Elasticity & Calorimetry | Physics Optional Notes for UPSC PDF Download

 Page 1


 
ELASTICITY & CALORIMETRY 
A body is called rigid when its parts don't change position relative to each other when 
external forces try to deform it. Diamond or carborundum are examples that come 
closest to being rigid. 
Nobody is perfectly rigid and everybody can be deformed more or less by the application 
of suitable forces. All these deformed bodies however regain their original shape or size, 
when the deforming forces are removed. 
Elasticity: The property of the body by virtue of which it tends to regain its original size 
& shape when the applied forces are removed, is known as elasticity & the deformation 
caused is known as elastic deformation. Quartz is a very nearly perfectly elastic body. 
However, if we apply force to a lump or mud or putty, they have no cross tendency to 
regain their previous shape & they get permanently deformed. Such substances are 
caused by plastic & the property is called plasticity. 
Examples: 
> Fluids, including liquids and gases, possess no definite shape, and therefore cannot 
possess elasticity. 
>  The volume of matter, whether this matter is solid or fluid, can be altered by the 
application of suitable forces, and in most cases, the original volume is regained when 
the forces cease to act; hence, all matter possesses volume elasticity. 
>  Any alteration produced in the shape or volume of matter is called a strain. 
Internal restoring force : 
 
When an external force acts on a substance, the intermolecular forces within the 
substance generate an internal resistance known as internal restoring force. 
At equilibrium, the numerical value of the internal restoring force is equal to the external 
force. 
Restoring mechanism: 
The restoring mechanism can be visualized by taking a model of the spring-ball system 
shown in Fig. Here the balls represent atoms and the springs represent interatomic 
forces. 
Page 2


 
ELASTICITY & CALORIMETRY 
A body is called rigid when its parts don't change position relative to each other when 
external forces try to deform it. Diamond or carborundum are examples that come 
closest to being rigid. 
Nobody is perfectly rigid and everybody can be deformed more or less by the application 
of suitable forces. All these deformed bodies however regain their original shape or size, 
when the deforming forces are removed. 
Elasticity: The property of the body by virtue of which it tends to regain its original size 
& shape when the applied forces are removed, is known as elasticity & the deformation 
caused is known as elastic deformation. Quartz is a very nearly perfectly elastic body. 
However, if we apply force to a lump or mud or putty, they have no cross tendency to 
regain their previous shape & they get permanently deformed. Such substances are 
caused by plastic & the property is called plasticity. 
Examples: 
> Fluids, including liquids and gases, possess no definite shape, and therefore cannot 
possess elasticity. 
>  The volume of matter, whether this matter is solid or fluid, can be altered by the 
application of suitable forces, and in most cases, the original volume is regained when 
the forces cease to act; hence, all matter possesses volume elasticity. 
>  Any alteration produced in the shape or volume of matter is called a strain. 
Internal restoring force : 
 
When an external force acts on a substance, the intermolecular forces within the 
substance generate an internal resistance known as internal restoring force. 
At equilibrium, the numerical value of the internal restoring force is equal to the external 
force. 
Restoring mechanism: 
The restoring mechanism can be visualized by taking a model of the spring-ball system 
shown in Fig. Here the balls represent atoms and the springs represent interatomic 
forces. 
 
Fig. Spring-ball model for the illustration of elastic behaviour of solids. 
If you try to displace any ball from its equilibrium position, the spring system tries to 
restore the ball to its original position. Thus elastic behavior of solids can be explained in 
terms of the microscopic nature of the solid. When a body is subjected to a deforming 
force, a restoring force is developed in the body. This restoring force is equal in 
magnitude but opposite in direction to the applied force. 
The internal restoring force acting per unit area of the cross-section of the deformed 
body is called stress. 
Stress =
 Internal restoring force 
 Area of cross section 
=
?? intemal 
?? =
?? external 
?? 
Stress depends on the direction of force as well as the direction of the area of application 
so it is tensor. 
SI Unit: N - m
-2
 
Dimensions: M
i
L
-1
 T
-2
 
There are three types of stress:- 
(a) Longitudinal Stress: 
When the stress is normal to the surface of the body, then it is known as longitudinal 
stress. There are two types of longitudinal stress 
(i) Tensile Stress: 
The longitudinal stress, produced due to an increase in the length of a body, is defined as 
tensile stress. 
 
