Question

state hooks law and derive expression for energy stored in stretched wire

Answer 1

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)
Hope it will help you