Question

How much load is needed to elongate a steel wire to 0.5 %of its original length ? The diameter of the wire is 2mm and youngest modulus of the material of the wire is 20×10^10 N/m^2

Answer 1

Given:

$\varepsilon=0.005$

$r=1\:\rm mm=10^{-3}\:\rm m$

$E=20*10^{10}\:\rm N/m^2$

The Hooke's law says

$$\sigma=\frac{F}{A}=\varepsilon E$$

Hence, the load

$$F=\varepsilon AE=\pi\varepsilon r^2E$$

$$F=3.14*0.005*(10^{-3})^2*20*10^{10}=\rm 3140\: N$$