Elasticity in Physics

Elasticity is the property of a material that enables it to return to its original shape and size after the distorting force is removed. Materials that do not return to their original shape are called plastic materials.

1. Hooke's Law

Hooke's law states that the extension (e) of an elastic material is directly proportional to the applied force (F), provided the elastic limit is not exceeded. It is expressed mathematically as:

F = ke

Where k is the force constant (stiffness) of the spring, measured in N/m.

2. Force-Extension Graph and Material Behavior

• Proportional Limit: The point up to which Hooke's law is strictly obeyed.
• Elastic Limit: The maximum force that can be applied to a body such that it still returns to its original shape.
• Yield Point: The point beyond which the material shows a large increase in extension for a very small increase in force.
• Breaking Point: The point where the material eventually snaps or fractures.

3. Young's Modulus (E)

Young's modulus is a measure of the stiffness of a solid material. It is defined as the ratio of tensile stress to tensile strain.

• Stress: Force per unit area (σ = F/A). Unit: N/m² or Pascals (Pa).
• Strain: Ratio of extension to original length (ε = e/L). It has no units.
• Young's Modulus Formula: E = Stress / Strain = (F/A) / (e/L) = FL / Ae.

4. Work Done in Springs (Elastic Potential Energy)

When a spring is stretched, work is done. This work is stored as elastic potential energy (W). If the limit of proportionality is not exceeded:

W = ½Fe = ½ke²

For work done per unit volume:

Energy per unit volume = ½ × Stress × Strain

5. Spring Balance

A spring balance is an instrument used to measure force or weight. It operates on the principle of Hooke's law, where the extension of the internal spring is calibrated to show the magnitude of the force applied.