if a stress is numerically equal to young's modulus the elongation will be
ans:
1.)equal to the original length.
but how?
Stress equals to young's modulus Y. That means the strain in unity so, change in length is equal to the length of wire
To understand why the elongation of a material under stress is equal to its original length when the stress is numerically equal to Young's modulus, let's break down the concept and the formula involved.
Young's modulus, represented by the symbol E, is a measure of the stiffness of a material. It quantifies how much a material will deform under a given amount of stress. Mathematically, Young's modulus is defined as the ratio of stress (σ) on a material to its strain (ε):
E = σ / ε
Where:
- E is Young's modulus in Pascal (Pa)
- σ is stress in Pascal (Pa)
- ε is strain, which is the ratio of the change in length (∆L) to the original length (L₀)
When the stress (σ) on a material is numerically equal to Young's modulus (E), it means:
σ = E
If we rearrange the formula for Young's modulus, we get:
ε = σ / E
Substituting the value of stress (σ) with E, we get:
ε = E / E
Simplifying the equation further, the Young's modulus cancels out:
ε = 1
This means that when stress is numerically equal to Young's modulus, the strain (ε) of the material is 1. Strain, represented by ε, is the ratio of the change in length (∆L) to the original length (L₀).
For example, if the original length of a material is 10 cm, and the stress applied is equal to the Young's modulus (E), the strain (∆L/L₀) will be 1. This implies that the material will elongate by the same amount as its original length, resulting in a total length of 20 cm.
Therefore, when the stress (σ) is numerically equal to Young's modulus (E), the elongation (∆L) will be equal to the original length (L₀).