/s
Incorrect. You calculated the total mechanical energy.

D. 150 kgm/s
Correct! Momentum is the product of mass and velocity.

A 5 kg box is sliding at 2 m/s at the top of a frictionless ramp. At the bottom of the ramp, the box is moving at 8 m/s. How tall is the ramp?

A. 3.27 m
Incorrect. You set the potential energy equal to the initial kinetic energy; it should equal the change in kinetic energy.

B. 3.06 m
Correct! The change in kinetic energy equals the change in potential energy.

C. 0.20 m
Incorrect. You set the potential energy equal to the final kinetic energy; it should equal the change in kinetic energy.

D. 3.47 m
Incorrect. You added the initial and final values of the kinetic energy; you should have subtracted.

A student is conducting an investigation about the conservation of momentum. She records information about the mass and velocity of two lab carts before and after a collision.

 

Cart A

Cart B

Mass

0.75 kg

1.25 kg

Velocity before the collision

4 m/s right

2 m/s left

Velocity after the collision

1 m/s left

 

Which of the following should fill in the empty cell in the chart in order for momentum to be conserved?

A. 3.8 m/s right
Incorrect. The velocities are in the opposite direction from each other, so they have opposite signs.

B. 3.8 m/s left
Incorrect. The velocities are in the opposite direction from each other, so they have opposite signs.

C. 1 m/s right
Correct! The velocities are in the opposite direction from each other, so they have opposite signs.

D. 1 m/s left
Incorrect. The velocities are in the opposite direction from each other, so they have opposite signs.

A 0.015 kg bullet is traveling at 400 m/s when it hits a thick piece of wood. How far will the bullet penetrate into the wood if it feels an average stopping force of 24,000 N?

A. 0.05 m
Correct! The change in energy of the bullet equals force times distance.

B. 0.00025 m
Incorrect. You set the momentum equal to force times distance; you should have used kinetic energy.

C. 0.0167 m
Incorrect. You set the initial velocity equal to force times distance; you should have used kinetic energy.

D. 0.000125 m
Incorrect. You forgot to square the velocity when you calculated the kinetic energy.

A 4 kg rock that is initially at rest feels a 15 N force for 3 seconds. What is the rock’s final velocity?

A. 3.75 m/s
Incorrect. You calculated the average acceleration of the rock.

B. 1.25 m/s
Incorrect. Impulse is force multiplied by time; you used force divided by time.

C. 11.25 m/s
Correct! The impulse equals the change in momentum.

D. 45 m/s
Incorrect. You found the final momentum; you need to divide this result by the mass of the rock.

You did 6000 J of work pushing a 20 kg lawn mower that is initially at rest across a grassy lawn, but the force of friction dissipated 5750 J. What is the final velocity of the lawn mower?

A. 5.0 m/s
Correct! The total work done equals the change in kinetic energy.

B. 24.5 m/s
Incorrect. You set the work you did equal to the change in kinetic energy; you need to use the total work.

C. 24.0 m/s
Incorrect. You set the work done by friction equal to the change in kinetic energy; you need to use the total work.

D. 34.3 m/s
Incorrect. The work done by friction should be subtracted from the work you did, not added.

A box feels a force of 15 N for 3 seconds while it moves 2 meters in the same direction as the force. What is the change in kinetic energy of the box?

A. 45 J
Incorrect. You calculated impulse, which is change in momentum; you need work.

B. 30 J
Correct! The work is the change in kinetic energy.

C. 5 J
Incorrect. You divided force by time; you needed to multiply by displacement.

D. 7.5 J
Incorrect. You need to multiply by displacement, not divide.

Two lab carts collide and stick together as shown below. What was the initial velocity of cart A?

A. -1.14 m/s
Incorrect. Be careful with positives and negatives.

B. 1.14 m/s
Incorrect. Be careful with positives and negatives.

C. -4.57 m/s
Incorrect. Be careful with positives and negatives.

D. 4.57 m/s
Correct! The cart must have been going right at 4.57 m/s.

A 0.5 kg rock is sitting on a 500 N/m vertical spring that is compressed by 0.1 m. How fast will it be moving at a height of 0.3 m above its original position?

A. 2.0 m/s
Correct! The elastic energy is transferred into both gravitational energy and kinetic energy.

B. 3.2 m/s
Incorrect. Some of the elastic energy is transferred into gravitational energy.

C. 4.0 m/s
Incorrect. You need to subtract the final gravitational energy, not add it.

D. 32.5 m/s
Incorrect. You forgot to square the compression when you calculated the elastic energy.

A student holds an iron bar over a flame in a lab and notices the part of the bar in his hand is getting warmer. Which method of heat transfer is responsible for this?

A. Conduction
Correct! Conduction is the transfer of heat by contact.

B. Induction
Incorrect. Induction is the interaction between electric and magnetic forces in a circuit.

C. Convection
Incorrect. Convection is the transfer of heat by upward movement of heated air.

D. Radiation
Incorrect. Radiation is heating the area directly around the Bunsen burner.

Which of the following is the temperature of water in a beaker?

A. The average velocity of the water molecules.
Incorrect. If the water is sitting in the beaker, then the average velocity of all of the water molecules is zero.

