Question

Bone has a Young's modulus of about

Answer 1

Answer: 4.74 mm

Explanation:

We can solve this problem with the following equation:

$Y=\frac{stress}{strain}$ (1)

Where:

$Y=1.8(10)^{10} Pa$ is the Young modulus for femur

$stress=\frac{F}{A}=1.58(10)^{8} Pa$ is the stress (force $F$ applied per unit of transversal area $A$) on the femur

$strain=\frac{\Delta l}{l_{o}}$

Being:

$\Delta l$ the compression the femur can withstand before breaking

$l_{o}=0.54 m$ is the length of the femur without compression

Writing the data in equation (1):

$Y=\frac{\frac{F}{A}}{\frac{\Delta l}{l_{o}}}$ (2)

$1.8(10)^{10} Pa=\frac{1.58(10)^{8} Pa}{\frac{\Delta l}{0.54 m}}$ (3)

Isolating $\Delta l$:

$\Delta l=\frac{(1.58(10)^{8} Pa)(0.54 m)}{1.8(10)^{10} Pa}$ (4)

$\Delta l=0.00474 m$ (5) This is the compression in meters

Converting this result to millimeters:

$\Delta l=0.00474 m \frac{1000 mm}{1 m}=4.74 mm$