Question

Which of the following would have MORE gravitational potential energy? Explain why.

1. a mic dropped from 5 meters above the surface of Earth OR a mic dropped from S meters above the surface of Jupiter

2. Someone jumping out of a plane at 5000 m OR someone jumping out at 8000 m?

Answer 1

Answer:

1. A microphone dropped 5 meters above the surface of Jupiter

2. Someone jumping out of a plane at 8000 meters

Explanation:

*Note: As clarified by the person who asked the question, the "S" in problem 1 is meant to be a 5.

The potential energy of an object is given by $PE=mgh$, where $m$ is the mass of the object, $g$ is acceleration due to gravity, and $h$ is the height of the object.

In problem 1, it is given that the height is the same for both objects and implied that the mass is the same for both objects. However, acceleration due to gravity is about 2.54 times greater on Jupiter than on Earth. Therefore, a microphone dropped 5 meters above the surface of Jupiter will have more potential energy than the same microphone  dropped 5 meters above the surface of Earth.

Similarly, in problem 2, mass and acceleration due to gravity are maintained. The only difference is the height the person is jumping out of. Since potential energy is directly proportional to height, the larger the height, the more potential energy. Thus, someone jumping out of a plane at 8000 meters will have more potential energy than someone of the same mass jumping out of a plane on the same planet at 5000 meters.