**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 **ℓ**.

**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,**

**Read the next article on-**

**Breaking Stress | Elongation due to Self Weight**

**Get more notes & other study material of the Chapter** **Mechanical Properties of Solids**.