Angular kinetics

Question

Suppose a person’s femoral diaphysis is idealized as a solid circular cylinder with a diameter of 2 cm. The ultimate stress in tension is 120×106 pa. Calculate the maximal tension force the femoral diaphysis can sustain.

Answer 1

The relation between Force (F), Cross-sectional Area (A), and Pressure (P) is P = F / A, or F = PA. In this problem, the force is the maximal tension force, pressure is the stress (120 x 10⁶ Pa), and area is the cross sectional area of the cylinder. The area is just the area of the circle, A = πr², where r is the radius. The problem tells us the diameter is 2 cm, so the radius half of that, so 1 cm or 0.01 m. So, A = π(0.01 m)² = 3.14 x 10^-4 m². Now that we have A and P, we can solve for F:

F = (120 x 10⁶ Pa)(3.14 x 10^-4 m²) = 3.77 x 10⁴ N