Question

A uniform steel rod of $5{mm}^2$ cross section is heated from $0^{\circ }C$ to ${25}^{\circ }C$. Calculate the force which must be exerted to prevent it from expanding. Also calculate strain.
($\alpha$ for steel $=12\times {10}^{-6}/{}^{\circ }C$ and $\gamma$ for steel $=20\times {10}^{10}N/m^2$)

Answer 1

$F={\gamma }_{steel}\times {\alpha }_{steel}\times \Delta T\times A$

$=20\times {10}^{10}\times 12\times {10}^{-6}\times 25\times 5\times {10}^{-6}$

$=30000\times {10}^{10}\times {10}^{-12}$

$=300N$

Strain $={\alpha }_{steel}\times \Delta T$

$=12\times {10}^{-6}\times 25$

$=300\times {10}^{-6}$

$=3\times {10}^{-4}$.