Question

When a block of mass M is suspended by a long wire of length L, the elastic potential energy stored in the wire is ½*stress*strain*volume. Show that it is equal to ½Mgl, where l is the extension. The loss in gravitational potential energy of the mass earth system is Mgl. Where does the remaining ½Mgl energy go?

Answer 1

Stress = Force/Area, {Where A is the cross-sectional area of the wire}  

∴ Strain = l/L.

Since the elastic potential energy ,

  U = 1/2 × Stress × Strain × Volume

⇒ U = 1/2 × Mg/A × l/L × AL

U = 1/2 × Mgl

The loss in the Gravitational Potential energy is Mgl. Half Potential energy has been converted into the kinetic energy of the System.

Therefore, mgl - 1/2mgl = 1/2 mgl

This remaining half mgl has been converted into Kinetic energy.

Hope it helps.