 
(ii) Compressive stress: 
Page 3


 
ELASTICITY & CALORIMETRY 
A body is called rigid when its parts don't change position relative to each other when 
external forces try to deform it. Diamond or carborundum are examples that come 
closest to being rigid. 
Nobody is perfectly rigid and everybody can be deformed more or less by the application 
of suitable forces. All these deformed bodies however regain their original shape or size, 
when the deforming forces are removed. 
Elasticity: The property of the body by virtue of which it tends to regain its original size 
& shape when the applied forces are removed, is known as elasticity & the deformation 
caused is known as elastic deformation. Quartz is a very nearly perfectly elastic body. 
However, if we apply force to a lump or mud or putty, they have no cross tendency to 
regain their previous shape & they get permanently deformed. Such substances are 
caused by plastic & the property is called plasticity. 
Examples: 
> Fluids, including liquids and gases, possess no definite shape, and therefore cannot 
possess elasticity. 
>  The volume of matter, whether this matter is solid or fluid, can be altered by the 
application of suitable forces, and in most cases, the original volume is regained when 
the forces cease to act; hence, all matter possesses volume elasticity. 
>  Any alteration produced in the shape or volume of matter is called a strain. 
Internal restoring force : 
 
When an external force acts on a substance, the intermolecular forces within the 
substance generate an internal resistance known as internal restoring force. 
At equilibrium, the numerical value of the internal restoring force is equal to the external 
force. 
Restoring mechanism: 
The restoring mechanism can be visualized by taking a model of the spring-ball system 
shown in Fig. Here the balls represent atoms and the springs represent interatomic 
forces. 
 
Fig. Spring-ball model for the illustration of elastic behaviour of solids. 
If you try to displace any ball from its equilibrium position, the spring system tries to 
restore the ball to its original position. Thus elastic behavior of solids can be explained in 
terms of the microscopic nature of the solid. When a body is subjected to a deforming 
force, a restoring force is developed in the body. This restoring force is equal in 
magnitude but opposite in direction to the applied force. 
The internal restoring force acting per unit area of the cross-section of the deformed 
body is called stress. 
Stress =
 Internal restoring force 
 Area of cross section 
=
?? intemal 
?? =
?? external 
?? 
Stress depends on the direction of force as well as the direction of the area of application 
so it is tensor. 
SI Unit: N - m
-2
 
Dimensions: M
i
L
-1
 T
-2
 
There are three types of stress:- 
(a) Longitudinal Stress: 
When the stress is normal to the surface of the body, then it is known as longitudinal 
stress. There are two types of longitudinal stress 
(i) Tensile Stress: 
The longitudinal stress, produced due to an increase in the length of a body, is defined as 
tensile stress. 
 
 
(ii) Compressive stress: 
The longitudinal stress, produced due to decrease in length of a body, is defined as 
compressive stress. 
 
Tensile 
 
?? =
?? ?? as ?? ? ?? 
Compressive 
 
Tangential Stress or Shear Stress: 
When the stress is tangential or parallel to the surface of a body then it is known as shear 
stress. Due to this stress, the shape of the body changes or it gets twisted. 
 
 
 Shear stress =
?? Area 
 
Volume Deformation: 
 
When a fluid presses on all sides of an object (as shown in the figure), it compresses the 
solid, reducing its volume. The fluid pressure P is the force exerted per unit surface area, 
which can also be thought of as the volume. 
Stress on the solid object. Pressure has the same units as the other kinds of stress: N/m
2
 
orPa . 
Page 4


 
ELASTICITY & CALORIMETRY 
A body is called rigid when its parts don't change position relative to each other when 
external forces try to deform it. Diamond or carborundum are examples that come 
closest to being rigid. 
Nobody is perfectly rigid and everybody can be deformed more or less by the application 
of suitable forces. All these deformed bodies however regain their original shape or size, 
when the deforming forces are removed. 
Elasticity: The property of the body by virtue of which it tends to regain its original size 
& shape when the applied forces are removed, is known as elasticity & the deformation 
caused is known as elastic deformation. Quartz is a very nearly perfectly elastic body. 
However, if we apply force to a lump or mud or putty, they have no cross tendency to 
regain their previous shape & they get permanently deformed. Such substances are 
caused by plastic & the property is called plasticity. 
Examples: 
> Fluids, including liquids and gases, possess no definite shape, and therefore cannot 
possess elasticity. 
>  The volume of matter, whether this matter is solid or fluid, can be altered by the 
application of suitable forces, and in most cases, the original volume is regained when 
the forces cease to act; hence, all matter possesses volume elasticity. 
>  Any alteration produced in the shape or volume of matter is called a strain. 
Internal restoring force : 
 
