Class 11 Physics Mechanical Properties of Solids Elastic Modulus

Elastic Modulus

  • Elastic modulus is ratio of stress and strain.
  • Elastic modulus is a characteristic value of each material. This means gold will have specific value of elastic modulus and rubber will have specific value of elastic modulus etc.
  • k=Stress/Strain where k= Elastic modulus.

Problem: - A piece of copper having a rectangular cross-section of 15.2 mm × 19.1 mm is pulled in tension with 44,500 N forces, producing only elastic deformation. Calculate the resulting strain?

Answer:

Length of the piece of copper, l = 19.1 mm = 19.1 × 10–3 m

Breadth of the piece of copper, b = 15.2 mm = 15.2 × 10–3 m

Area of the copper piece:

A = l × b = 19.1 × 10–3 × 15.2 × 10–3 = 2.9 × 10–4 m2

Tension force applied on the piece of copper, F = 44500 N

Modulus of elasticity of copper, η = 42 × 109 N/m2

Modulus of elasticity, η = Stress/Strain 

= (F/A)/Strain

Strain = F/ (A η) =44500/2.9x10–4x42x109

= 3.65 × 10–3

 

Types of Elastic Modulus

  1. Young’s Modulus
  2. Shear Modulus
  3. Bulk Modulus

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