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1. Notes of chapter Mechanical properties of solids.....​

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Deforming Force

A force which produces a change in configuration of the object on applying it, is called a deforming force.

Elasticity

Elasticity is that property of the object by virtue of which it regain its original configuration after the removal of the deforming force.

Elastic Limit

Elastic limit is the upper limit of deforming force upto which, if deforming force is removed, the body regains its original form completely and beyond which if deforming force is increased the body loses its property of elasticity and get permanently deformed.

Perfectly Elastic Bodies

Those bodies which regain its original configuration immediately and completely after the removal of deforming force are called perfectly elastic bodies. e.g., quartz and phosphor bronze etc.

Perfectly Plastic Bodies

Those bodies which does not regain its original configuration at all on the removal of deforming force are called perfectly plastic bodies, e.g., putty, paraffin, wax etc.

Stress The internal restoring force acting per unit area of a deformed body is called stress.

Stress = Restoring force / Area

Its unit is N/m2 or Pascal and dimensional formula is [ML-12T-2].

Stress is a tensor quantity.

Stress is of Two Types

(i) Normal Stress If deforming force is applied normal to the area, then the stress is called

normal stress.

If there is an increase in length, then stress is called tensile stress.

If there is a decrease in length, then stress is called compression stress.

(ii) Tangential Stress If deforming force is applied tangentially, then the stress is called tangential stress.

Strain The fractional change in configuration is called strain.

Strain = Change in the configuration / Original configuration

It has no unit and it is a dimensionless quantity.

According to the change in configuration, the strain is of three types

(1) Longitudinal strain= Change in length / Original length

(2) Volumetric strain = Change in volume / Original volume

(iii) Shearing strain = Angular displacement of the plane perpendicular to the fixed surface.

Hooke’s Law

Within the limit of elasticity, the stress is proportional to the strain.

Stress &infi; Strain

or Stress = E * Strain

where, E is the modulus of elasticity of the material of the body.

Types of Modulus of Elasticity

1. Young’s Modulus of Elasticity

It is defined as the ratio of normal stress to the longitudinal strain Within the elastic limit.

y = Normal stress / Longitudinal strain

y = FΔl / Al = Mg Δl / πr2l

Its unit is N/m2 or Pascal and its dimensional formula is [ML-1T-2].

2. Bulk Modulus of Elasticity

It is defined as the ratio of normal stress to the volumetric strain within the elastic limit.

K = Normal stress / Volumetric strain

K = FV / A ΔV = &DElta;p V / Δ V

where, Δp = F / A = Change in pressure.

Its unit is N/m2 or Pascal and its dimensional formula is [ML-1T-2].

3. Modulus of Rigidity (η)

It is defined as the ratio of tangential stress to the shearing strain, within the elastic limit.

η = Tangential stress / Shearing strain

Its urut is N/m2 or Pascal and its dimensional formula is [ML-1T-2].

Compressibility

Compressibility of a material is the reciprocal of its bulk modulus of elasticity.

Compressibility (C) = 1 / k

Its SI unit is N-1m2 and CGS unit is dyne-1 cm2.

Steel is more elastic than rubber. Solids are more elastic and gases are least elastic.

For liquids. modulus of rigidity is zero.

Young’s modulus (Y) and modulus of rigidity (η) are possessed by solid materials only.

Limit of Elasticity

The maximum value of deforming force for which elasticity is present in the body is called its limit of elasticity.

Breaking Stress

The minimum value of stress required to break a wire, is called breaking stress.

Breaking stress is fixed for a material but breaking force varies with area of cross-section of the wire.

Safety factor = Breaking stress / Working stress

Elastic Relaxation Time

The time delay in restoring the original configuration after removal of deforming force is called elastic relaxation time.

For quartz and phosphor bronze this time is negligible.

Elastic After Effect

The temporary delay in regaining the original configuration by the elastic body after the

removal of deforming force, is called elastic after effect.

Elastic Fatigue

The property of an elastic body by virtue of which its behaviour becomes less elastic under the action of repeated alternating deforming force is called elastic fatigue.

Ductile Materials

The materials which show large plastic range beyond elastic limit are called ductile materials, e.g., copper, silver, iron, aluminum, etc.

Ductile materials are used for making springs and sheets.

Brittle Materials

The materials which show very small plastic range beyond elastic limit are called brittle materials, e.g., glass, cast iron, etc.

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