9. What is the relationship between the kinetic energy of the feather and of the hammer just before they hit the surface of the Moon?
Answer: A
The hammer has more kinetic energy than the feather because it has a greater mass.
Kinetic energy is determined by both mass and velocity. Since the hammer has a greater mass compared to the feather and they fall at the same velocity on the Moon, the hammer will indeed have more kinetic energy just before impact.
A) The hammer has more kinetic energy than the feather because it has a greater mass.
This option is correct because kinetic energy is calculated using the formula KE = 0.5 * m * v^2, where m is mass and v is velocity. Although both objects fall at the same velocity due to the absence of air resistance, the hammer's greater mass results in a higher kinetic energy compared to the feather.
B) Both objects have the same kinetic energy because they fell with the same velocity.
This option is incorrect. While it is true that they fell with the same velocity, kinetic energy also depends on mass. The feather, having much less mass than the hammer, therefore possesses significantly less kinetic energy despite having the same velocity.
C) The hammer has more kinetic energy than the feather because it will accelerate faster than the feather.
This option is also incorrect. Both objects accelerate at the same rate due to gravity on the Moon, which is 1.6 m/s². Therefore, the notion that the hammer accelerates faster than the feather is false; they both experience the same acceleration.
D) Both objects have the same kinetic energy because gravity pulls on both objects equally.
This choice is incorrect as well. Although gravity acts equally on both objects, resulting in the same acceleration, it does not mean they have the same kinetic energy. The hammer's greater mass leads to a higher kinetic energy compared to the feather.
Conclusion
In conclusion, the correct answer is that the hammer has more kinetic energy than the feather because it has a greater mass. While both objects fall with the same velocity, their differing masses directly affect their kinetic energy, making option A the only accurate choice. All other options fail to recognize the crucial role of mass in determining kinetic energy.