# Elastic Potential Energy In Stretched Wire

## Elastic Potential Energy In A Stretched Wire-

 Elastic Potential Energy stored in a stretched wire is defined as the amount of work done by an external force to stretch the wire.

Consider-

• A wire of length L and area of cross-section A is suspended freely from a rigid support.
• Let a force F be applied to stretch the wire.
• Let ℓ be the length through which the wire is stretched.
• Let ΔL be the total elongation through which the wire is stretched.

Let us consider an intermediary stage where the wire is stretched by the amount .

The tensile stress on the wire is given by-

The longitudinal strain produced in the wire is given by-

Now, the Young’s Modulus of Elasticity of the material of wire is given by-

The work done in stretching the wire further through a small distance dℓ is given by-

Now, the total work done in stretching the wire through ΔL can be calculated by integrating dW between the limits ℓ = 0 to ℓ = ΔL as-

This work is stored in the form of elastic potential energy of the stretched wire.

Thus, elastic potential energy of the stretched wire is given by-

### Elastic Energy Density-

 The elastic potential energy stored in the stretched wire per unit volume of the wire is called as elastic energy density.

It is calculated as-

Thus,