Elasticity

The external force acting on a body on account of which its size or shape or both change is defined as the deforming force. The force which restores the size and shape of the body when deformation forces are removed is called restoring force.

Deforming force and restoring force are not action reaction pair. Restoring force opposes the change in the size and shape of a body.

Rigid body: A body whose shape and size cannot be changed however large the applied force is called rigid body. There is no perfectly rigid body in nature.

Elasticity: The property of a body by virtue of which it regains its original size and shape immediately after the deformation forces are removed is called elasticity. Elasticity is a molecular phenomenon. It is because of cohesive forces.

A body which shows elastic behaviour is called elastic body. For example, steel, rubber. Quartz is very nearly perfectly elastic body.

Plastic body: A body which does not show elastic behaviour is called plastic body. For example,  putty, clay, mud, wax, lead, dough, chewing gum, butter wax.

Out of the given materials, a body in which it is more difficult to produce strain is more elastic. The body which requires greater deforming force to produce a certain change in dimension is more elastic.

By the process of hammering or rolling the body elasticity increases. By the process of annealing, the elastic property of a body is reduced.

Factors Effecting Elasticity

Effect of temperature: In general as the temperature increases the elastic property of a material decreases.

Effect of impurities: Addition of impurity to metal may increase or decrease the elasticity. If the impurity has more elasticity than the material to which it is added, it increases the elasticity. If the impurity is less elastic than the material it decreases the elasticity.

Stress

The restoring force developed per unit area of cross-section of the deformed body is called stress.

Stress = F/A

Dimensional formula: M1L-1T-2

Difference Between Pressure and Stress

  1. Pressure is always normal to the area, while stress can be either normal or tangential.
  2. Pressure on a body is always compressive, while stress can be compressive or tensile.
  3. Pressure is a scalar, while stress is a tensor.

Types of Stress

Longitudinal stress: If the restoring forces are perpendicular to the area of cross-section and are along the length of the wire, the stress is called longitudinal stress. During longitudinal stress, the body undergoes change in length but not in shape and volume.

Tangential stress (or shearing stress): If the restoring forces are parallel to the surface, the stress is called shearing stress.

Bulk stress (or volume stress): If a body is subjected to equal forces normally on all the faces, the stress involved is called bulk stress.

Strain

The deformation produced per unit magnitude is called strain.

Hooke's Law

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

  • Within the proportionality limit stress-strain graph is a straight line passing through the origin.
  • A spring balance works on the principle of Hooke’s law.
  • Modulus of elasticity does not depend upon the dimensions of the body but is a property of the material of the body.
  • Within the proportionality limit, the load extension graph is a straight line passing through the origin.