# What is the gravitational potential energy of a  2 kg object on a shelf  3/2 m  high?

Jan 14, 2016

Gravitational potential energy is given by ${E}_{p} = m g h$ and in this case the gravitational potential is simply $3 \cdot g$ or about $29.4 J$.

#### Explanation:

Gravitational potential energy is energy an object has because of its position in a gravitational field. It is always measured relative to another point in the field: in this case, the height of the shelf compared with the gravitational energy of the same object if it was on the floor. We have defined the floor as 'zero' height for the purposes of this question.

The gravitational potential energy depends on the strength of the local gravitational field, the mass of the object and its height above (or below - in which case the gravitational potential would be negative) our zero level. The formula is:

${E}_{p} = m g h$

(some books use $P E$ for the gravitational potential energy instead)

Where:

${E}_{p}$ = gravitational potential energy
$m$ = mass$\left(k g\right)$
$g$ = gravitational field strength $\left(N k {g}^{-} 1\right)$ (= $9.8 N k {g}^{-} 1$ near earth's surface)
$h$ = height $\left(m\right)$

For this particular case, $m = 2$ and $h = \frac{3}{2}$, so:

${E}_{p} = m g h = 2 \cdot g \cdot \frac{3}{2} = 3 \cdot g = 29.4 J$

A note here: $g$ is usually referred to as 'acceleration due to gravity' and stated in units of $m {s}^{-} 2$, but the units of $N k {g}^{-} 1$ are equivalent, and what we're really talking about in this case is how strong the local gravitational field is. This value would be different if, for example, the shelf and the object were on the surface of the moon.