A 91 -kg man's thighbone has a relaxed length of 0.50 m, a cross-sectional area of 7.0 ×10^-4 m^

step 1 For this question we are told that a man has a mass of 91 kilograms and a typhon with a length o

A 91 -kg man's thighbone has a relaxed length of 0.50 m, a...

A 91 -kg man's thighbone has a relaxed length of $0.50 \mathrm{m},$ a cross-sectional area of $7.0 \times 10^{-4} \mathrm{m}^{2},$ and a Young's modulus of $1.1 \times 10^{10} \mathrm{N} / \mathrm{m}^{2} .$ By how much does the thighbone compress when the man is standing on both feet?

Key Concepts

Young's Modulus

Young's modulus is a material property that measures its stiffness, defined as the ratio of stress (force per unit area) to strain (relative deformation) in the elastic region. It is crucial for determining how much a material will deform under a given load.

Hooke's Law for Axial Deformation

Hooke's law for axial deformation states that, within the elastic limit, the change in length of a material (compression or elongation) is directly proportional to the applied force. The relationship is often expressed as ?L = (F * L) / (A * E), where ?L is the change in length, F is the applied force, L is the original length, A is the cross-sectional area, and E is Young's modulus.

Stress and Strain

Stress is the intensity of internal forces acting within a material per unit area, while strain is the measure of deformation representing the relative change in length. The proportionality between stress and strain in the elastic region is governed by Young's modulus, ensuring that deformation can be predicted based on applied force.

Load Distribution

Load distribution is the concept of how an applied force, such as the weight of a person, is shared among multiple supports. When standing on two feet, the total weight is typically divided equally between them. This principle helps determine how much force is applied to each leg or bone, which is essential when calculating the deformation of a structure under load.

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