Question

When subjected to a force of compression, the length of a bone (compression Young's modulus 9.4 x 109 N/m2, tensile Young's modulus 1.6 x 1010 N/m2) decreases by 3.7 x 10-5 m. When this same bone is subjected to a tensile force of the same magnitude, by how much does it stretch?

Answer 1

To solve this problem it is necessary to apply the definition of Young's Module which states that

$Y_1 = \frac{\frac{F}{A}}{\frac{\Delta l_0}{l}}$

Where,

F = Force

A = Cross sectional Area

L = Length

$L_0$ = Initial Length

We need to find the ratio between the two values when the another values are constant, that is

$\frac{Y_1}{Y_2} = \frac{\frac{\frac{F}{A}}{\frac{\Delta l_1}{l}}}{\frac{\frac{F}{A}}{\frac{\Delta l_2}{l}}}$

$\frac{Y_1}{Y_2} = \frac{\Delta l_2}{\Delta l_1}$

Re-arrange to find $\Delta l_2,$

$\Delta l_2 = \frac{9.4*10^9}{1.6*10^{10}}*3.7*10^{-5}$

$\Delta l_2 = 2.17*10^{-5} m$

Therefore the bone stretch around $2.17*10^{-5} m$