# Physics with Calculus/Mechanics/Energy and Conservation of Energy/Potential energy

Potential energy is the energy stored in an object due to its position. There are several types of potential energy.

## GravitationalEdit

Gravitational potential energy, involves the line integral of the force between two objects ( and ). By Newton's universal law of gravity, the force is

We integrate to get potential energy:

Here, we have taken the reference point (where the potential energy equals zero) to be at . Sometimes, when dealing with small distances where the difference in acceleration due to gravity will be negligeable we simplify the energy equation by assuming that , where is the Earth's radius and is the height above the Earth's surface. Taking to be the mass of the planet:

.

Note that the vector points in the direction. Inserting this into the integral for :

,

where now, the reference point is on the surface of the Earth.

## ElasticEdit

Elastic potential energy is the energy stored in a compressed or elongated object (a spring, for example). The amount of energy stored in the object depends on spring constant ( ) and the displacement from the rest position ( ). It should be noted that the amount of energy is the same regardless whether the object is compressed or elongated. Given the force:

We integrate to get energy: