Friction | Physics Optional Notes for UPSC PDF Download

 Page 1


FRICTION 
FRICTION 
When things rub against each other or try to move past each other, they create friction. 
Friction is like a force that pushes back against this movement, trying to stop it or slow it 
down. It's what makes it hard to slide a heavy box across the floor or stop a car when you 
press the brakes. And here's a neat thing: the friction on one object is matched by an equal 
and opposite friction on the other object, following Newton's third law of motion. 
Types of Friction: 
Before we proceed further into a detailed account of frictional phenomena, it is advisable 
to become familiar with different types of frictional forces. All types of frictional 
phenomena can be categorized into dry friction, fluid friction, and internal friction. 
1. Dry Friction: It exists when two solid un-lubricated surfaces are in contact under 
the condition of sliding or tendency of sliding. It is also known as Coulomb 
friction. 
 Fluid Friction 
1. Internal Friction 
Frictional forces exist everywhere in nature and result in a loss of energy that is primarily 
dissipated in the form of heat. Wear and tear of moving bodies is another unwanted 
result of friction. Therefore, sometimes, we try to reduce their effects - such as in 
bearings of all types, between the piston and the inner walls of the cylinder of an IC 
engine, the flow of fluid in pipes, and aircraft and missile propulsion through the air. 
Though these examples create a negative picture of frictional forces, there are other 
situations where frictional forces become essential and we try to maximize the effects. It 
is the friction between our feet and the earth's surface, which enables us to walk and run. 
Both the traction and braking of wheeled vehicles depend on friction. 
Consider a situation in which a block is kept on a rough horizontal surface on which a 
variable horizontal force ' ?? ' is acting. 
 
 
At every value of ' ?? ' resistance force that is friction force ( ?? ) offered by rough 
horizontal surface is calculated and graph is plotted. 
In part 'OA' of the graph block remains at rest w.r.t. ground and value of friction force (f) 
is equal to applied force ' ?? ' and is called static friction force. 
Page 2


FRICTION 
FRICTION 
When things rub against each other or try to move past each other, they create friction. 
Friction is like a force that pushes back against this movement, trying to stop it or slow it 
down. It's what makes it hard to slide a heavy box across the floor or stop a car when you 
press the brakes. And here's a neat thing: the friction on one object is matched by an equal 
and opposite friction on the other object, following Newton's third law of motion. 
Types of Friction: 
Before we proceed further into a detailed account of frictional phenomena, it is advisable 
to become familiar with different types of frictional forces. All types of frictional 
phenomena can be categorized into dry friction, fluid friction, and internal friction. 
1. Dry Friction: It exists when two solid un-lubricated surfaces are in contact under 
the condition of sliding or tendency of sliding. It is also known as Coulomb 
friction. 
 Fluid Friction 
1. Internal Friction 
Frictional forces exist everywhere in nature and result in a loss of energy that is primarily 
dissipated in the form of heat. Wear and tear of moving bodies is another unwanted 
result of friction. Therefore, sometimes, we try to reduce their effects - such as in 
bearings of all types, between the piston and the inner walls of the cylinder of an IC 
engine, the flow of fluid in pipes, and aircraft and missile propulsion through the air. 
Though these examples create a negative picture of frictional forces, there are other 
situations where frictional forces become essential and we try to maximize the effects. It 
is the friction between our feet and the earth's surface, which enables us to walk and run. 
Both the traction and braking of wheeled vehicles depend on friction. 
Consider a situation in which a block is kept on a rough horizontal surface on which a 
variable horizontal force ' ?? ' is acting. 
 
 
At every value of ' ?? ' resistance force that is friction force ( ?? ) offered by rough 
horizontal surface is calculated and graph is plotted. 
In part 'OA' of the graph block remains at rest w.r.t. ground and value of friction force (f) 
is equal to applied force ' ?? ' and is called static friction force. 
Beyond ' A ' graph represents the situation in which block is moving w.r.t ground. In this 
situation it is found that friction force acting on the block becomes constant and is called 
kinetic friction force. 
KEY POINT 
? Friction do not opposes motion instead it opposes Relative motion to the surface 
applying friction force. 
? Friction acts along the surface in contact. 
 
STATIC FRICTION FORCE 
If there is a tendency of relative slipping (only tendency and not actual) between two 
surfaces in contact then the friction force acting between them is called static friction 
force. 
It is a variable force whose value is equal to requirement to stop relative slipping till it 
reaches its limiting value. 
Laws of static friction: 
?? st 
 law: Static friction force acting between two surfaces in contact does not depend on 
the area of contact. 
2nd law: Maximum value of static friction (Limiting friction) is directly proportional to 
the normal force acting between the two surfaces. 
(?? ?? ) ? ?? 
(?? ?? )
max
= ?? s
N f
s
= Limiting friction ; ?? s
= coefficient of static friction  
KINETIC FRICTION 
?  Kinetic friction comes into picture when relative slipping occurs. 
? It acts in direction opposite to relative velocity. 
? Its value is constant. 
Laws of kinetic friction: 
Page 3


FRICTION 
FRICTION 
When things rub against each other or try to move past each other, they create friction. 
Friction is like a force that pushes back against this movement, trying to stop it or slow it 
down. It's what makes it hard to slide a heavy box across the floor or stop a car when you 
press the brakes. And here's a neat thing: the friction on one object is matched by an equal 
and opposite friction on the other object, following Newton's third law of motion. 
Types of Friction: 
Before we proceed further into a detailed account of frictional phenomena, it is advisable 
to become familiar with different types of frictional forces. All types of frictional 
phenomena can be categorized into dry friction, fluid friction, and internal friction. 
1. Dry Friction: It exists when two solid un-lubricated surfaces are in contact under 
the condition of sliding or tendency of sliding. It is also known as Coulomb 
friction. 
 Fluid Friction 
1. Internal Friction 
Frictional forces exist everywhere in nature and result in a loss of energy that is primarily 
dissipated in the form of heat. Wear and tear of moving bodies is another unwanted 
result of friction. Therefore, sometimes, we try to reduce their effects - such as in 
bearings of all types, between the piston and the inner walls of the cylinder of an IC 
engine, the flow of fluid in pipes, and aircraft and missile propulsion through the air. 
Though these examples create a negative picture of frictional forces, there are other 
situations where frictional forces become essential and we try to maximize the effects. It 
is the friction between our feet and the earth's surface, which enables us to walk and run. 
Both the traction and braking of wheeled vehicles depend on friction. 
Consider a situation in which a block is kept on a rough horizontal surface on which a 
variable horizontal force ' ?? ' is acting. 
 
 
At every value of ' ?? ' resistance force that is friction force ( ?? ) offered by rough 
horizontal surface is calculated and graph is plotted. 
In part 'OA' of the graph block remains at rest w.r.t. ground and value of friction force (f) 
is equal to applied force ' ?? ' and is called static friction force. 
Beyond ' A ' graph represents the situation in which block is moving w.r.t ground. In this 
situation it is found that friction force acting on the block becomes constant and is called 
kinetic friction force. 
KEY POINT 
? Friction do not opposes motion instead it opposes Relative motion to the surface 
applying friction force. 
? Friction acts along the surface in contact. 
 
STATIC FRICTION FORCE 
If there is a tendency of relative slipping (only tendency and not actual) between two 
surfaces in contact then the friction force acting between them is called static friction 
force. 
It is a variable force whose value is equal to requirement to stop relative slipping till it 
reaches its limiting value. 
Laws of static friction: 
?? st 
 law: Static friction force acting between two surfaces in contact does not depend on 
the area of contact. 
2nd law: Maximum value of static friction (Limiting friction) is directly proportional to 
the normal force acting between the two surfaces. 
(?? ?? ) ? ?? 
(?? ?? )
max
= ?? s
N f
s
= Limiting friction ; ?? s
= coefficient of static friction  
KINETIC FRICTION 
?  Kinetic friction comes into picture when relative slipping occurs. 
? It acts in direction opposite to relative velocity. 
? Its value is constant. 
Laws of kinetic friction: 
?? st 
 law: Kinetic friction acting between two surfaces in contact does not depend on area 
of contact. 
2nd law: The value of kinetic friction force is directly proportional to the normal force 
acting between the two surfaces in contact. 
?? ?? ? ?? ?? ?? = ?? ?? ?? ?? ?? = coefficient of kinetic friction 
 
FEW IMPORTANT POINTS 
(1) The value of ?? k
 is always less than ?? s
(?? k
< ?? s
) from experimental observation. 
(2) If only the coefficient of friction (?? ) is given by a problem then ?? ?? - ?? ?? = ?? 
(assumption for) 
(3) The value of ?? ?? and ?? ?? is independent of surface area it depends only on surface 
properties of the contact surface. 
(4) ?? k
 is independent of relative speed. 
(5) ?? s
&?? k
 are properties of a given pair of surfaces i.e. for wood-to-wood combination ?? 1
, 
then for wood-iron ?? 2,
 and so on. 
Example. A block of mass 1 kg is at rest on a rough horizontal surface, where 
coefficients of static and kinetic friction are 0.2 and 0.15. Find the frictional forces if a 
horizontal force (?? = 9.8 m/s
2
) 
 
