Question

Bone has a Young’s modulus of about 1.8 × 1010 Pa . Under compression, it can withstand a stress of about 1.62 × 108 Pa before breaking. Assume that a femur (thigh bone) is 0.45 m long, and calculate the amount of compression this bone can withstand before breaking. Answer in units of mm.

Answer 1

Answer:

Explanation:

Given

Young's modulus $E=1.8\times 10^{10}\ Pa$

It can withstand a stress of $\sigma =1.62\times 10^8\ Pa$

Length of bone $L=0.45\ m$

We know

young's modulus$(E)=\frac{stress}{strain}$

$strain(\epsilon )=\frac{stress}{E}$

$\epsilon =\frac{1.62\times 10^8}{1.8\times 10^{10}}$

$\epsilon =0.009$

and $strain=\frac{change\ in\ length}{Total\ length}$

$0.009=\frac{\Delta L}{0.45}$

$\Delta L=4.05\times 10^{-3}\ m$

$\Delta L=4.05\ mm$

so bone suffers a compression of 4.05 mm