Mathematical Interpretation of Young’s Modulus
Consider a wire of radius r and length L. Let a force F be applied on the wire along its length i.e., normal to the surface of the wire as shown in the figure. If △L is the change in length of the wire, then Tensile stress (σ = F/A), where A is the area of the cross-section of the wire and the Longitudinal strain (ϵ = △L/L).
Therefore, Young’s Modulus for this case is given by:
Y = (F/A) / (△L/L)
= (F × L) / (A × △L)
If the extension is produced by the load of mass m, then Force, F is mg, where m is the mass and g is the gravitational acceleration.
And the area of the cross-section of the wire, A is πr2 where r is the radius of the wire.
Therefore, the above expression can be written as:
Y = (m × g × L) / (πr2 × △L)
Young’s Modulus
Young’s Modulus is the ratio of stress and strain. It is named after the famous British physicist Thomas Young. Young’s Modulus provides a relation between stress and strain in any object. When a certain load is added to a rigid material, it deforms. When the weight is withdrawn from an elastic material, the body returns to its original form, this property is called Elasticity.
Elastic bodies have a steady linear Young’s modulus. Young’s modulus of Steel is 2×1011 Nm-2. Young Modulus is also called the Modulus of Elasticity. In this article, we will learn about Young’s Modulus, its Young’s Modulus formula, unit, Stress, Strain, and how to calculate Young’s Modulus.
Table of Content
- What Is Young’s Modulus?
- Young’s Modulus Definition
- Young’s Modulus of Elasticity
- Young’s Modulus Formula
- Units of Young’s Modulus
- Other Form of Young’s Modulus Formula
- Notations in Young’s Modulus Formula
- Young’s Modulus Factors
- How to Calculate Young’s Modulus
- Young’s Modulus of Some Materials
- Mathematical Interpretation of Young’s Modulus
- Factors Affecting Young’s Modulus
- Solved Examples on Young’s Modulus
- Practice Problems on Young’s Modulus