Question

The elastic limit of steel is $8\times {10}^{8}N{m}^{-2}$ and its Young modulus $2\times {10}^{11}N{m}^{-2}$. Find the maximum elongation of a half-metre steel wire that can be given without exceeding the elastic limit.

Answer 1

Elastic limit of steel $=\frac{F}{A}=8\times {10}^{5}N/m^2$

Young's modulus of steel of $Y=2\times {10}^{11}N/m^2$

length of steel wire $L=\frac{1}{2}m=0.5m$

$Y=\frac{F}{A}\frac{L}{\Delta L}$

$\Rightarrow \Delta L=\frac{FL}{AY}$

$=\frac{8\times {10}^5\times \left(0.5\right)}{2\times {10}^{11}}$

$=2\times {10}^{-3}m$

$\Delta L=2mm$