Question

The femur bone in the human leg has a minimum effective cross section of about 3.0 cm². How much compressive force can it wthstand before breaking? (compressive strength of bone= 170 x 10⁶ N/m)

Answer 1

To calculate the maximum force a femur bone can handle, we multiply its minimum effective cross-sectional area (3.0 cm²) by the compressive strength of bone (170 x 10⁶ N/m²), leading to a maximum compressive force of 51,000 N before breaking.

Step-by-step explanation:

The question involves calculating the compressive force a femur bone can withstand before breaking. To find this, we need to know the compressive strength of bone and the cross-sectional area of the femur. The compressive strength of bone is given as 170 x 106 N/m2 and the minimum effective cross section of the femur bone is 3.0 cm2 which equals 3.0 x 10-4 m2. To calculate the maximum compressive force (Fmax) the femur can withstand, we apply the formula for stress (σ = F/A), where F is the force and A is the area.

The following steps outline the calculation:

1. First, convert the cross-sectional area from cm2 to m2: 3.0 cm2 = 3.0 x 10-4 m2.
2. Then, multiply the compressive strength of bone with the area to find Fmax: Fmax = 170 x 106 N/m2 x 3.0 x 10-4 m2.
3. Fmax = 51000 N, so the femur can withstand a force of 51,000 N before breaking.

This calculation indicates that the femur has a high threshold for withstanding compressive forces, which aligns with the fact that it is one of the strongest bones in the human body.