How will the modulus of elasticity of the human femur change?

The elastic modulus of the human femur will change when the stress increases from 5 Pa to 11 Pa, if the relative deformation is 0.025 and 0.055, respectively.

Solution to problem 10782: From the conditions of the problem, the values ​​of the initial (ε1 = 0.025) and final (ε2 = 0.055) relative deformations of the femur are known, as well as the initial (σ1 = 5 Pa) and final (σ2 = 11 Pa) stresses. It is necessary to determine the change in elastic modulus (E) of the femur material.

To solve this problem, Hooke's law is used, which establishes a linear relationship between stress and deformation of elastic materials:

σ = E,

where σ is stress, E is elastic modulus, ε is relative deformation.

You can also use the formula to determine the change in elastic modulus:

ΔE = E(σ2 - σ1)/(σ1(ε2 - ε1)).

Substituting the known values, we get:

ΔE = E(11 - 5)/(5(0.055 - 0.025)) = E/2.

From here:

E = 2ΔE = 2(5 Pa) = 10 Pa.

So, the change in elastic modulus of the human femur is 10 Pa.

This digital product is a detailed solution to problem number 10782, which will help you determine how the modulus of elasticity of the human femur changes when the stress on it changes.

The design of this product uses beautiful html code, which makes it easier to perceive information and makes the process of learning the material more fun.

You will find here a brief statement of the problem, as well as formulas and laws used in the solution. The calculation formula and answer to the problem are also given in this product.

This digital product is ideal for students, teachers and anyone who is interested in the mechanics of materials and wants to deepen their knowledge in this field.

This digital product is a detailed solution to problem number 10782, which will help you determine how the modulus of elasticity of the human femur changes when the stress on it changes. It is known that at a stress of 5 Pa the relative deformation is 0.025, and when the stress increases to 11 Pa it becomes equal to 0.055. To solve this problem, Hooke's law is used, which establishes a linear relationship between stress and deformation of elastic materials. Using the formula for determining the change in elastic modulus, it can be calculated that the change in elastic modulus of the human femur is 10 Pa. The design of this product uses beautiful html code, which makes it easier to perceive information and makes the process of learning the material more fun. You will find here a brief statement of the problem, as well as formulas and laws used in the solution. The calculation formula and answer to the problem are also given in this product. This digital product is ideal for students, teachers and anyone who is interested in the mechanics of materials and wants to deepen their knowledge in this field. If you have any questions about the solution, do not hesitate to write, I will try to help.

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The elastic modulus (also known as Young's modulus) of the human femur determines its ability to resist deformation under stress. If at a stress of 5 Pa the relative strain is 0.025, and when the stress increases to 11 Pa it becomes equal to 0.055, then Young’s modulus can be determined as follows:

E = (σ2 - σ1) / (ε2 - ε1)

where E is Young's modulus, σ1 and ε1 are the initial stress and relative strain, respectively, and σ2 and ε2 are the final stress and relative strain, respectively.

Substituting the values ​​into the formula, we get:

E = (11 Pa - 5 Pa) / (0.055 - 0.025) = 320 Pa

Thus, the modulus of elasticity of the human femur is 320 Pa.

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