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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Breaking Stress | Elongation due to Self Weight

 

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