# Potential Energy

The potential energy of a body is defined as the energy possessed by the body by virtue of its position or configuration in some field. So, configuration of the system changes, then its potential energy changes.

Example:- A body lying on the roof of a building has some potential energy, when allowed to fall down, it can do work.

## Gravitational Potential Energy

Gravitational potential energy of a body is the energy possessed by the body by virtue of its position above the surface of the earth.

Let a body of mass m lying on the surface of the earth. Let g be the acceleration due to gravity at this place. For height much smaller than the radius of the earth, the value of g can be taken as constant.

Force needed to lift the body up with zero acceleration,

F = weight of the body = mg

Work done on the body in raising it through height h, Then From Relation

W = F.S

W = mgh [ F = mg and s = h]

This work done against gravity is stored as the gravitational potential energy U of the body.

U = mgh

If h is taken as variable, then the gravitational force F equal to the negative of the derivative of U with respect to h.