# How far up an object is its gravitational potential energy taken from? [closed]

This is quite a brief question but,

Is the $h$ value in $mgh$ taken from an object's base, middle of top. For example, if a person was $1.5m$ in height and they were standing on a hill of height $10m$, what is their GPE expression?

1. mg(10)
2. mg(10.75) or
3. mg(11.5)

## Visualization

The difference in height $h$ is always the same (here 10 m)!

## Remark

This is of course only true if $g$ is constant, e. g. $h$ does not change "much". See also Wikipedia.

• It is also only true if the body can be considered rigid and in the same orientation before and after, or symmetric enough that you don't care. Otherwise, you split up the body into lots of small bits, compute the change in height of each bit, and add them up. Aug 31 '15 at 2:27

Potential energy is given only as a difference of energies at different heights. So, if you want to know just how much does the person gain energy (or rather loose by friction in their muscles and joints) by walking down the hill, you might just use their height of their heels on the top of the hill and under the hill.

But remember, you always have to use the same reference point! You can verify yourself that when using either of the options 1.,2. or 3. you state, you will get the same difference in potential energy if you check that same reference point after walking downhill.

But this works only if the body stays upright the whole time. If the person were to lay on the ground, it gets more complicated. In fact, you should compute the potential energy of every part of the body, and check how does the potential energy change after the action. For example, if the person is simply standing at one point and bends over, their head, hands and chest obtains kinetic energy (again, almost immediately absorbed by friction).

For a rigid body without all these flexible parts such as hands and bending backs you can separate the motion into the motion of the center of mass and some kind of rotation about it. Hence, depending on the kind of problem you are solving, it might be also useful to place your reference into the center of mass and somehow approximate the very gooey and flexible person as a rigid body.