!!!Stress Question help?!!!!?

Question

Compressive strength of our bones is important in everyday life. Young's modulus for bone is about 1.4 x 10^10 Pa. Bone can take only about a 1% change in its length before fracturing.

a) What is the maximum force that can be applied to a bone whose minimum cross-sectional area is 3 cm^2? (This is approximately the cross-sectional area of a tibia, or shin bone, at its narrowest point.)

b) Estimate the maximum height from which a 70 kg man could jump and not fracture the tibia. Take the time between when he first touches the floor and when he has stopped to be 0.03 s, and assume that the stress is distributed equally between his legs.

Thanks for the help!!!

Answer 1

a) F = P*A = E*ε*A = 1.4E10*(.01)*3E-4 = 42000 N

b) mV = Ft → V = (2*42000)*.03/70 = 36 m/s.... h = V²/(2g) = 36²/(2*9.8) = 66.12 m

Answer 2

Young's modulus gives stress/strain.

Given the maximum strain (1% before fracturing), we can compute the maximum stress.

Stress is in units of force/area. We have the area so we can compute the maximum force.

Fort part b, Force = Mass x Acceleration. We have the force (twice that of one leg) and the mass, so we can compute the acceleration.

When the man jumps, his final velocity should be 0, the acceleration and the total time is know, so we can use the equation for constant acceleration to compute the maximum initial velocity:

Vf = Vi + A T

If the man jumps from height H with intial velocity 0 and ends with initial velocity Vi from the above, then we can use the same equation (with A the acceleration due to gravity) to get the time for the jump Tj

Then we can use the distance equation for constant acceleration to compute H:

H = Vs Tj + (1/2) A Tj^2

where Vs is 0 in this case.