The document discusses the concepts of elasticity and plasticity in materials, explaining their definitions, properties, and behaviors under applied forces. It covers aspects such as elastic and plastic deformation, stress and strain, Young’s modulus, and different types of materials including elastic, plastic, brittle, and ductile. Additionally, it touches on practical applications and factors affecting elasticity, as well as the principles of static equilibrium in physics.

1. Unit 3: Elasticity and Static
Equilibrium of a rigid body
What do you think are the important
elastic and plastic properties of
bridges and ladders?

2. 3.1 Elasticity and Plasticity
• Elasticity and Plasticity are properties of
materials that describe how they respond to
applied forces.
• Elasticity is the property of a solid material
that allows it to restore its shape after a
deforming force is removed.
• Plasticity is the property of a solid substance
that allows it to keep its deformed shape even
when the applied force is removed.

3. Elastic Material
• Elastic materials are stretchy and can regain
their shape after being stretched or
compressed. The deformation caused is
known as elastic deformation.
• Examples: rubber, foam balls, elastic bands,
and springs.

4. Elasticity
• Proportional limit is the point at which stress and strain are
directly proportional to one another. Hooke's law is valid up
to this limit.
• Hooke’s Law :
𝑭𝑎𝑝𝑝 = 𝑘𝒙 𝑜𝑟 𝑭𝑅 = −𝑘𝒙,
where k is the spring constant.
• Elastic limit is the maximum stress up to which the body
completely recovers its original state after the removal of
the deforming forces. Beyond this limit, a material will
deform plastically or break.
• Elastic limit is the property of a body whereas elasticity is
the property of material of the body.

5. Plasticity
• Plasticity is the ability of a material to undergo permanent
deformation when a force is applied beyond its elastic limit.
• Deformation of plastic material is irreversible; it does not
return to its original shape.
• Examples:
– A piece of clay being molded.
– A metal rod bending permanently after excessive force.
• Yield Point: The point beyond elastic limit, at which the
length of wire starts increasing without increasing stress.
• Breaking point the position where the strain becomes so
large that the wire breaks down at last.

6. Inelastic Materials
• Inelastic materials do not return to their
original shape after being deformed. There are
two types of inelastic materials:
– Brittle: These materials crack or fracture easily
without much stretching. e.g. Glass
– Ductile: These materials can be stretched, drawn,
or compressed into a deformed shape without
breaking. e.g. Silly putty (at room T)

7. Factors that affect a material's elasticity
• All materials deform to some degree under pressure,
but the amount of deformation depends on the
material's elasticity. Factors that affect a material's
elasticity include:
• Temperature: Heating a material decreases its
elasticity.
• Impurities: The presence of impurities can increase or
decrease a material's elasticity.
• Annealing: Annealing decreases a material's elasticity.
• Hammering and rolling: These processes can increase
a material's elasticity.

8. Practical applications of elasticity

9. 3.2 Density and Specific gravity

10. 3.2 Density and Specific gravity
• 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
→𝜌=
𝑚
𝑉
• SI unit of density is 𝑘𝑔 𝑚3
• Density is a characteristic property of any pure
substance. It is used in determining whether
an object sinks or floats in a fluid.
• Specific gravity = 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑎 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒
𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑎𝑡 4℃
• 𝑠. 𝑔. = 𝜌𝑠
𝜌𝑤 𝑎𝑡 4℃

11. Some applications of specific gravity

12. Density and specific gravity of
substance at 0℃ and 1 atm.

13. Activity 3.4
• Suppose that a block of brass and a block of
wood have exactly the same mass. If both
blocks are dropped in a tank of water, which
one floats and which one sinks? why?

14. Review Questions on page 67

15. 3.3 Stress and Strain
• Stress is a quantity that describes the magnitude of forces that
cause deformation. Stress is generally defined as force per unit
area. Its SI unit is 𝑁 𝑚2
• Tensile stress occurs when a force is applied at a right angle to a
surface. It's the ratio of the force to the cross-sectional area of the
material. i.e. Te𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑓𝑜𝑟𝑐𝑒
𝑎𝑟𝑒𝑎
=
𝐹
𝐴
• An object under stress becomes deformed. The quantity that
describes this deformation is called strain.
• Tensile strain is given as a fractional change in length. It is strain
under a tensile stress. strain is a dimensionless number.
i.e. Te𝑛𝑠𝑖𝑙𝑒 𝑙𝑖𝑛𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛 = ∆𝐿
𝐿0

16. Tensile Stress

17. Shear stress and strain
• Shear stress occurs when a force is applied parallel to a
surface. It's caused by two equal and opposite external
forces applied parallel to the cross-sectional area of a
solid body. i. e. Shear 𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑓𝑜𝑟𝑐𝑒
𝑎𝑟𝑒𝑎
=
𝐹
𝐴
• Shear strain is given as a fractional change in geometry
(strain caused by shear stress)
• Shear 𝑠𝑡𝑟𝑎𝑖𝑛 = ∆𝑥
𝐿0

18. Volume strain
• Volume stress (bulk
stress) occurs when a
deforming force acts from
all dimensions, causing a
change in the volume of
an object.
• Volumetric strain is given
as a fractional change in
volume (strain under bulk
stress)
• Volume 𝑠𝑡𝑟𝑎𝑖𝑛 = ∆𝑉
𝑉0

19. Relation between stress and strain
• In 1678, Robert Hooke obtained the stress-strain curve
experimentally for a number of solid substances and
established a law of elasticity known as Hooke’s law.
• According to this law, within elastic limit,
Stress ∝ Strain ⇒ 𝑆𝑡𝑟𝑒𝑠𝑠 = 𝑘 × 𝑆𝑡𝑟𝑎𝑖𝑛
• This constant of proportionality K is a measure of
elasticity of the substance and is called modulus of
elasticity.
• As strain is a dimensionless quantity, the modulus of
elasticity has the same dimensions (or units) as stress.
• K value is independent of the stress and strain but
depends on the nature of the material.

