Elasticity

Chapter Content :
1. Elasticity , Stress , Strain & its types
2. Hooke’s law & Modulus of elasticity
3. Relation b/w stress & strain for wire
4. Elastic potential energy
5. Elongation of Rod under its own weight

The existence of three states of matter i.e. solid, liquid and gas can be explained on the basis of interatomic and intermolecular forces.

A solid has a definite shape, size and volume but a liquid possesses a definite volume and not a definite shape, whereas a gas has neither a definite shape, nor a definite volume.

These states differ from each other due to the following two factors:

1. The magnitudes of the interatomic and intermolecular forces.

2. The extent of random thermal motion of the atoms and molecules of a substance (which depends upon temperature.)

Elasticity: The property of the body to regain its original configuration (length, volume or shape) when the deforming forces are removed is called elasticity.

Some terms related to elasticity

(a) Deforming Force : If a force applied on a body causes a change in the shape or size of the body (either in length, volume or shape,) then this force is deforming force.

(b) Perfectly Elastic Body: A body which regains its original within immediately and completely after the removal of deforming force from it, is called a perfectly elastic body. Quartz and phosphor bronze are the examples of nearly perfectly elastic bodies

(c) Perfectly Plastic Body: A body which does not regain its original shape or size at all after the removal of the deforming force, however small the deforming force may be is called a perfectly plastic body.

Stress :

When a deforming force is applied to a body, it changes the shape or size of the body by changing the normal positions of the molecules or atoms of the body.

As a result, an internal restoring force comes into play, which tends to bring the body back to its initial shape or size. This internal restoring force acting per unit area is called stress.

i.e. Stress = Restoring force / area

Normal Stress : When force acting normal to the surface then Stress setup in the body is called Normal Stress .

Normal Stress = Normal restoring Force/Area of Cross section = Fn/A

Tangential Stress : When force acting tangential to the surface then Stress setup in the body is called Tangential Stress .

Tangential Stress = Tangential restoring Force/Area of Cross section = Ft/A

Volumetric Stress : When normal stress changes the volume of the body then it is called volumetric stress (or) bulk stress.

Strain :

When a deforming force is applied on a body, there is a change in the shape or size of the body. The body is said to be strained or deformed. The ratio of change in dimension to the original dimension is called strain.

Strain = (change in dimension)/(original dimension)

i.e. Strain being the ratio of two like quantities has no units and dimensions.

Longitudinal Strain :

Longitudinal Strain = (change in Length)/(original length)

= ∆L/L

Shearing strain:

Shearing strain = (relative displacement between two extreme layers)/(perpendicular distance between the layers)

= ∆x/L

Volumetric strain (or) Bulk strain:

Volumetric strain (or) Bulk strain =(change in volume)/(original volume) = ∆V/V

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