CLASS 11 MECHANICAL PROPERTIES OF SOLID
MECHANICAL PROPERTIES OF SOLID
✤ SOLID: those substances in which atoms/Particles have fixed position i.e maximum interatomic force.
❈ ELASTIC LIMIT: It is the maximum external force within which it regain its configuration after the removal it.
❢ Stress:- It is defined as external force (deforming force) per unit area.
i.e Stress= Force / Area
SI-Unit: Nm-2
dim [ML-1T-2]
It is scalar.
❈ DEFORMING FORCE: It is an external force which try can try to Change the shape or size of a body
❈ RESTORING FORCE: It is the internal force which act opposite to deforming force.
* STEEL HAS THE MOST RESTORING FORCE
* CLAY HAS THE MINIMUM RESTORING FORCE
❈ ELASTICITY: It is the property of material by which it gain its initial shape & size, after the removal of deforming force & the bodies are called elastic body.
Example: Steel, Quartz etc.
✤ PLASTIC BODY: Those bodies which can't gain its initial configurationfter the removal of deforming force.
Example: Clay, Plastic Wood etc.
Cause of stress is Restoring Force i.e [internal force]
➤ TENSILE STRESS
➤ COMPRESS STRESS
➤ HYDROLIC STRESS
➤ TANGENTIONAL STRESS
❈ STRAIN: It is defined as the ratio of change in configuration & Original Configuration
STRAIN = Change / Original
Unitless dim [MLT-1]
* TYPES:
(1) LONGITUDINAL STRAIN :-
long. Strain = Change in length
/ Original length
= Δl / l
(2) VOLUMETRIC STRAIN :-
= Change in Volume / Original Volume
= ΔV / V
(3) SHEARING STRAIN :-
Ө = Δl / l
* HOOKE'S LAW :-
• It states that within elastic limit stress is always proportional to strain.
Stress DC Strain
Stress = E Strain
E = Stress/Strain Here E is called modulus of elasticity.
Unit is Nm⁻² or Pa
dim [ML⁻¹T⁻²]
> E does not depends stress & strain
> E depends upon the nature of matter
* TYPES OF MODULUS OF ELASTICITY :-
→ YOUNG'S MODULUS :- It is defined the ratio of Normal stress & longitudinal strain.
Y = Normal stress / Longitudinal strain
Y = F/A / Δl/l
Y = F l / AXΔl Units Pascal or Nm⁻²
Young's Modulus is directly proportional to temp.
NOTE:- 1- Y = PXL / Δl
2- mg l / AXΔl
3. Y does not depend upon force & other physical factor.
4. Y depend upon nature of matter.
* Bulk Modulus :-
It is defined as the ratio of normal stress & volumetric strain
B = Normal stress / Vol. Strain
B = F/A / ΔV/V
B= F x V / AXΔV Stand: Nm⁻²
dim [ML⁻¹T⁻²]
✤ Note:- For min ΔV, B should be maximum
Compressibility: It is the reciprocal of Bulk Modulus.
C = 1/ B for less value of B, C is maximum.
Modulus of Rigidity :- It describe how strong a substance is.
Shear Modulus :- It is defined as the ratio of tangential stress & shearing strain
n = tangential stress / Ө
n = F/A / Δl/l
n = F l / AXΔl Pascal, Nm⁻²
✤ Short notes Point to remember:-
→the nearest approach to a perfectly elastic body is quartz fibre.
→Putty are nearly perfectly plastic body.
→Nobody is perfectly inelastic nature or perfectly plastic.
→Shear strain = θ (or) tanθ = @
→Elastomers are the material which can be elastically stretched to
→Large Values of strain are called elastomer. For example: Rubber
→Percentage increase in length
Δl/l x100 = F /AY X 100
→Long range order means that similar patterns of atoms or molecules repeat over a large distance in a crystal.
→Glassy solids there exists no such long range order in the arrangement of atoms or molecules. In case of Glassy solids, the orderly arrangement of atoms is limited to very short range & in this respect they are similar to liquids.
→Amorphous solids are called super cooled liquid of High Viscosity.
→Pressure is the external force per unit area while stress is the Internal force.
→The slope of stress - Strain Graph Gives modulus of elasticity.
Tips for Solving Questions:-
→Mass= Volume x density. On A = Mass/ Lx P
If area is not given Breaking stress = lpg
Pg water = 10⁻³ kg m³
1mm = 0.001m , 1cm² = 10⁻⁴ m² exp
1cm = 0.01m, 1mm² = 10⁻⁶ m²
Area = πr²
Stress Vs Strain :-
A = Proportional limit
B = elastic limit
C = yield point
CD = Plastic limit
F = Breaking Point
• Types of Material :-
Ductile :- It shows large distance b/w prop. limit & breaking limit.
Example: Metals (Gold)
Brittle :- 
Example: Cast iron , Quartz
Elastomer :- 
*POISSON'S RATIO :- It is defined as the ratio of lateral strain & longitudinal strain.
σ = (ΔR/R) / (Δl/l)
✤ Energy stored in stretched wire :-
Let a wire of length l is stretched by small
length Δl by external force *F*.
So average force
= O+F/2 = F/2
work done in Δl displacement
w=force x displacement
=1/2*F*Δl
=1/2*F*Δl*xV/A*l
=1/2*(F/A)*(Δl/l)*xV
w=1/2*(Stress/Strain)*x(Strain)²xV
w=1/2*xV*(Strain)²xV
This work is stored in the form P.E.
U=1/2*xV*(Strain)²x volume
Energy per unit volume
=1/2*x(Strain)²
*NOTE:-*
1. Bulk modulus is applied in solids, liquid & gases.
2. Young's Modulus & Shear modulus are applied in solids only.
3. For perfectly rigid leady bulk modulus is infinite.
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