Question

A human bone is subjected to a compressive force of $5.0\times {10}^{5}N$. The bone is $25cm$ long and has an approximate cross sectional area of $4.0{cm}^2$. If the ultimate compressive strength of the bone is $1.70\times {10}^{8}N/m^2$, will the bone be compressed or will it break under this force?

Answer 1

$F=5\times {10}^{5}N$

$A=4\times {10}^{-4}{m}^2$

$l=\frac{l}{4}m$

$S_{max}$(bone) $=1.7\times {10}^{8}N/m^2$

$S_{Force}=\frac{5\times {10}^5}{4\times {10}^{-4}}=\frac{5}{4}\times {10}^9$

$=\frac{50}{4}\times {10}^{8}N/m$

$=12.5\times {10}^{8}N/m$

$S_{Force}>S_{max}$(bone)

Therefore bone will break.