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

Apr 14, 2018

$73.5 J$

#### Explanation:

Take $g = 9.81 m {s}^{-} 2$ for the purpose of this question.

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

Since the mass $m = 12$, and "height" $h = \frac{5}{8}$:

${E}_{g} = 12 \times 9.81 \times \frac{5}{8}$

${E}_{g} = \frac{2943}{40}$
${E}_{g} = 73.5 J$ (3 sig fig).

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

Derivation of the formula - a little bonus

$\text{Work done} = F \times s$

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

$W = m g$

Say the object is lifted a distance $h \text{m}$. Then our formula for work becomes:

$\text{Work done} = m g h$

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

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