 
(a) F = 1 N 
(b) F = 1.96 N 
(c) F = 2.5 N is applied on a block 
Solution: Maximum force of friction is the timing friction f
sm
= 0.2 × 1 × 9.8 N = 1.96 N 
(a) For F = 1 N, F < f
sm
 
So, the body is at rest means static friction is present, and hence  f
s
= F = 1 N 
(b) For ?? = 1.96 N,  F = f
cm
= 1.96 N. The block is about to slide, therefore f = 1.96 N 
(c) For = 2.5 N, So F > f
sm
 
Now the body is sliding and kinetic friction acts 
Therefore f = f
k
= ?? k
N = ?? k
mg= 0.15 × 1 × 9.8 = 1.47 N 
Page 4


FRICTION 
FRICTION 
When things rub against each other or try to move past each other, they create friction. 
Friction is like a force that pushes back against this movement, trying to stop it or slow it 
down. It's what makes it hard to slide a heavy box across the floor or stop a car when you 
press the brakes. And here's a neat thing: the friction on one object is matched by an equal 
and opposite friction on the other object, following Newton's third law of motion. 
Types of Friction: 
Before we proceed further into a detailed account of frictional phenomena, it is advisable 
to become familiar with different types of frictional forces. All types of frictional 
phenomena can be categorized into dry friction, fluid friction, and internal friction. 
1. Dry Friction: It exists when two solid un-lubricated surfaces are in contact under 
the condition of sliding or tendency of sliding. It is also known as Coulomb 
friction. 
 Fluid Friction 
1. Internal Friction 
Frictional forces exist everywhere in nature and result in a loss of energy that is primarily 
dissipated in the form of heat. Wear and tear of moving bodies is another unwanted 
result of friction. Therefore, sometimes, we try to reduce their effects - such as in 
bearings of all types, between the piston and the inner walls of the cylinder of an IC 
engine, the flow of fluid in pipes, and aircraft and missile propulsion through the air. 
Though these examples create a negative picture of frictional forces, there are other 
situations where frictional forces become essential and we try to maximize the effects. It 
is the friction between our feet and the earth's surface, which enables us to walk and run. 
Both the traction and braking of wheeled vehicles depend on friction. 
Consider a situation in which a block is kept on a rough horizontal surface on which a 
variable horizontal force ' ?? ' is acting. 
 
 
At every value of ' ?? ' resistance force that is friction force ( ?? ) offered by rough 
horizontal surface is calculated and graph is plotted. 
In part 'OA' of the graph block remains at rest w.r.t. ground and value of friction force (f) 
is equal to applied force ' ?? ' and is called static friction force. 
Beyond ' A ' graph represents the situation in which block is moving w.r.t ground. In this 
situation it is found that friction force acting on the block becomes constant and is called 
kinetic friction force. 
KEY POINT 
? Friction do not opposes motion instead it opposes Relative motion to the surface 
applying friction force. 
? Friction acts along the surface in contact. 
 
STATIC FRICTION FORCE 
If there is a tendency of relative slipping (only tendency and not actual) between two 
surfaces in contact then the friction force acting between them is called static friction 
force. 
It is a variable force whose value is equal to requirement to stop relative slipping till it 
reaches its limiting value. 
Laws of static friction: 
?? st 
 law: Static friction force acting between two surfaces in contact does not depend on 
the area of contact. 
2nd law: Maximum value of static friction (Limiting friction) is directly proportional to 
the normal force acting between the two surfaces. 
(?? ?? ) ? ?? 
(?? ?? )
max
= ?? s
N f
s
= Limiting friction ; ?? s
= coefficient of static friction  
KINETIC FRICTION 
?  Kinetic friction comes into picture when relative slipping occurs. 
? It acts in direction opposite to relative velocity. 
? Its value is constant. 
Laws of kinetic friction: 
?? st 
 law: Kinetic friction acting between two surfaces in contact does not depend on area 
of contact. 
2nd law: The value of kinetic friction force is directly proportional to the normal force 
acting between the two surfaces in contact. 
?? ?? ? ?? ?? ?? = ?? ?? ?? ?? ?? = coefficient of kinetic friction 
 
FEW IMPORTANT POINTS 
(1) The value of ?? k
 is always less than ?? s
(?? k
< ?? s
) from experimental observation. 
(2) If only the coefficient of friction (?? ) is given by a problem then ?? ?? - ?? ?? = ?? 
(assumption for) 
(3) The value of ?? ?? and ?? ?? is independent of surface area it depends only on surface 
properties of the contact surface. 
(4) ?? k
 is independent of relative speed. 
(5) ?? s
&?? k
 are properties of a given pair of surfaces i.e. for wood-to-wood combination ?? 1
, 
then for wood-iron ?? 2,
 and so on. 
Example. A block of mass 1 kg is at rest on a rough horizontal surface, where 
coefficients of static and kinetic friction are 0.2 and 0.15. Find the frictional forces if a 
horizontal force (?? = 9.8 m/s
2
) 
 
