Physics Elasticity - Study Material For JEE Main
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The document details the concepts of elasticity, deformation, and their respective forces, explaining properties of elastic and plastic bodies. It discusses stress, strain, and the various types of stresses and strains, as well as Hooke's law and different modulus of elasticity. Additionally, it covers Poisson's ratio and provides examples and applications related to these principles.
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3. Shearing Strain
Shearing Strain
Lateral displacement of any layer
its distance from a fixed layer
EE'
h
tan
Usually θ is very small. For small values of θ,
measured in radian, tan θ = θ
∴ Shearing strain = θ
As the strain is a ratio of two similar quantities, its
value is purely numerical or it doesn’t have any unit
and hence, the dimensions. Or Its dimensions can
0 0 0
be written as [M L T ].
10](https://image.slidesharecdn.com/xii-physics-elasticity-01-11-2012-131203013711-phpapp02/85/Physics-Elasticity-Study-Material-For-JEE-Main-10-320.jpg)
![9011041155 / 9011031155
3. Modulus of Rigidity (n)
It is the ratio of shearing stress to shearing strain.
Shearing Stress
Shearing Strain
If a force F acting on area A of a body moves the
layers of the body through angle θ
Shearing stress = F/A, Shearing strain = tanθ
F
A tan
F
A
As strain is a unitless quantity, modulus of elasticity
has the units of stress, that are, N/m2 in S.I. or
1 -1 -2
dyne/cm2 in C.G.S. Its dimensions are [M L T ]
14](https://image.slidesharecdn.com/xii-physics-elasticity-01-11-2012-131203013711-phpapp02/85/Physics-Elasticity-Study-Material-For-JEE-Main-14-320.jpg)
Physics Elasticity - Study Material For JEE Main
- 1. 9011041155 / 9011031155 • Live Webinars (online lectures) with recordings. • Online Query Solving • Online MCQ tests with detailed solutions • Online Notes and Solved Exercises • Career Counseling 1
- 3. 9011041155 / 9011031155 Deformation When balanced forces are applied on a material body, dimension/s of the body (i.e. size volume, shape or all three) may change. Such changes are called deformation. Deforming Forces The forces which cause deformation of the body are called deforming forces. e.g. When rubber band is stretched from both the sides, its length increases. This is called deformation and the forces are called deforming forces. Elasticity It is the property possessed by a material body by virtue of which the body opposes any change in its dimensions, within elastic limit & regain them when deforming forces are removed. 3
- 4. 9011041155 / 9011031155 Elastic body The body which possesses the property of elasticity is called elastic body. OR It is the body which opposes the deformation, within the elastic limit and regain its original dimensions after removal of deforming forces. e.g. rubber, copper, steel, gold, silver etc. Plastic body The body which do not possess the property of elasticity OR the body which do not oppose the deformation and can not regain its original dimensions after removal of deforming forces is called a plastic body. OR A body which can be deformed when very small deforming force is applied and which doesn’t regain its original dimensions when the forces are removed, is called plastic body. e.g. clay, chalk, Plasticine etc. 4
- 5. 9011041155 / 9011031155 Restoring Forces When deforming forces are applied on a material body, some internal forces are developed in the body, which try to oppose the changes in the dimension/s. These forces are called restoring forces. If the magnitude of deforming forces is greater than that of restoring forces, the deformation takes place. As the restoring forces are directly proportional to the deformation, this increases the magnitude of deforming forces. If it is still less then that of the deforming forces, deformation continues. The process continues till the equilibrium is reached, when the restoring forces balance the deforming forces and the deformation stops. 5
- 6. 9011041155 / 9011031155 Stress stress can be defined as applied force per unit area. Stress internal restoring force area Stress applied deforming force area Depending upon changes in size, volume and shape, there are three kinds of stresses. Longitudinal or Tensile 1. Tensile stress Force Area 6 Mg r2 stress :-
- 7. 9011041155 / 9011031155 2. Volume stress :- Volume stress Applied Force Area Change in pressure 3. Shearing Stress or Shear :- Shearing Stress Applied force Area 7 F A dP
- 8. 9011041155 / 9011031155 Explanation of elasticity on the basis of molecular model 8
- 9. 9011041155 / 9011031155 Strain Strain Change in original dimensions Original dimensions There are three types of strains. 1. Longitudinal or Tensile strain Tensile Strain Change in the original length Original length Tensile Strain L 2. Volume Strain Volume Strain Change in the volume Original Volume Volume Strain dV V 9
- 10. 9011041155 / 9011031155 3. Shearing Strain Shearing Strain Lateral displacement of any layer its distance from a fixed layer EE' h tan Usually θ is very small. For small values of θ, measured in radian, tan θ = θ ∴ Shearing strain = θ As the strain is a ratio of two similar quantities, its value is purely numerical or it doesn’t have any unit and hence, the dimensions. Or Its dimensions can 0 0 0 be written as [M L T ]. 10
- 11. 9011041155 / 9011031155 Q.1 A body remains perfectly elastic if (a.1) The compression is large (b.1) The extension is large (c.1) The compression or extension is small (d.1) It does not undergo a deformation Q.2 The dimensional formula for stress is the same as that for (a.2) Work (b.2) Power (c.2) Pressure (d.2) Force Q.3 Steel is more elastic than rubber because for a given load the stain produced in steel, as compared to that produced in rubber is (a.3) More (b.3) Less (c.3) Equal (d.3) Very large 11
- 12. 9011041155 / 9011031155 Hooke’s law Within elastic limit, the ratio of stress to strain is constant for the given material. This constant is the property of the material. It is called modulus of elasticity. Stress Strain Modulus of Electricity Depending upon different stresses and strains, there are three elastic modulii or elastic constants. 1. Young’s Modulus (Y) It the ratio of tensile stress to tensile strain. Y tensile stress tensile strain When a metal rod of length L and radius r is elongated through l by applying force Mg, Tensile Stress Mg , Tensile Strain 2 r 12 L
- 13. 9011041155 / 9011031155 MgL r 2 Y 2. Bulk Modulus (k) It is the ratio of volume stress to volume stain. k Volume Stress Volume Strain If a balloon of volume V is compressed by changing pressure on it by dP, its volume changes by dV ∴ Volume Stress = dP and VolumeStrain k dV V dp V dV 13
- 14. 9011041155 / 9011031155 3. Modulus of Rigidity (n) It is the ratio of shearing stress to shearing strain. Shearing Stress Shearing Strain If a force F acting on area A of a body moves the layers of the body through angle θ Shearing stress = F/A, Shearing strain = tanθ F A tan F A As strain is a unitless quantity, modulus of elasticity has the units of stress, that are, N/m2 in S.I. or 1 -1 -2 dyne/cm2 in C.G.S. Its dimensions are [M L T ] 14
- 15. 9011041155 / 9011031155 Poisson’s Ratio (σ). “Within the elastic limit, the ratio of lateral strain to the tensile strain is constant, which is known as Poisson’s ratio”. ∴ Lateral strain = d/D and Tensile strain = ℓ / L As Lateral Strain Tensile Strain dL D For homogeneous isotropic material, 1 σ 0.5 In actual practice σ is always positive. 0.2 σ 0.4 σ for cork → 0, metal → 0.3, rubber → 0.5 Poisson's ratio is unitless and dimensionless quantity. 15
- 16. 9011041155 / 9011031155 • Ask Your Doubts • For inquiry and registration, call 9011041155 / 9011031155. 16