Topic – 1 Elasticity
Which is more elastic Glass or Rubber. Give reasons.
Glass is more elastic than rubber because restoring forces are more and less elongation for
deformed force, for same force in rubber more deformation will occur. Young’s modulus also
greater value for glass
What is the possible value of Poisson’s ratio?
The Poisson's ratio of a stable, isotropic, linear elastic material cannot be less than −1.0 nor
greater than 0.5 due to the requirement that Young's modulus, theshear modulus and bulk
modulus have positive values. Most materials have Poisson's ratio values ranging between 0.0
and 0.5.
Differentiate between elastic body and inelastic body.
Elastic Body
Inelastic Body
Process
It is irreversible.
It is reversible.
Ductility
They are highly ductile in nature.
It is less ductile in nature.
Resilience
They have low yield strength.
They have high yield
strength.
Modulus of
The ratio of stress to strain is high.
elasticity (ratio)
Toughness
The ratio of stress to strain is
low or equal.
They do not have the ability to absorb
They have the ability to
energy up to a fracture.
absorb energy up to a
fracture.
Bonds
The molecular bonds are fractured.
The molecular bonds do not
get fractured.
Shape and size
The shape and size changes permanently.
The shape and size does
change permanently,
Example
Plasticine.
Rubber.
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Topic – 1 Elasticity
What is deforming force and restoring force?
The externally applied balanced forces producing deformation are called deforming forces. The
internally balanced forces which arise in response to deforming forces by virtue of elasticity of
an object, which resist deformation and restore the object to its original shape and size upon
withdrawal of deforming forces, are called restoring force.
The deformed object remains in equilibrium due to deforming and restoring forces balancing
each other.
State Hooke’s law and give two examples.
Hooke's law - (physics) the principle that (within the elastic limit) the stress applied to a solid is
proportional to the strain produced
1) the spring in the pens and the laed pencils which hold the refill in position.
2) the flyovers are constructed keeping in mind Hookes Law.
Mention the factors affecting elasticity.
(i)
Effect of Stress: Due to the application of large constant stress or repeated number cycles of
stresses on a body a gradual decrease in elasticity of a body results.
(ii) Effect of Temperature: Generally, the elasticity decreases with increase in temperature. For
example, at room temperature, carbon filament is in elastic state. When it is heated by passing a
current, it is converted into plastic state.
Note: However elasticity remains unaffected with change in a temperature in a material like invar
steel.
(iii) Effect of Hammering and rolling: the elastic properties of solids are increased while doing
operations like hammering and rolling.
(iv) Effect of annealing: when solid materials are annealed( heating or cooling), it results in the
formation of uniform crystalline structure along with the formation of larger crystal grains.
Thus the softening of materials takes place. Therefore, the elastic property of the materials
decreases due to annealing.
(v) Effect of impurities: when small impurities like carbon and potassium are added to molten iron
and gold, it enhances their elastic property. The addition of impurity increases the compactness
of materials and hence, elastic property.
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Topic – 1 Elasticity
Sketch origin of elasticity by sketching energy vs distance curve.
Elasticity by sketching energy vs distance curve
A typical potential well indicating bonding energies E and forces for two interacting atoms.
As two atoms approach one another, they at first experience an attraction.
They repel one another when they are brought very close. r0 is the equilibrium distance.
The type of bonding in a solid depends on the behavior of the atoms' outer “valence” electrons.
Metallic:
outer electrons shared in a cloud or sea. Ionic Cations have given up one or more electrons Anions have
gained one or more electrons
Covalent:
atoms share outer electrons Mixed ionic and covalent
Van der Waals:
electrostatic due to non-uniform charge distribution.
Modulus of eleasticity E is proportional to slope of the force versus inter atomic separation curve at
equilibrium spacing.
Slope of the curve at r = ro position is steep for very stiff materials and shallower for flexible materials.
The energy interatomic distance curve, illustrates that as modulus of elasticity E decreases, energy
Related to Unit – II Property’s of Material
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Topic – 1 Elasticity
minima decreases and hence the strength of the bond.
Values of modulus of eleasticity E are highest for ceramics, higher for metals and lower for polymers
which is a direct consequence of the different types of atomic bonding.
Explain stress-strain and their types.
