Question

A compressive force of 2.7×104N is exerted on the end of a 23-cm-long bone of cross-sectional area 3.8 cm2 . The elastic modulus for bone is 1.5×1010N/m2, and the compessive strength for bone is 1.7×108N/m2.

Answer 1

Question

By how much does it shorten?

Answer:

1.089 mm

Explanation:

Compression stress, $\sigma$ is given by

$\sigma=\frac {F}{A}$ where F is force and A is area

Strain is given by

$\epsilon=\frac {\triangle l}{L}$ where L is original length and \triangle l is change in length

Young's modulus, $E=\frac {\sigma}{\epsilon}$ hence

$\triangle l=\frac {FL}{AE}$

$\triangle l= \frac {2.7*10^{4}*0.23}{3.8*10^{-4}*1.5*10^{10}}$

$\triangle l=0.001089474 m\approx 1.089 mm$