Question

What is the gravitational potential energy of a `12 kg` object on a shelf `5/8 m` high?

Answer 1

`73.5J`

Explanation:

Take `g=9.81 ms^-2` for the purpose of this question.

`E_g=mgh`

Since the mass `m=12`, and "height" `h=5/8`:

`E_g=12xx9.81xx5/8`

`E_g=2943/40`
`E_g=73.5J` (3 sig fig).

Since this is energy, the unit is joules (J)

Derivation of the formula - a little bonus

We can think about this formula as the work done lifting an object.

`"Work done"=Fxxs`

When work is done lifting an object against its weight, the force work is done to is its weight.

`W=mg`

Say the object is lifted a distance `h"m"`. Then our formula for work becomes:

`"Work done"=mgh`

This is equal to the gain in gravitational energy. Therefore:

`E_g=mgh`