20. Stress vs strain

21. Review Questions
1. Review the relationship between stress and strain.
Can you find any similarities between the two
quantities?
2. Can compressive stress be applied to a rubber band?
3. A nylon string that has a diameter of 2 mm is pulled
by a force of 100 N. Calculate the tensile stress.
4. A load of 2.0 kg is applied to the ends of a wire 4.0 m
long, and produces an extension of 0.24 mm. If the
diameter of the wire is 2.0 mm, find the stress on the
wire and the strain it produces

22. 3.4 Young’s Modulus
(Elasticity of length)
Young's modulus describes tensile and
compressive elasticity, or the tendency of an object
to deform along an axis when opposing forces are
applied along that axis.
The Young modulus of the material(Y) is the ratio of
tensile (or compressive) stress to the longitudinal
(tensile) strain.
i.e. 𝑌 =
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑒𝑠𝑠
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑎𝑖𝑛
=
𝐹
𝐴
∆𝐿
𝐿𝑜
SI unit Young’s Modulus is
𝐹
𝑚2 𝑜𝑟 𝑃𝑎.

23. Young’s Modulus

24. Young’s modulus of different substances

25. Exercise 3.5
• A copper wire is 1.0 m long and its diameter is
1.0 mm. If the wire hangs vertically, how much
weight must be added to its free end in order
to stretch it 3.0 mm?

26. Review Questions
1. In the Young experiment, if the length of the wire and the radius
are both doubled, what will happen to the value of the Young
modulus?
2. A wire increases by 10−3 of its length when a stress of 1 ×
108 𝑁
𝑚2 is applied to it. Calculate the Young modulus of material of
the wire.
3. A wire is stretched by 0.01 m by a certain force F. Another wire of
same material whose diameter and length are double to the
original wire is stretched by the same force. What will be its
elongation?
4. A 200 kg load is hung on a wire having a length of 4.0 m, cross-
sectional area 0.20 × 10−5𝑚2, and the Young modulus
8.00 × 1010 𝑁
𝑚2. What is its increase in length?

27. Shear Modulus (Elasticity of shape)
• The shear modulus or modulus of rigidity (S)
describes an object's tendency to shear (the
deformation of shape at constant volume)
when acted upon by opposing forces;
• it is defined as shear stress over shear strain.
S=
𝐹
𝐴
∆𝑥 ℎ
• The shear modulus is part of the derivation
of viscosity.

28. Shear Modulus (Elasticity of shape)

29. Bulk Modulus (Volume Elasticity)
• The bulk modulus (B) describes volumetric
elasticity, or the tendency of an object to deform
in all directions when uniformly loaded in all
directions;
• it is defined as volumetric stress over volumetric
strain, and is the inverse of compressibility. i.e.
𝐵 = −
∆𝑃
∆𝑉 𝑉0
Where ∆𝑃 is change in pressure
• The bulk modulus is an extension of Young's
modulus to three dimensions.

30. Bulk Modulus (Volume Elasticity)

31. Typical values of elastic modulus

32. 3.5 Static Equilibrium
Exercise 3.6
• List examples of bodies that are in static
equilibrium from your surroundings
Exercise 3.6
• When is a system or an object considered to
be in static equilibrium?

33. Linear Equilibrium
The first condition of equilibrium states that the
sum of the forces acting on a body must add up
to zero
𝐹𝑛𝑒𝑡 = 𝐹 = 0
𝑖𝑓 𝑎 𝑏𝑜𝑑𝑦 𝑖𝑠 𝑖𝑛 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚.
𝐹𝑥 = 0, 𝐹𝑦 = 0, 𝑎𝑛𝑑 𝐹𝑧 = 0

34. Examples

35. Rotational Equilibrium
Torque is the turning effect of force. 𝜏 = 𝑟 × 𝐹
The second condition necessary to achieve
equilibrium is that the net external torque on a
system must be zero
𝜏𝑛𝑒𝑡 = 𝜏 = 0
𝑖𝑓 𝑎 𝑏𝑜𝑑𝑦 𝑖𝑠 𝑖𝑛 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚.

36. Examples

37. Static Equilibrium
Static equilibrium is a type of equilibrium that occurs
when a body is at rest and there is no net force or net
torque acting on it.
1. A book placed on top of a table
2. A seesaw balanced by two children

38. Activity 1
• For the situation shown below, find the values
of 𝑇1 and 𝑇2 if the weight is 600N

39. Activity from your TB

42. End of Unit of Questions and Problems
• Try all the questions (#1-13) on page 89-90.