When an external force acts on a substance, the intermolecular forces within the 
substance generate an internal resistance known as internal restoring force. 
At equilibrium, the numerical value of the internal restoring force is equal to the external 
force. 
Restoring mechanism: 
The restoring mechanism can be visualized by taking a model of the spring-ball system 
shown in Fig. Here the balls represent atoms and the springs represent interatomic 
forces. 
 
Fig. Spring-ball model for the illustration of elastic behaviour of solids. 
If you try to displace any ball from its equilibrium position, the spring system tries to 
restore the ball to its original position. Thus elastic behavior of solids can be explained in 
terms of the microscopic nature of the solid. When a body is subjected to a deforming 
force, a restoring force is developed in the body. This restoring force is equal in 
magnitude but opposite in direction to the applied force. 
The internal restoring force acting per unit area of the cross-section of the deformed 
body is called stress. 
Stress =
 Internal restoring force 
 Area of cross section 
=
?? intemal 
?? =
?? external 
?? 
Stress depends on the direction of force as well as the direction of the area of application 
so it is tensor. 
SI Unit: N - m
-2
 
Dimensions: M
i
L
-1
 T
-2
 
There are three types of stress:- 
(a) Longitudinal Stress: 
When the stress is normal to the surface of the body, then it is known as longitudinal 
stress. There are two types of longitudinal stress 
(i) Tensile Stress: 
The longitudinal stress, produced due to an increase in the length of a body, is defined as 
tensile stress. 
 
 
(ii) Compressive stress: 
The longitudinal stress, produced due to decrease in length of a body, is defined as 
compressive stress. 
 
Tensile 
 
?? =
?? ?? as ?? ? ?? 
Compressive 
 
Tangential Stress or Shear Stress: 
When the stress is tangential or parallel to the surface of a body then it is known as shear 
stress. Due to this stress, the shape of the body changes or it gets twisted. 
 
 
 Shear stress =
?? Area 
 
Volume Deformation: 
 
When a fluid presses on all sides of an object (as shown in the figure), it compresses the 
solid, reducing its volume. The fluid pressure P is the force exerted per unit surface area, 
which can also be thought of as the volume. 
Stress on the solid object. Pressure has the same units as the other kinds of stress: N/m
2
 
orPa . 
 
Fig. Forces on an object when submerged in a fluid 
Volume stress = pressure =
F
A
= P 
Example. Find out longitudinal stress and tangential stress on a fixed block. 
 
Solution: Longitudinal or normal stress ?? 1
=
100sin 30
°
5×2
= 5 N/m
2
 
Tangential stress 
?? 2
=
100cos 30
°
5 × 2
= 5v 3 N/m
2
 
Example. 
 
Find longitude stress & shear stress on A
'
 ? 
Solution: ?? ?
= ?? sin ?? , ?? ?? = ?? cos ?? 
? Longitud stress =
?? sin ?? ?? /sin ?? =
?? sin
2
 ?? ?? ? Shear stress =
?? cos ?? ?? /sin ?? =
?? sin ?? cos ?? ?? ? sin ?? =
?? ?? '
?? '
=
?? sin ?? 
Page 5


 
ELASTICITY & CALORIMETRY 
A body is called rigid when its parts don't change position relative to each other when 
external forces try to deform it. Diamond or carborundum are examples that come 
closest to being rigid. 
Nobody is perfectly rigid and everybody can be deformed more or less by the application 
of suitable forces. All these deformed bodies however regain their original shape or size, 
when the deforming forces are removed. 
Elasticity: The property of the body by virtue of which it tends to regain its original size 
& shape when the applied forces are removed, is known as elasticity & the deformation 
caused is known as elastic deformation. Quartz is a very nearly perfectly elastic body. 
However, if we apply force to a lump or mud or putty, they have no cross tendency to 
regain their previous shape & they get permanently deformed. Such substances are 
caused by plastic & the property is called plasticity. 
Examples: 
> Fluids, including liquids and gases, possess no definite shape, and therefore cannot 
possess elasticity. 
>  The volume of matter, whether this matter is solid or fluid, can be altered by the 
application of suitable forces, and in most cases, the original volume is regained when 
the forces cease to act; hence, all matter possesses volume elasticity. 
>  Any alteration produced in the shape or volume of matter is called a strain. 
Internal restoring force : 
 
