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 = (F)/(A)`

`250 * 10^6 = (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