Elasticity and Hooke’s Law

Before using a particular material for construction purposes, tests are done on the material to make sure that the material can withstand the stress to which the material is subjected. Industrial laboratories use a special type of apparatus to perform these tests. Where stretching forces are involved brittle substances cannot be used, in that case, elastic material like steel is used.

**Elasticity**

Elasticity is the study of bodies under the influence of external force. Bodies that do not experience any deformation on the application of external force are called rigid bodies. In real life, we do not come across such bodies. Generally, bodies that undergo very small deformation when a very large force is applied are called rigid bodies. Bodies that resist the deformation and completely regain their original shape when the deforming force is removed are called elastic bodies. The bodies that retain their deformed shape after the external force is removed are called perfectly plastic bodies. **Elasticity** is the property of a material to recover its original shape or condition when the external force applied is removed.

**Elastic Stress and Strain**

When there is a uniform force F applied on the surface of area A, then stress is defined as the force applied per unit area.

Therefore, Stress = F/A

F is the force applied

A is the area of the surface

The S.I unit of stress is N/m^{2}.

The fractional change in the dimension of the body produced by the external force is known as the stain. Stain does not have any unit since it is the ratio of two physical quantities of the same kind.

**Hooke’s Law**

Hooke’s Law is the fundamental law of elasticity. This law was stated by Robert Hooke. The statement of **Hooke’s law** is that, provided the strain is small, stress will be directly proportional to the strain. The ratio of stress to strain is constant when the strain is very small. The constant value is called the modulus of elasticity.

Modulus of elasticity, E = Stress/Strain

E can also be called the coefficient of elasticity

**Modulus of Elasticity**

The modulus of elasticity or coefficient of elasticity is of three types depending on the type of strain. The three types of strain are

- Longitudinal strain or tensile strain
- Shearing strain or tangential strain
- Volume strain or Bulk strain

**Young’s Modulus**

The Young’s modulus is the measure of the resistance of a solid to the change in length. When the change in the length of the object is due to the applied external force, the strain caused is called the longitudinal strain. It is measured by the change in length per unit length.

Young’s Modulus = Stress/Longitudinal strain = (F/A)/(ΔL/L)

**Bulk Modulus**

It is the measure of the body’s resistance to the change in its volume. When the change in the volume takes place without any change in the shape is called the volume strain. It is measured by the change in volume by the actual volume.

Bulk Modulus = Stress/Volume strain = (F/A)/(ΔV/V)

**Rigidity Modulus**

It is the measure of the body’s resistance to the change in shape. The strain is called shearing strain. There is a change in the shape of the body but the volume does not change.

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