Elastic Modulus Examples
Example 1. A wire is 2m long and has cross-sectional area of 10-6m2 A load of 980 N is suspended. Calculate the stress, the strain and, the energy stored in the wire
Given: Y = 12 × 1010 N m-2
Solution:
Stress = F / A = 980 / 10-6 = 98 × 107 N m-2
Strain = Stress / Y = 98 × 107 / 12 × 1010 = 8.17 × 10-3
Energy = 1/2 × (stress × strain) × volume = 1/2 × (98 × 107 × 8.17 × 10-3) × 2 × 10-6 = 8 Joules.
Example 2. A Metallic Cube with side 0.20 m is undergoes a shearing force of 1000 N. The top surface is displaced through 0.40 cm with respect to the bottom. Find the shear modulus of elasticity of the metal.
Solution:
Here, L = 0.20 m, F = 1000 N, x = 0.40 cm = 0.004 m and
Area A = L2= 0.04 m2
Therefore, Shear modulus = (1000/ 0.04) × (0.20 / 0.004) = 1.25 × 106 N m-2.
Example 3. What must be the elongation of a wire 5 m long so that the strain is 1% of 0.1? If the wire has cross-selection of 1 mm2 and is stretched by 10 kg, what is the stress?
Solution:
L = 5m, Strain = 1% of 0.1 = 1 × 10-2 × 0.1 = 1 × 10-3, Area of cross-section = 1 mm² = 1 × 10-6 m²
F = 10 kg= 10 × 9.8 N
Extension = Stress × L = 5mm
Stress = Force / Area = (10 × 9.8) / (1 × 10-6) = 9.8 × 107 N/m².
Modulus of Elasticity
Modulus of Elasticity or Elastic Modulus is the measurement of resistance offered by a material against the deformation force acting on it. Modulus of Elasticity is also called Young’s Modulus. It is given as the ratio of Stress to Strain. The unit of elastic modulus is megapascal or gigapascal
Modulus of Elasticity is one of the most important concepts of material science and engineering. It is the property of material that measures stiffness to elastic deformation under stress. In this article, we will discuss about Modulus of Elasticity, including its definition, types, and fundamental concepts along with its various applications in day-to-day life.
Table of Content
- What is Modulus of Elasticity
- How to Calculate Modulus of Elasticity
- Modulus of Elasticity Formula
- Modulus of Elasticity of Different Materials
- Modulus of Elasticity vs Modulus of Rigidity