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

Step-by-step 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`