# Derivation of Potential Energy

The derivation of potential energy is provided here. Potential energy is defined as the energy that is held by an object because of its position with respect to other objects. The SI unit of potential energy is joule whose symbol is J. Potential energy term was introduced by Scottish engineer and physicist William Rankine in the 19th century.

The gravitational potential energy of an object, elastic potential energy of an extended spring, and electric potential energy of an electric charge are the most common type of potential energies observed.

## Potential Energy Derivation

Potential energy is the work done to take a body to a certain height. For a body with mass m, h is the distance to which it is raised and g is the gravitational force acting on the body, then work done W is given as:

W = force * displacement

W = mg * h

∴ W = mgh

As the work done is equal to mgh which is gained by the object, potential energy Ep is given as:

Ep = mgh

Therefore, the above is the derivation of potential energy.

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