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 unit = $8\times {10}^{5}N/m^2$

Y = $2\times {10}^{11}N/m^2$

L = $\frac{1}{2}m=0.5m$

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

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

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

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