Question

within elastic limit, prove that the stress required to double the length of wire is the Young's modulus of its material.

Answer 1

stress α strain
y=stress /strain
2times the strain this is equal to y
stress =2 y

Answer 2

The relationship between stress and strain in a material can be described by Hooke's Law, which states that within the elastic limit, the stress applied to a material is directly proportional to the strain produced.

Mathematically, this can be expressed as:

σ = E × ε

where σ is the stress, E is the Young's modulus (also known as the elastic modulus) of the material, and ε is the strain.

Strain is defined as the change in length of the material per unit length, and it can be expressed as:

ε = ΔL / L

where ΔL is the change in length of the material and L is the original length of the material.

Let's assume that the wire is subjected to a stress that doubles its length, so that ΔL = L. Then, the strain can be calculated as:

ε = ΔL / L = L / L = 1

By substituting the value of strain into the equation for stress, we get:

σ = E × ε = E × 1

This means that the stress required to double the length of the wire is equal to the Young's modulus of the material.

Hence, within the elastic limit, the stress required to double the length of the wire is the Young's modulus of its material.

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