Question

Consider a human femur of length l = 448 mm. model the bone as a hollow cylinder, with inner radius ra = 4.87 mm and outer radius rb = 14.61 mm. if a 65 kg person's weight is supported by one leg, calculate the stress on the femur; express your answer as a percentage of the ucs, where the ucs of a bone under compression is 162 mpa. ignore the weight of the leg and round your answer to the second decimal place.

Hint: to express as a percentage of the ucs multiply the stress by 100/ucs.

Answer 1

To calculate the stress on a femur as a hollow cylinder supporting a 65 kg weight, we first calculate the force of weight, determine the cross-sectional area, calculate stress, and then express it as a percentage of UCS.

Step-by-step explanation:

The question asks to calculate the stress on a human femur modeled as a hollow cylinder when a 65 kg person's weight is supported by one leg, and then express that stress as a percentage of the ultimate compressive strength (UCS).

First, we calculate the force exerted by the person's weight (W = m * g), where m is the mass (65 kg) and g is the acceleration due to gravity (9.81 m/s2). Then we find the cross-sectional area (A) of the hollow cylinder using the formula A = π * (rb2 - ra2), where ra is the inner radius and rb is the outer radius. Stress (σ) is calculated using the formula σ = F / A. Finally, to find the percentage, we use the given UCS value (162 MPa) and the formula (Stress * 100) / UCS. Remember to convert all units to be consistent.