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

To determine which object has more gravitational potential energy, the height from the reference level and local gravitational acceleration are considered. A mic dropped from the same height on Jupiter will have more potential energy than one dropped on Earth due to Jupiter's higher gravity. Similarly, a person jumping from a higher altitude has more potential energy.

Step-by-step explanation:

Gravitational potential energy depends on three factors: the mass of the object (m), the height above the reference level (h), and the gravitational acceleration (g) at that location. The formula to calculate gravitational potential energy is U = mgh.

1. In comparing the potential energy of a mic dropped from a height above Earth versus a height above Jupiter, assuming the height (h) and the mass of the mic (m) remain constant, the main difference is in the gravitational acceleration (g). Since Jupiter's gravitational acceleration is higher than Earth's, a mic dropped from the same height on Jupiter would have more potential energy due to its stronger gravitational field.

2. For a person jumping out of a plane, gravitational potential energy again depends on the height (h) from which they jump. The greater the height, the more potential energy. Therefore, someone jumping from 8000 m would have more gravitational potential energy than someone jumping from 5000 m, because the value of h in the equation U = mgh is larger.

Answer 2

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

2. Someone jumping out of a plane at 8000 meters

Step-by-step 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.