Question

Calculate the strain energy per unit volume in a brass wire of length $3m$ and area of cross-section $0.6m{m}^2$ when it is stretched by $3mm$ and a force of $6kgwt$ is applied to its free end.

Answer 1

$L=3m$ $A=0.6m{m}^2=6\times {10}^{-7}{m}^2$ $l=3\times {10}^{-3}m$ $F=6\times 9.8N$

Strain energy$=\frac{1}{2}\times load\times extension$

Strain energy per unit volume $=\frac{energy}{volume}$

$=\frac{F\times l}{L\times A}=\frac{6\times 9.8\times 3\times {10}^{-3}}{3\times 6\times {10}^{-7}}=9.8\times {10}^4=98000$ $Joule/m^3$