Question

A uniform steel wire of length $3m$ and are of cross section $2m{m}^2$ is extended through $3mm$ Calculate the energy stored in the wire, if the elastic limit is not exceeded

Answer 1

Given, initial length of the wire $L_0=3m$

Change in length of the wire$\Delta L=3mm=3\times {10}^{-3}m$

youngs modulus $Y_{steel}=20\times {10}^{10}N/m$

$w=\frac{1}{2}P\times \Delta LY=\frac{PL}{A\Delta L}=>P=\frac{YA\Delta L}{L}$

$W=\frac{1}{2}P\Delta L=\left(\frac{YA\Delta L}{2L}\right)\Delta L$

$\frac{20\times {10}^{10}\times 2\times {10}^{1-6}\times 9\times {10}^{-6}}{2\times 3}=60\times {10}^{-2}=0.6J$