Write down the expression for the elastic potential energy of a stretched wire .

Explanation

Consider a wire whose un-stretch length is L and area of cross section is A. Let a force produce an extension l.
The work done by the force F is equal to the energy gained by the wire.
The work done in stretching the wire by d/,dW = F d/ the total work done in stretching the wire from 0 to l is
W ` int_(0)^(1) Fdl`
From Young 's mdulus of elasticity
` Y = F/A xx L/l Rightarrow F = ( YAI)/L`
substituting equation (2) in equation (1), we get
` W = int_(0)^(1) ( YAl)/L dl = (YAl^(2))/(L.2) = 1/2 . Fl`
` W = int_(0)^(1) ( YAl)/l ( dl) = ( YA)/L ((l^(2))/2)| = (YA)/L l^(2)/2 = 1/2 ( (YAl)/L) l = 1/2 = Fl`
` W = 1/2 F1 ` = Elastic potential energy .