1. Elasticity Yashwantarao Chavan Institute of Science Satara Physics
Rayat Shikshan Sanstha’s
Yashwantarao Chavan Institute of Science Satara
Physics
Std –XII Section – I
Presentation on
Elasticity By
Mr. Ranmale V.B.
&
Mrs. Patil V.S.

2. Elasticity F Introduction i.e. body moves form its initial position
When a force is applied to a body, there are two possibilities 1)
either state of the body changes
i.e. body moves form its initial position F

3. Elasticity F 2) or shape and/or size changes
If shape and/or size changes then that change is called as Deformation
and the corresponding force is called as deforming force .

4. Elasticity
By the use of Deformation all bodies can be classified as -
Bodies
Rigid
Non-rigid
Elastic
Plastic

5. Elasticity What is Rigid body ??
Rigid body is a body whose shape and/or size does not change even if a very high force is applied.
e.g. : diamond or steel sphere
Note : No body is rigid but for practical purposes we assume body to be a rigid body

6. Elasticity What is Non-Rigid body ??
Non rigid body is a body whose shape and/or size changes if a very large force is applied.
e.g. : Rubber band, steel or iron rod

7. Elasticity Elasticity
Property possessed by material body by virtue of which a material body opposes to change its shape or size or both when subjected to deforming force and regains its original shape and size when deforming forces are removed
Elastic Body :
An elastic body is a body which regains its original shape and/or size when deforming forces are removed.
e.g. : Rubber

8. Elasticity Plasticity :
Property possessed by material bodies by virtue of which it do not regain its original shape or size or both after removal of external deforming force
Plastic Body :
A plastic body is a body which does not regain its original shape and/or size when deforming forces are removed.
e.g. : clay, dough etc.

9. Elasticity Distinguish between Elastic Body Plastic Body
Elastic bodies regain original dimensions after removal of external forces
Plastic bodies do not regain original dimensions after removal of external forces
In elastic bodies intermolecular forces are strong
In Plastic bodies intermolecular forces are weak
Magnitude of external force required to change dimension is larger
Magnitude of external force required to change dimension is small
E.G. Steel ,Iron , Quartz etc…
E.G. Mud , clay , Pleistocene etc…

10. Elasticity elastic forces or restoring forces
When external force is applied on a body , it gets deformed
during deformation of body , internal forces are produced in body which opposes the change in dimensions of body
such force are called as elastic forces or restoring forces
The direction of internal restoring force is exactly opposite to applied force
and magnitude is same as that of applied force.
Deforming force
Internal restoring force

11. Elasticity Definition of Stress and strain Stress Strain
Stress is defined as the internal
restoring force per unit area.
Strain is defined as the ratio of change in dimension to original dimension.
The internal restoring force is equal and opposite to the deforming force. i.e. the applied force.
Since strain is the ratio of identical quantities therefore, it has no units and dimensions.
Hence Stress is also defined as
the applied force per unit area.
Strain =
Change in Dimensions
Original Dimensions
Units :
S.I.. Unit : N/m2
C.G.S. Unit : dyne/cm2
Dimensions : [M1 L-1 T-2]

12. Elasticity Types of Stress and strain
Depending on nature of deformation stress and strain is of three types
1 ) Tensile Stress
1 ) Tensile Strain
When force is applied at right angle to cross sectional area of wire then wire gets elongated and gives to stress which is perpendicular to cross sectional area. This stress is called as tensile stress
Is define as change in length per unit original length
Tensile Strain
If a force F = mg is applied to a wire of radius r having area of cross section A = r2
Applied Force
Area
Tensile stress = L Mg l

13. Elasticity Types of Stress and strain 2 ) Volume Stress
2 ) Volume Strain
When a body is subjected to increase in pressure then body is compressed .
Change in volume per unit original volume is called as volume strain
Thus the volume of body changes.
Stress produced in body due to change in volume is called as volume stress
dv V
Volume strain =
V-dv
F A
Volume stress =
= dP
= Change in Pressure

14. Elasticity Types of Stress and strain 3 ) Shearing Stress
When a tangential force is applied to one face of body with other face of body as fixed then the shape changes and stress is produced in the body .
The stress produced due to change in shape of body is called as shearing stress A B A A B B F P Q P P Q Q   D C D C S R S R
Shearing stress

15. Elasticity Types of Stress and strain 3 ) Shearing Strain
Ration of lateral displacement of layer to its distance from fixed layer is called as shearing strain F P P Q Q x h S R 
Lateral displacement of any layer
Shearing strain =
Its perpendicular distance from the fixed layer
PP' = PS x = h
Shearing Strain =
tan    [ ... x <<< h
hence tan    ]

16. Elasticity Elastic Limits
The maximum stress which can be applied to a body without permanently deforming it is called its elastic limit.

