Question

derive an expression for energy store in a wire due to extension

Answer 1

Let me help you here:

Hooke's Law, F = -kx, where F is the force and x is the elongation.

The work done = energy stored in stretched string = F.dx

The energy stored can be found from integrating by substituting for force,

and we find,

The energy stored = kx2/2, where x is the final elongation.

The energy density = energy/volume

= (kx2/2)/(AL)

=1/2(kx/A)(x/L) = 1/2(F/A)(x/L) = 1/2(stress)(strain)

Answer 2

Hope it helps for the given question