# Potential energy

Potential energy is a form of stored energy. For example, when a rock is brought up a hill and is left on the hill, the rock gains gravitational potential energy. When we stretch a rubber band, we say that the rubber band has gained elastic potential energy. Food that we eat has chemical potential energy. Batteries also have chemical potential energy.

Potential energy is divided into three different types of energy.

## Gravitational Potential Energy

Gravitational potential energy is experienced by an object when height and mass is a factor in the system. Gravitational potential energy causes objects to move towards each other. If an object is lifted a certain distance from the surface from the Earth, the force experienced is caused by weight and height. Work is defined as force over a distance, and work is another word for energy. This means Gl Potential Energy is equal to:

$U = F \Delta h$
where
$F$ is the force of gravity
$\Delta h$ is the change in height

or

$U = mgh$

Total work done by Gravitational Potential Energy in a moving object from position 1 to position 2 can be found by:

$\Delta W = U_1-U_2$

or

$\Delta W = mgh_1-mgh_2$
where
$m$ is the mass of the object
$g$ is the acceleration caused by gravity (constant)
$h_1$ is the first position
$h_2$ is the second position

The Gravitational Potential Energy formula used here is only used when the objects are very near the surface of the Earth, because the acceleration must be the same during the change in height.

## Electric Potential Energy

Electric Potential Energy is experienced by charges both different and alike, as they repel or attract each other. Charges can either be positive (+) or negative (-), where opposite charges attract and similar charges repel. If two charges were placed a certain distance away from each other, the potential energy stored between the charges can be calculated by:

$U = \frac{kQq}{r}$
where
$k$ is 1/4πє (for air or vacuum it is $9 x 10^9 N m^2/C^2$)
$Q$ is the first charge
$q$ is the second charge
$r$ is the distance apart

## Elastic Potential Energy

Elastic Potential Energy is experienced when a rubbery material is pulled away or pushed together. The amount of potential energy the material has depends on the distance pulled or pushed. The longer the distance pushed, the greater the Elastic Potential Energy the material has. If a material is pulled or pushed, the potential energy can be calculated by:

$U = \frac{1}{2}kx^2$
where
$k$ is the spring force constant (how well the material stretches or compresses)
$x$ is the distance the material moved from its original position

## Sources

Duncan, Tom. Advanced Physics for Hong Kong: Volume 1 Mechanics & Electricity. John Murray Ltd, 1995. Wai, Loo Kwok. Longman A-Level Course in Physics: Volume 1. Pearson Education South Asia Pte Ltd, 2003.