Question

Derive an expression for elastic potential energy of a stretched metallic wire? Also find the elastic energy density stored inside the wire?​

Answer 1

EXPLANATION:

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

Hence, the work done = energy stored in stretched string = F.dx

Thus, the energy that has been stored can be found from integrating by substituting for force,

and we get,

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)

Thus, the given expression is the formula for finding out the elastic potential energy of a stretched metallic wire.