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 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,

 

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