# A hat weighing 5"N" is placed on a hook 1.5"m" above the ground. What is the potential energy of the hat?

Dec 23, 2016

${U}_{g} = 7.5 J$

#### Explanation:

Gravitational potential energy is given as

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

where $m$ is the mass of the object, $h$ is the object's height above the ground (surface of the earth), and $g$ is the free-fall acceleration constant, $9.8 \frac{m}{s} ^ 2$.

We're given the weight of the hat, however, not the mass. The weight of a stationary object is given as the force of gravity acting upon it, which is the product of its mass and $g$.

$W = {\vec{F}}_{g} = m g$

So, $m g = 5 N$ and $h = 1.5 m$

$\implies {U}_{g} = \left(5 N\right) \left(1.5 m\right) = 7.5 N m = 7.5 J$