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.
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.
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.