Answer
The vertical compression of the bone is $2.90\times 10^{-5}~m$
Work Step by Step
$Y = \frac{F/A}{\Delta L/L}$
$Y$ is Young's modulus
$F$ is the force
$A$ is the cross-sectional area
$\Delta L$ is the change in length
$L$ is the original length
When the person is standing on both feet, we can assume that each leg supports half the person's weight. We can find the force exerted on the thigh bone by the body weight:
$F = \frac{1}{2}\times mg$
$F = \frac{1}{2}\times (91~kg)(9.80~m/s^2)$
$F = 445.9~N$
We can find the vertical compression:
$\Delta L = \frac{F~L}{Y~A}$
$\Delta L = \frac{(445.9~N)(0.50~m)}{(1.1\times 10^{10}~N/m^2)(7.0\times 10^{-4}~m^2)}$
$\Delta L = 2.90\times 10^{-5}~m$
The vertical compression of the bone is $2.90\times 10^{-5}~m$.
