# Gravitational potential energy

Gravitational potential energy ($\displaystyle E_{\text{g}}$) is a type of potential energy due to an object’s position in a system such that gravity can do work on it.

For example, the water behind a dam is just a stationary body of water, but it has the potential to do large amounts of work because it is elevated (and so it has gravitation potential energy). Another example: when you lift a bowling ball off the ground, you are doing work on it (using up your own energy), but in doing so you transfer potential energy to the bowling ball. If you let it fall from a metre above the ground, it will trade its potential energy for kinetic energy, and by the time it reaches the ground it will be moving very fast.

We usually talk about changes in potential energy, not potential energy itself. When does $\displaystyle E_{\text{g}} = 0$? On the surface of the Earth? At the centre of the Earth? You don’t need to worry about it with this formula:

$\displaystyle W = \Delta{} E_{\text{g}} = m g{\Delta{}} h$.

If the height of a 2.5 kg object increases by 15 m, then its potential energy increases by $\displaystyle \left ( 2.5 \, \text{kg} \right ) \left ( 9.80 \, \text{N/kg} \right ) \left ( 15 \, \text{m} \right ) = 367.5 \, \text{J}$. Simple as that.