Derive equation of Young's Modulus

Young's Modulus (also known as the modulus of elasticity or elastic modulus) is a measure of the stiffness of a material . It is denoted by the symbol E and defined as the ratio of stress (σ) to strain (ε) in a material undergoing deformation. The equation for Young's Modulus is derived from Hooke's Law, which states that the stress is directly proportional to the strain within the elastic limit.

Stress (σ) is the force (F) applied per unit area (A).

σ=F/A

Strain (ε) is the ratio of the change in length (ΔL) to the original length (L₀).

ε=ΔL/L₀

Hooke's Law relates stress to strain within the elastic limit.

σ=εE

Substitute stress and strain expressions into Hooke's Law equation.

F/A=E(ΔL/L₀)

E=FL₀/AΔL

The formula expresses the ratio of stress to strain. Stress is represented by F/A, and strain is represented by ΔL/L_0. The Young's Modulus is essentially a material property that indicates how much a material deforms (strain) under a certain amount of applied force (stress).

Real-Life Examples of Young's Modulus

Steel, with a high Young's Modulus, is used in construction for stability.
Rubber bands, with a low Young's Modulus, are elastic and used in various applications.
Concrete, with a moderate Young's Modulus, balances rigidity and flexibility in construction.
Aluminum alloys, with a specific Young's Modulus, provide strength and lightness in aerospace applications.
Bones in the human body have varying Young's Modulus, providing strength and flexibility.

Derive equation of Young's Modulus

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