B. The average kinetic energy of the water molecules.
Correct! Temperature is the average molecular kinetic energy.

C. The total velocity of the water molecules.
Incorrect. Temperature is related to energy, not velocity.

D. The total energy of the water molecules.
Incorrect. This is the heat content, not the temperature.

How much work is done if I lift a 10 kg box of books 1 meter into the air, carry it 5 meters down the hall, and set it back down on the floor?

A. 98 J
Incorrect. This is the work done when I lift it, but I also set it down.

B. 490 J
Incorrect. I do no work while walking down the hallway because the force and displacement are perpendicular to each other.

C. 0 J
Correct! The total vertical displacement of the box is 0, so the total work is also 0.

D. 588 J
Incorrect. I do no work while walking down the hallway because the force and displacement are perpendicular to each other.

What is the kinetic energy of a 40 kg child riding a skateboard at 5 m/s?

A. 200 J
Incorrect. You calculated the momentum, not the kinetic energy.

B. 100 J
Incorrect. You forgot to square the velocity.

C. 1000 J
Incorrect. You forgot to multiply by one-half.

D. 500 J
Correct! The kinetic energy is 500 J.

Which of the following situations describes a situation where entropy is decreasing?

A. Food coloring spreads out when added to water so that the color is eventually uniform.
Incorrect. Entropy in this case is increasing.

B. Two different temperature gasses come to the same temperature when mixed.
Incorrect. Entropy in this case is increasing.

C. A deck of cards is shuffled.
Incorrect. Entropy in this case is increasing.

D. A deck of cards is put in order by suit.
Correct! Entropy is decreasing when the deck is organized.

How much work is required to push a 10 kg box the frictionless ramp shown in the figure below?

box at the bottom of a 5 m tall ramp that spans a 12 m distance from a ledge

A. 490 J
Correct! The work done is equal to the weight multiplied by the height.

B. 1176 J
Incorrect. Use the height, not the horizontal displacement.

C. 1274 J
Incorrect. Use the height, not the length of the ramp.

D. 98 J
Incorrect. You need to multiply by the height of the ramp.

Which of the following Energy vs. Height graphs best models the kinetic energy and gravitational potential energy of an object thrown straight up?

A
Incorrect. The gravitational potential energy is directly proportional to height.

B
Incorrect. The gravitational potential energy is directly proportional to height.

C
Incorrect. The gravitational potential energy is directly proportional to height.

D
Correct! The gravitational potential energy is directly proportional to height.

How much will the velocity of a 5 kg object increase if I push on it with a force of 7 N for 3 seconds?

A. 2.9 m/s
Incorrect. Impulse is the change in momentum, not kinetic energy.

B. 4.2 m/s
Correct! Impulse is the change in momentum.

C. 0.47 m/s
Incorrect. Impulse is force multiplied by time, not divided.

D. 105 m/s
Incorrect. Velocity is momentum divided by mass, not multiplied.

Two students are facing each other while wearing roller skates. They push off from one another and move apart. The first student has a mass of 50 kg, and winds up moving to the left at 3 m/s. If the second student has a mass of 35 kg, find his velocity.

A. 2.1 m/s to the right
Incorrect. The 50 kg student had a velocity of 3 m/s; you solved as if the 35 kg student had a velocity of 3 m/s.

B. 2.1 m/s to the left
Incorrect. The 50 kg student had a velocity of 3 m/s; you solved as if the 35 kg student had a velocity of 3 m/s.

C. 4.3 m/s to the right
Correct! The student will gain an equal and opposite momentum.

D. 4.3 m/s to the left
Incorrect. If the first student moves left, the second student must move to the right.

Which law of physics best describes why a rocket engine causes a rocket to change velocity?

A. Conservation of mechanical energy
Incorrect. The system involved has several types of energy, not just mechanical.

B. Conservation of momentum
Correct! The hot gasses from the engine and the rocket gain equal and opposite momentum.

C. Conservation of mass
Incorrect. The conservation of mass does not explain the change in velocity.

D. Entropy
Incorrect. Entropy does not explain the change in velocity.

A 40 kg child jumps from the 10 m platform at a swimming pool. If she plunges 2 m deep into the water, what was the average stopping force provided by the water?

A. 2352 N
Correct! Her total change in energy was 4704 J, which requires 2352 N to stop in 2 meters.

B. 3920 N
Incorrect. She fell a total of 12 m, not 10 m.

C. 392 N
Incorrect. This is her weight, that is the force needed to stop her from accelerating.

D. 588 N
Incorrect. You treated the water like a spring and solved for the spring constant. You need the stopping force from the total work done.

What is the total energy of a 3 kg rock that is moving 15 m/s at a height of 4 m?

A. 337.5 J
Incorrect. You found the kinetic energy, now add the potential energy.

B. 117.6 J
Incorrect. You found the potential energy, now add the kinetic energy.

C. 455.1 J
Correct! That is the total energy.

D. 45 J
Incorrect. You found momentum; you need to calculate potential and kinetic energy.

How much power is required to lift a 5 kg bucket of water 12 meters out of a well in 20 seconds?

A. 29.4 W
Correct! That is the change in energy over time.

B. 3 W
Incorrect. You forgot to multiply by the acceleration due to gravity.

C. 11760 W
Incorrect. You multiplied by time; you need to divide by time.

D. 2.45 W
Incorrect. You divided by the displacement; you need to multiply.