Question

A load of 10 kg is suspended by a metal wire 3 m long and hvaing a cross- sectional area $4m{m}^2$. Find (a) the stress (b) the strain and (c) the elongation. Young modulus of the metal is 2.0 $\times {10}^{11}N{m}^{-2}$.

Answer 1

m = 0 kg

L = 3 m

A = 4 $m{m}^2$ = 4 $\times {10}^{-6}{m}^2$

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

(a) F = mg

Stress = $\frac{F}{A}=\frac{10\times 10}{4\times {10}^{-6}}$

= $2.5\times {10}^{7}N/m^2$

(b) Strain = $\frac{\Delta L}{L}$

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

$\Rightarrow \frac{\Delta L}{L}=\frac{F}{YA}$

= $\frac{10\times 10}{2\times {10}^{11}\times 4\times {10}^{-6}}$

$=1.25\times {10}^{-3}N/m^2$

(c) $\Delta L=\left(\frac{F}{YA}\right)L$

$\Rightarrow 1.25\times {10}^{-4}\times 3=3.75\times {10}^{4}m$