Bone has a Young's modulus of about 1.8×10^10 Pa. Under compression, it can withstand a stress of about 1.5x10^8 Pa before breaking.

Question

Assume that a femur (thigh bone) is 0.56 m Jong, and calculate the amount of compression this bone can withstand before breaking.
Answer in units of mm.

Answer 1

To calculate the amount of compression the bone can withstand before breaking, we can use the formula for stress:

Stress = Force/Area

Given that the bone can withstand a stress of 1.5x10^8 Pa before breaking, and the bone has a Young's modulus of 1.8x10^10 Pa, we can calculate the force (F) needed to reach this stress:

1.5x10^8 Pa = F/Area
F = 1.5x10^8 Pa * (pi*(d/2)^2)

Now we can relate this force to the compression of the bone before breaking. This can be calculated using Hooke's Law:

F = k * x
1.5x10^8 Pa * (pi*(d/2)^2) = 1.8x10^10 Pa * x

Solving for x:

x = (1.5x10^8 Pa * (pi*(d/2)^2)) / 1.8x10^10 Pa
x = 3.96x10^-4 m

Converting this to millimeters:

x = 3.96x10^-4 m * 1000 mm/m
x = 0.396 mm

Therefore, the femur bone can withstand a compression of 0.396 mm before breaking.