Question

One of the greatest olympic weightlifters of all times- Soviet athlete Vasily Alekseyev- was once able to life 256 kg above his head in the upright (fully standing) position. Assume that this entire weight was supported equally by both femora. Compute the amount of compression (meaning change in length) of the athletes femora due to the lifted weight, assuming a Young’s modulus for the femur of 1.8 x 10^10 Pa, a femoral length of 50cm, and a femoral diameter of 3.0 cm. Ignore the weight of the athlete himself in this calculation. Assume the femur is cylindrical in shape. Hint: remember that there are two femora.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass lifted by the athlete = m = 256 kg

There are two femora therefore the load will be distributed in both of them.

Load on each femora = W

W = mg/2

W = (256)(9.81)/2

W = 1255.68 N

Young's modulus for the femur = E = 1.8 x 10¹⁰ Pa

Femoral length = L = 50 cm = 0.5 m

Femoral diameter = D = 3 cm = 0.03 m

Cross-sectional area of the femur = A

A = D²/4

A = (0.03)²/4

A = 7.07 x 10^-4 m²

Change in length of the femora = L

Stress in the femora = = F/A

Strain in the femora = = L/L

L = 4.93 x 10^-5 m

Amount the athlete's femora compresses due to the lifted weight = 4.93 x 10^-5 m