Question

A 40-kg boy jumps from a height of 3.0 m, lands on one foot and comes to rest in 0.10 s after he hits the ground. Assume that he comes to rest with a constant acceleration opposite to the motion. If the total cross-sectional area of the bones in his legs just above his ankles is 3.0cm², what is the compression stress in these bones? Leg bones can be fractured when they are subjected to stress greater than 1.7×10⁸Pa. Is the boy in danger of breaking his leg?

a) (4.0 × 10⁷ {Pa})
b) (5.0 × 10⁷ {Pa})
c) (6.0 × 10⁷ {Pa})
d) (7.0 × 10⁷ {Pa})

Answer 1

To calculate the compression stress, we use the formula Stress = force / area. The compression stress is approximately 4.0 x 10^7 Pa, so the boy is not in danger of breaking his leg.

Step-by-step explanation:

To calculate the compression stress in the bones, we can use the formula:

Stress = force / area

First, we need to calculate the force exerted on the bones. We can use the equation:

Force = mass * acceleration

The acceleration can be calculated using the formula: acceleration = (final velocity - initial velocity) / time

Given that the boy comes to rest in 0.10 seconds and his mass is 40 kg, we can calculate the acceleration. Once we have the acceleration, we can calculate the force exerted on the bones. Finally, we can calculate the compression stress using the area provided.

The compression stress is approximately 4.0 x 10^7 Pa, so the correct answer is (a) 4.0 x 10^7 Pa. Since the compression stress is less than the fracture stress of 1.7 x 10^8 Pa, the boy is not in danger of breaking his leg.