Question

Question #8d062

Answer 1

I tried this using the definition `U=mgh`:

Explanation:

Potential Energy, in these cases Gravitational Potential Energy `U`, is a measure of the "possibility" of a system to do work or of the stored energy available for a system to do something.

You need two key ingredients to quantify this potential energy:
1) Mass `m`: this is quite important because you store energy by working "against" gravity that depends (I mean, the weight) on mass and acceleration of gravity. So basically you use energy (muscular or chemical, for example) to oppose gravity and in doing so you transfer energy to your system that now acquires this energy "potentially" ready to do something else;

2) Position or height `h` (relative to a reference point): this also is quite important because in our idea to "oppose" gravity we need to change position in order to store energy into the system (this movement is only vertical because the horizontal component doesn't matter as gravitational force is conservative). The change in height will signal an increase in energy (Potential) into the system.

So resuming we have that to store potential energy we need to oppose gravity, represents by weight or `mg` and change height to get to a height `h`; so:
Potential Energy (Gravitational): `U=mgh`

In your four questions you need the highest position or the more massive system to give you a higher value of `U`:

Answer 2

Potential Energy of a body having mass `m`, situated at a height `h` above the surface of earth; due to gravity is given by the expression

`PE=mgh`
where `g` is acceleration due to gravity.

Explanation:

In the given problem it is assumed that `g` for the two items being compared is constant.

a) A 25 kg mass OR a 30 kg mass at the top of the hill.
For both locations, `g and h` are same. Only change is the difference in masses. Using above equation we see that higher mass will have higher potential energy.

b) A car at the top of the hill OR the bottom of the hill.
Assuming the masses of both the cars are same. Therefore, in both cases, `g and m` are same. Only change is the difference in height. Using above equation we see that car located at the top of hill will have higher potential energy.

c) A plane on the ground OR a plane in the air.
Assuming the masses of both the planes are same. Therefore, in both cases, `g and m` are same. Only change is the difference in altitude. Using above equation we see that plane in the air will have higher potential energy.

d) A full plane OR an empty plane (both are flying).
Assuming that both the planes are flying at the same height. Therefore, in both cases, `g and h` are same. Only change is the difference in masses. Using above equation we see that full plane will have higher potential energy.