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.

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-

Now, the work done in stretching the wire further through a distance dℓ is given by-

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-

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