Difficulty: Easy

Average Score: 82%

While exploring the Moon during the Apollo 15 mission, astronaut David Scott held a 1.32-kg geological hammer in one hand and a 0.03-kg falcon feather in the other, releasing them from the same height. The Moon has no air resistance and the acceleration due to gravity is only 1.6 m/s'. The two objects landed on the surface of the Moon at the same time.

What is the relationship between the kinetic energy of the feather and of the hammer just before they hit the surface of the Moon?

Diagram for question

Rationale

The hammer has more kinetic energy than the feather because it has a greater mass.

Kinetic energy is determined by both mass and velocity, specifically expressed in the formula KE = 1/2 mv². While both the hammer and feather will fall at the same velocity in the Moon's gravitational field, the hammer's greater mass results in a higher kinetic energy upon impact.

A (The hammer has more kinetic energy than the feather because it has a greater mass.) CORRECT

This statement is correct, as kinetic energy increases with mass. Since the hammer has a greater mass than the feather and both objects fall at the same velocity on the Moon, the hammer will possess significantly more kinetic energy at the moment of impact.

B (Both objects have the same kinetic energy because they fell with the same velocity.) YOUR ANSWER

While it's true that both objects fall with the same velocity, kinetic energy also depends on mass. The feather's smaller mass means it has less kinetic energy compared to the hammer, despite the same falling speed.

C (The hammer has more kinetic energy than the feather because it will accelerate faster than the feather.) YOUR ANSWER

This statement is misleading. On the Moon, both the hammer and feather experience the same gravitational acceleration. The difference in kinetic energy is not due to differing rates of acceleration, but rather the difference in mass.

D (Both objects have the same kinetic energy because gravity pulls on both objects equally.) YOUR ANSWER

This choice incorrectly implies that gravitational force alone determines kinetic energy. While gravity does act equally on both objects, it is the mass and velocity that ultimately define their kinetic energy. Since the hammer is more massive, it has greater kinetic energy.

Conclusion

The relationship between the kinetic energies of the hammer and feather is primarily influenced by mass. The hammer possesses more kinetic energy due to its greater mass, even if both objects fall at the same velocity in the Moon's gravitational field. Understanding this relationship is crucial in physics, as it highlights the interplay between mass, velocity, and kinetic energy.

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