First slide

Stress and strain

Question

A steel wire can support a maximum load of W before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?

Moderate

A

W
B

$\frac{W}{2}$
C

$\frac{W}{4}$
D

4W

Solution

Breaking force = Breaking stress $\times$ Area of cross section
For a given material of the wire, breaking stress is constant.
$\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}$
$F_{2} = F_{1} (\frac{A_{2}}{A_{1}}) = F_{1} (\frac{\frac{A_{1}}{4}}{A_{1}}) = \frac{F_{1}}{4} = \frac{W}{4}$

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