Elasticity

When you stretch a rubber band and release it, it returns to its original shape. When you bend a steel ruler slightly, it springs back. This property of materials to regain their original shape after the deforming force is removed is called elasticity.

Elastic and Plastic Behaviour

An elastic body returns to its original shape when the deforming force is removed (e.g., spring, rubber band). A plastic body does not return to its original shape (e.g., clay, putty).

Elastic limit: The maximum stress up to which a body can recover its original shape. Beyond this, permanent deformation occurs.

Stress

Stress is the restoring force per unit area developed inside a body when it is deformed.

Stress = Force / Area = F / A (Unit: N/m² or Pascal, Pa)

Types of stress:

• Tensile stress: Due to stretching
• Compressive stress: Due to compression
• Shear stress: Due to tangential forces

Strain

Strain is the ratio of change in dimension to the original dimension. It has no unit (dimensionless).

Longitudinal strain = Change in length / Original length = delta L / L

Hooke's Law

Within the elastic limit, stress is directly proportional to strain.

Stress = E x Strain (where E is the modulus of elasticity)

Young's Modulus (Y)

Young's modulus measures the stiffness of a material under tension or compression:

Y = Tensile stress / Longitudinal strain = (F/A) / (delta L / L) = FL / (A delta L)

Unit: Pascal (Pa) or N/m²

Worked Example

A steel wire of length 2 m and cross-sectional area 1 mm² = 1 x 10⁻⁶ m² is stretched by a force of 200 N. If Young's modulus for steel is 2 x 10¹¹ Pa, find the extension.

Solution:

• Y = FL / (A delta L)
• delta L = FL / (AY) = 200 x 2 / (1 x 10⁻⁶ x 2 x 10¹¹)
• delta L = 400 / (2 x 10⁵) = 2 x 10⁻³ m = 2 mm

Real-World Connection

In construction across Nepal, understanding elasticity is critical. Steel rods used in reinforced concrete buildings must withstand stress without permanent deformation. The cables of suspension bridges (like those found in rural Nepal) rely on the elastic properties of steel.

Key Takeaways

• Elasticity is the ability to regain original shape after deformation
• Stress = Force/Area; Strain = Change in dimension/Original dimension
• Hooke's law: Stress is proportional to strain within the elastic limit
• Young's modulus measures material stiffness; higher Y means stiffer material