When an external force acts on a substance, the intermolecular forces within the 
substance generate an internal resistance known as internal restoring force. 
At equilibrium, the numerical value of the internal restoring force is equal to the external 
force. 
Restoring mechanism: 
The restoring mechanism can be visualized by taking a model of the spring-ball system 
shown in Fig. Here the balls represent atoms and the springs represent interatomic 
forces. 
 
Fig. Spring-ball model for the illustration of elastic behaviour of solids. 
If you try to displace any ball from its equilibrium position, the spring system tries to 
restore the ball to its original position. Thus elastic behavior of solids can be explained in 
terms of the microscopic nature of the solid. When a body is subjected to a deforming 
force, a restoring force is developed in the body. This restoring force is equal in 
magnitude but opposite in direction to the applied force. 
The internal restoring force acting per unit area of the cross-section of the deformed 
body is called stress. 
Stress =
 Internal restoring force 
 Area of cross section 
=
?? intemal 
?? =
?? external 
?? 
Stress depends on the direction of force as well as the direction of the area of application 
so it is tensor. 
SI Unit: N - m
-2
 
Dimensions: M
i
L
-1
 T
-2
 
There are three types of stress:- 
(a) Longitudinal Stress: 
When the stress is normal to the surface of the body, then it is known as longitudinal 
stress. There are two types of longitudinal stress 
(i) Tensile Stress: 
The longitudinal stress, produced due to an increase in the length of a body, is defined as 
tensile stress. 
 
 
(ii) Compressive stress: 
The longitudinal stress, produced due to decrease in length of a body, is defined as 
compressive stress. 
 
Tensile 
 
?? =
?? ?? as ?? ? ?? 
Compressive 
 
Tangential Stress or Shear Stress: 
When the stress is tangential or parallel to the surface of a body then it is known as shear 
stress. Due to this stress, the shape of the body changes or it gets twisted. 
 
 
 Shear stress =
?? Area 
 
Volume Deformation: 
 
When a fluid presses on all sides of an object (as shown in the figure), it compresses the 
solid, reducing its volume. The fluid pressure P is the force exerted per unit surface area, 
which can also be thought of as the volume. 
Stress on the solid object. Pressure has the same units as the other kinds of stress: N/m
2
 
orPa . 
 
Fig. Forces on an object when submerged in a fluid 
Volume stress = pressure =
F
A
= P 
Example. Find out longitudinal stress and tangential stress on a fixed block. 
 
Solution: Longitudinal or normal stress ?? 1
=
100sin 30
°
5×2
= 5 N/m
2
 
Tangential stress 
?? 2
=
100cos 30
°
5 × 2
= 5v 3 N/m
2
 
Example. 
 
Find longitude stress & shear stress on A
'
 ? 
Solution: ?? ?
= ?? sin ?? , ?? ?? = ?? cos ?? 
? Longitud stress =
?? sin ?? ?? /sin ?? =
?? sin
2
 ?? ?? ? Shear stress =
?? cos ?? ?? /sin ?? =
?? sin ?? cos ?? ?? ? sin ?? =
?? ?? '
?? '
=
?? sin ?? 
 
STRAIN 
The ratio of change of any dimension to its original dimension is called strain. 
Strain =
 change in size of the body 
 original size of the body 
 
It is a unit less and dimensionless quantity. 
There are three types of strain: Type of strain depends upon the directions of applied 
force. 
(a) Longitudinal strain =
 change in length of the body 
 initial length of the body 
=
??? ?? 
 
(b) Volume strain =
 change in volume of the body 
 original volume of the body 
=
?V
V
 
 
(c) Shear strain: 
When a force is applied to a body parallel to its surface, causing a change in its shape (but 
not its size), the resulting strain is called shear strain. This strain occurs when neighboring 
layers of the material slide past each other.