17. Elasticity
Hook’s Law

18. Elasticity
Hook’s Law
Within elastic limits stress is directly proportional to strain
. . .
Stress  Strain
Stress
i.e. =
Constant = E
Strain
Robert Hook
E is a constant of proportionality, or
modulus of elasticity or coefficient of elasticity
Units :
S.I. Unit : N/m2
Hooke's Law is obeyed only if the deformation is within the elastic limit.
C.G.S. Unit : dyne /cm2
Dimensions :
[M1 L-1 T-2]
If the body is stretched beyond the elastic limit, stress is not proportional to the strain and Hooke's law is not obeyed.

19. Elasticity Elastic Constants 1) Young’s Modulus( Y)
The ration of tensile stress to tensile strain is called as Young’s Modulus
. . .
. . .
. . .
. . .
Only Solids have definite length.
Therefore,
Young’s modulus is the property of solids only
Units :
S.I. Unit : N/m2
C.G.S. Unit : dyne /cm2
Dimensions :
[M1 L-1 T-2]

20. Elasticity Elastic Constants 2) Bulk Modulus( K)
The ratio of volume stress to volume strain is called as Bulk Modulus
. . .
. . .
. . .
Solid , liquid and gases all have Bulk modulus
Reciprocal of Bulk modulus is called as compressibility
Units :
S.I. Unit : N/m2
C.G.S. Unit : dyne /cm2
Dimensions :
[M1 L-1 T-2]

21. Elasticity Elastic Constants 3) Modulus of rigidity ( η)
The ratio of shearing stress to shearing strain is called as Modulus of Rigidity
. . .
. . .
If θ is small then tanθ = 0
Particular shape.
Therefore,
Only solids possess modulus of rigidity
. . .
Units :
S.I. Unit : N/m2
C.G.S. Unit : dyne /cm2
Dimensions :
[M1 L-1 T-2]

22. Elasticity Elastic Constants Value of Poisson’s ratio lies between
The ration of lateral contraction strain to longitudinal extension (Tensile) strain is called as Poisson’s ratio
. . .
. . .
s =
. . .
Value of Poisson’s ratio lies between
-1 to 0.5
. . .

23. Elasticity Wire length =1.80m Wire diameter =0.27mm
Relations between the elastic constants Y, K h and s 1)
Y = 3K (1 – 2s) 3) 2)
Y = 2h (1 + s) 4) or

24. Elasticity Determination of Young’s modulus by Searle’s Method
Apparatus

25. Elasticity R S P Q H
S Level
Fixed
Variable

26. Elasticity R S P Q H
S Level
Variable
Fixed

27. Elasticity R S P Q H
S Level
Variable
Fixed

28. Elasticity Why do we require Searle’s Appt ?
It is one of the correct method to determine elongation in the wire when it is loaded and this method is used to determine Young’s modulus of material of wire
We know
Load (M)
That means to find Y
we need to find l. O
Extension (l)
Graph is a straight line which shows that extension is proportional to the load according to Hooke’s Law.
From this Y is Calculated as :

29. Elasticity
Errors in the determination of elongation of wire and its elimination
1) Yielding of support
Due to load to the wire the rigid support might bend by small amount.
2) Effect of temperature
A change in room temp, will change the length of the wire as well
Precautions
By using two identical wires, so that if the rigid support bends, it will lower both the wires equally.
Also if the temp. changes both wires will have equal change in length.

30. Elasticity

31. Elasticity Observation on a wire under applied increasing load
Behavior of wire under increasing load is studied by applying load to the wire until wire breaks & corresponding elongation is noted by Searle’s apparatus
Consider a long wire fixed to a rigid support & the other end stretched by suspending increasing loads. N Y E B
P = Proportionality limit
E = Elastic limit P
Stress
Y = Yield point
N = Neck point
B = Break point O O¢
Strain

32. Elasticity
Point P : proportionality limit : It is the point up to which stress is directly proportional to strain.
Point E : Elastic limit : It is the point of maximum stress to which the wire can be subjected without permanent deformation.
That means beyond E the wire will be stretched permanently even if the load is reduced and wire will not come back to original length.
Point Y yield point : It is the point on the graph beyond which the wire becomes plastic such that strain increases even without stress.
Point N : It is point on the graph where the length increases on its own due to the formation of a neck.
Point B : It is the point where the wire breaks.

33. Elasticity
Work done in stretching a thin uniform wire by calculus method
When load is applied to a wire is elongated .During elongation of wire work is done on the wire by applied force. This work is stored in the form of potential energy called as strain energy
Young’s modulus of material of wire is - L A x 
…… (i) F
If wire if further elongated through dx ,
then the work done during the elongation is…
dW = f dx

34. Elasticity L F A x
Work done in stretching a thin uniform wire by calculus method
Total work done during elongation of wire from 0 to l is
W = ∫ dW
This work is stored in the form of potential energy called as strain energy 
Volume of cylindrical wire
V = A L
……from (i)

35. Work done per unit volume in stretching a wire
Elasticity
Therefore ,
Work done per unit volume in stretching a wire or strain energy per unit volume is …
Strain energy is work done on the wire.
Therefore,
Work done per unit volume in stretching a wire
As … OR

36. Elasticity