Question

what is the maximum force a hammer can apply to a steel nail 2.5 mm in diameter of the nails elastic limit is not to be exceeded

Answer 1

Yield strength of mild steel is given as

$Y = 250 MPa$

here we know that

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

$250 * 10^6 = \frac{F}{\pi r^2}$

now we can rearrange it as

$F = \pi r^2 * 250* 10^6$

here we know that

$r = 1.25 mm = 1.25 * 10^{-3} m$

$F = \pi*(1.25*10^{-3})^2* 250* 10^6$

$F = 1.23 * 10^3 N$

so maximum applied force will be F = 1.23 * 10^3 N