Question

The femur is a bone in the leg whose minimum cross-sectional area is about 3.70 10-4 m2. A compressional force in excess of 6.60 104 N will fracture this bone. (a) Find the maximum stress that this bone can withstand. (b) What is the strain that exists under a maximum-stress condition

Answer 1

Answer:

178378378.37 Pa

0.01897

Explanation:

F = Force = $6.6\times 10^4\ N$

A = Area = $3.7\times 10^{-4}\ m^2$

Y = Young's modulus of bone under compression = $9.4\times 10^{9}\ Pa$

$\varepsilon$ = Strain

Stress is given by

$\sigma=\frac{F}{A}\\\Rightarrow \sigma=\frac{6.6\times 10^4}{3.7\times 10^{-4}}\\\Rightarrow \sigma=178378378.37\ Pa$

The maximum stress that this bone can withstand is 178378378.37 Pa

Compression force is given by

$F=Y\varepsilon A\\\Rightarrow \varepsilon=\frac{F}{YA}\\\Rightarrow \varepsilon=\frac{6.6\times 10^4}{9.4\times 10^{9}\times 3.7\times 10^{-4}} \\\Rightarrow \varepsilon=0.01897$

The strain that exists under a maximum-stress condition is 0.01897