PASSAGE 1 (Questions 1 – 5 pertain to this passage.)
Two physicists, both of mass 50 kg, climb up identical ropes suspended from the ceiling of a gymnasium. The ropes are 15 meters long. Physicist 1 reaches the top twice as quickly as physicist 2 does. After physicist 2 also reaches the top, the they argue about who did more work against gravity:
Physicist 1
“I did more work fighting gravity, because I was overcoming gravity more quickly. Your climb was lazier, and therefore, you did less work.”
Physicist 2
“No way. I did more work fighting gravity, because I spent more time climbing the rope. Since we both ended up at the same height, but I spent more time getting there, I had to work harder.”

1. | Which physicist, if either, did more work against gravity while climbing from the floor to the ceiling?

A. | . Physicist 1 did more work.

B. | Physicist 2 did more work.

C. | Both physicists did the same positive work.

D. | Neither physicist did any work.

2. | Physicist 1 climbed her rope in 30 seconds. What average power did she exert fighting gravity?

A. | 25 watts

B. | 250 watts

C. | 1500 watts

D. | 15,000 watts

3. | Physicist 2 started at rest from the floor and ended at rest near the ceiling. Which of the following best expresses the net energy transfer during this process?

A. | Chemical to kinetic

B. | Chemical to potential

C. | Kinetic to chemical

D. | Kinetic to potential

4. | Physicist 2 now lets go of the rope and falls onto a heavily-padded cushion, safely coming to rest. During this process, the energy transfer is best described as:

A. | Potential to kinetic to chemical

B. | Potential to kinetic to heat

C. | Kinetic to potential to chemical

D. | Kinetic to potential to heat

5. | When physicist 2 has fallen one third of the way from the ceiling to the floor, her kinetic energy is approximately:

A. | 10 joules

B. | 250 joules

C. | 1000 joules

D. | 2500 joules

PASSAGE 2 (Questions 6 – 9 pertain to this passage.)
Any two spherical objects gravitationally attract each other with force Fgrav = , where M and m are the masses of the two objects, and r is the distance from the center of one object to the center of the other. The potential energy of the system is Ugrav = – ; the old formula U = mgh does not apply.
Two astronomers are figuring out the speed with which a spherical meteor of mass m1 will crash into the Earth, which has mass ME and radius RE. To make the calculation simpler, the astronomers assume that the meteor starts at rest a distance D from the center of the Earth, where D is several times bigger than RE. They also neglect air resistance and treat the Earth as fixed. But the astronomers disagree about how to proceed from there.
Astronomer 1:
“Let's invoke Newton's 2nd law and kinematics. First, using = m1a, we can find the meteor's acceleration. Given that acceleration, we can then use those old constant-acceleration kinematic formulas, such as
v2 = + 2ax, to find the speed with which the meter hits the Earth.”
Astronomer 2:
“Let's use conservation of energy. The meteor starts with potential energy – . All of that potential energy converts into kinetic energy as the meteor rushes towards the Earth. So, we can set the magnitude of the initial potential energy equal to the final kinetic energy:
=
Just solve for v to find the speed with which the meteor crashes into the Earth.

6. | Which astronomer will correctly find the speed with which the meteor hits the Earth?

A. | Astronomer 1 only

B. | Astronomer 2 only

C. | Astronomer 1 and astronomer 2

D. | Neither astronomer 1 nor astronomer 2

7. | Neglecting air resistance, the speed with which the meteor hits the Earth does not depend on:

A. | ME

B. | m1

C. | RE

D. | G

8. | As the meteor gets closer to the Earth, the gravitational force on it:

A. | Increases

B. | Stays constant

C. | Decreases, but stays above zero

D. | Decreases to zero

9. | Which of the following best describes the transfer of energy as the meteor crashes? (The “crash” begins when the meteor first touches the Earth.)

A. | Potential to kinetic

B. | Potential to heat

C. | Kinetic to potential

D. | Kinetic to heat

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