Question

Derive an expression for strain energy per
unit volume of the material of a wire.​

Answer 1

Answer:

Young's modulus of elasticity for a material of a wire is constant. i.e. strain energy per unit volume is directly proportional to the square of the stress. Thus the strain energy per unit volume is proportional to Young's modulus of the material of the wire.

mark as brainliest...

Answer 2

The expression for strain energy is 1/2 × stress × strain.

The energy stored in a body is the strain energy, and the per unit volume is strain energy density, when a work is done on it by an external force to stretch or deform the body.

Strain energy = U = 0.5 Fl,  where f is external force applied to produce an extension 'i.

The strain energy density, u = U/V = (0.5 F l)/V

or u = 1/2 F/A l/L where A is the area and L is the length of the body before the external force is applied V = AL)

or u = 1/2 × stress × strain

Thus the energy density of a strained wire or the potential energy per unit volume of a stretched wire is derived.