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What is the allowable stress in section a-a?

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Final answer:

To determine the compression stress in a boy's leg bones after jumping from a height, one should calculate the impact force using the potential energy at height and the stopping time upon landing, then divide this force by the cross-sectional area of the bones.

Step-by-step explanation:

The question is asking to determine whether the compression stress in the leg bones of a boy, who jumps from a height and lands on one foot, is within safe limits to avoid fracture. To find this stress, we use the relationship that stress is the force per unit area.

Stress = Force / Area

Firstly, we'll calculate the impact force using the equation from Newton's laws for constant acceleration. The boy with a mass of 40 kg has potential energy at the start, which converts to kinetic energy: PE = mgh = (40 kg)(9.81 m/s2)(3.0 m). He stops in a time of 0.10 s, so the force can be found as F = (change in momentum) / (time) = (mv - mu) / t, where u is initial velocity (just before impact) and v is zero (at rest).

With the force, we calculate compression stress = F / A, where A is 3 cm2. Finally, we compare this stress to the breaking stress of 1.7 x 108 Pa to see if the stress exceeds it, indicating potential for fracture.

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