Stress
When some external forces are applied to a body, then the body offers internal resistance to these
forces. This internal internal opposing force per unit area is called 'stress'. It is denoted by symbol σ and
its S.I. unit is Pascal or N/m2. Mathematically the stress formula we can obtain as
Stress = Force / Area
Types of Stress
Stress is of two different types mainly :
(i) Normal Stress
(ii) Shearing or Tangential Stress .
Normal Stress : If the stress is normal to the surface, it is called normal stress. Stress is always normal in
the case of a change in length or a wire or in the case of change in volume of a body
Longitudinal Stress : When a normal stress change the length of a body then it is called longitudinal
stress which is given by
Longitudinal Stress = Deforming Force / Area of cross section = F / A
The longitudinal stress can be further divided into two types. When a wire or a rod is stretched at the two
ends by equal and opposite forces, the stress is called tensile stress. When a rod is pushed at the two
ends by equal and opposite forces, it will be under compression. The stress in such a case is called
compressive stress.
Volume Stress (or ) Bulk Stress : When a normal stress changes the volume of a body then it is called
volume stress. When a solid body is immersed in a fluid, the force at any point is normal to the surface of
the body and the magnitude of the force on any small area is proportional to the area i.e., the body is
under the action of a pressure P.
Bulk Stress = Force / Area = Pressure
Shearing Stress : When the Stress is tangential to the surface due to the application of forces parallel to
the surface, then the stress is called tangential or shearing stress. It changes the
shape of the body.
Shearing Stress = Force / Surface Area = F / A
Strain
The ratio of change produced in the dimensions of a body by a system of forces or
couples, in equilibrium, to its original dimensions is called strain.
Strain = Change in Dimension / Original Dimension
Types of Strain
Strain is of three types depending upon the change produced in a body and the
stress applied.
The three types of strain are
Longitudinal Strain
Volume Strain and
Shearing Strain
Longitudinal Strain : It is the ratio of the change in length of a body to the
original length of the body. If L is the original length of a wire or a rod and the
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final length of the wire or the rod is L+ΔL under the action of a normal stress, the change in lengtis ΔL.
Longitudinal Strain = Change in length/Original length = ΔL/L
If the length increases due to tensile stress, the corresponding strain is called tensile strain. If the length
decreases due to compressive stress, the strain is called compressive strain.
Volume Strain : It is the ratio of the change in volume of a body to its original volume. If V is the original
volume of a body and V+ΔV is the volume of the body under the action of a normal stress, the change in
volume is ΔV.
Volume Strain = Change in volume / Original volume = ΔV / V.
Shearing Strain : If is the angle through which a face originally perpendicular to the fixed face is turned.
(or) It is the ratio of the displacement of a layer to its distance from the fixed layer.
Units of Strain : As strain is a ratio , it has no units and dimensions.
State three moduli of elasticity.
Three moduli of elasticity
Depending upon the type of strain in the body there are three
different types of modulus of elasticity. They are
(i)Young’s modulus
(ii) Bulk modulus
(iii) Rigidity modulus
Young’s modulus of elasticity
Consider a wire of length l and cross sectional area A stretched by a force F acting
along its length. Let dl be the extension produced.
∴ Longitudinal stress = Force F / Area A
Longitudinal strain = change in length / original length = dl / l
Young’s modulus of the material of the wire is defined as the ratio of longitudinal
stress to longitudinal strain. It is denoted by q.
Young’s modulus = longitudinal stress / longitudinal strain
(i.e) q = (F / A) / (dl / l)
Bulk modulus of elasticity
Suppose euqal forces act perpendicular to the six faces of
a cube of volume V
Due to the action of these forces, let the decrease in
volume be dV
Now, Bulk stress = Force F / Area A
Bulk Strain = change in volume / original volume = −
dV/V
(The negative sign indicates that volume decreases.)
Bulk modulus of the material of the object is defined as
the ratio bulk stress to bulk strain.
It is denoted by k
Bulk modulus = Bulk stress / Bulk strain
(i.e) k = (F/A) / (dV / V) = − P / (dV / V)
Rigiditymodulus or shear modulus
Let us apply a force F tangential to the top surface of a
block whose bottom AB is fixed, Under the action of this
tangential force, the body suffers a slight change in shape,
its volume remaining unchanged. The side AD of the block
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is sheared through an angle θ
To the position AD’.
If the area of the top surface is A , then shear stress = F/A
Shear modulus or rigidity modulus of the material of the object is defined as the ratio of shear stress
to shear strain. It is denoted by n.
Rigidity modulus= shear stress / shear strain
(i.e) n = (F / A θ)
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