Question

A steel wire of diameter $1\times {10}^{-3}m$ is stretched by a force of $20N$. Calculate the strain energy per unit volume. ($Y$ steel $=2\times {10}^{11}N/m^2$)

Answer 1

Given $d=1\times {10}^{-3}m$, $F=20N$

$Y=2\times {10}^{11}N/m^2$, $r=\frac{d}{2}=0.5\times {10}^{-3}m=5\times {10}^{-4}m$

$\therefore$ Cross sectional area $A=\pi r^2=3.142\times 25\times {10}^{-8}{m}^2$

Strain energy per unit volume of the wire $=\frac{1}{2Y}{\left(stress\right)}^2$

$=\frac{{\left(F/A\right)}^2}{2Y}$

$=\frac{F^2}{2A^{2}Y}$

$=\frac{{\left(20\right)}^2}{2\times {(3.142\times 25\times {10}^{-8})}^2\times 2\times {10}^{11}}$

$=1622J/m^3$.