Question

Assume Young's modulus for bone is 1.5 x 10¹⁰N/m². The bone breaks if stress greater than 1.5 x 10⁸ N/m² is imposed on it. 1) What is the maximum force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.5 cm? 2) If this much force is applied compressively, by how much does the 25 cm long bone shorten?

Answer 1

Pressure(P)=$\frac{F}{A}$

$F=P\times A$

Area

$A={\pi }\times{\frac{2.5^2\times10^{-4}}{4}}$

$$F=1.5\times10^{8}\times\pi \times\frac{2.5^2\times10^{-4}}{4}=7.35\times10^4N$$

We know that

$Y=\frac{P}{\frac{∆L}{L}}$

$∆L=\frac{P\times L}{Y}$

Put value

$$∆L=\frac{1.5\times10^{8}\times 0.25}{1.5\times10^{10}}=0.0025m=2.5mm$$