 
(a) F = 1 N 
(b) F = 1.96 N 
(c) F = 2.5 N is applied on a block 
Solution: Maximum force of friction is the timing friction f
sm
= 0.2 × 1 × 9.8 N = 1.96 N 
(a) For F = 1 N, F < f
sm
 
So, the body is at rest means static friction is present, and hence  f
s
= F = 1 N 
(b) For ?? = 1.96 N,  F = f
cm
= 1.96 N. The block is about to slide, therefore f = 1.96 N 
(c) For = 2.5 N, So F > f
sm
 
Now the body is sliding and kinetic friction acts 
Therefore f = f
k
= ?? k
N = ?? k
mg= 0.15 × 1 × 9.8 = 1.47 N 
Example. Find unit vector in the direction of friction force acting on the block 
?? ?
?? = 7??ˆ - 2??ˆ, ?? ?
?? = 3??ˆ + ??ˆ 
Solution: ?? ?
?? /?? = 3??ˆ + ??ˆ - (7??ˆ - 2??ˆ) 
 
On ???? /?? of ?? ?? ˆ
?? = -?? ˆ
?? /?? = -
4
5
??ˆ +
3
5
??ˆ 
Objective: Kinetic friction opposes relative velocity. 
Example. ?
5mg/s
 Im 
 
After what time will it stop? if ?? s
= 0.5, ?? k
= 0.4 
Solution: ?? = 20 
 ? f
k
= ?? k
× N
f
k
= 0.4 × 20
f
k
= 8 N
 ? a = -4 m/s
2
 ? ?? = 0, ?? = -4, ?? = 5
0 = 5 - 4?? ?? =
5
4
 sec. 
 
 
Example. ?
6 N
2 kg 
 
Starting from rest ?? s
= 0.5, ?? k
= 0.4, find friction acting on the block? 
Solution: 
 
Page 5


FRICTION 
FRICTION 
When things rub against each other or try to move past each other, they create friction. 
Friction is like a force that pushes back against this movement, trying to stop it or slow it 
down. It's what makes it hard to slide a heavy box across the floor or stop a car when you 
press the brakes. And here's a neat thing: the friction on one object is matched by an equal 
and opposite friction on the other object, following Newton's third law of motion. 
Types of Friction: 
Before we proceed further into a detailed account of frictional phenomena, it is advisable 
to become familiar with different types of frictional forces. All types of frictional 
phenomena can be categorized into dry friction, fluid friction, and internal friction. 
1. Dry Friction: It exists when two solid un-lubricated surfaces are in contact under 
the condition of sliding or tendency of sliding. It is also known as Coulomb 
friction. 
 Fluid Friction 
1. Internal Friction 
Frictional forces exist everywhere in nature and result in a loss of energy that is primarily 
dissipated in the form of heat. Wear and tear of moving bodies is another unwanted 
result of friction. Therefore, sometimes, we try to reduce their effects - such as in 
bearings of all types, between the piston and the inner walls of the cylinder of an IC 
engine, the flow of fluid in pipes, and aircraft and missile propulsion through the air. 
Though these examples create a negative picture of frictional forces, there are other 
situations where frictional forces become essential and we try to maximize the effects. It 
is the friction between our feet and the earth's surface, which enables us to walk and run. 
Both the traction and braking of wheeled vehicles depend on friction. 
Consider a situation in which a block is kept on a rough horizontal surface on which a 
variable horizontal force ' ?? ' is acting. 
 
 
At every value of ' ?? ' resistance force that is friction force ( ?? ) offered by rough 
horizontal surface is calculated and graph is plotted. 
In part 'OA' of the graph block remains at rest w.r.t. ground and value of friction force (f) 
is equal to applied force ' ?? ' and is called static friction force. 
Beyond ' A ' graph represents the situation in which block is moving w.r.t ground. In this 
situation it is found that friction force acting on the block becomes constant and is called 
kinetic friction force. 
KEY POINT 
? Friction do not opposes motion instead it opposes Relative motion to the surface 
applying friction force. 
? Friction acts along the surface in contact. 
 
STATIC FRICTION FORCE 
If there is a tendency of relative slipping (only tendency and not actual) between two 
surfaces in contact then the friction force acting between them is called static friction 
force. 
It is a variable force whose value is equal to requirement to stop relative slipping till it 
reaches its limiting value. 
Laws of static friction: 
?? st 
 law: Static friction force acting between two surfaces in contact does not depend on 
the area of contact. 
2nd law: Maximum value of static friction (Limiting friction) is directly proportional to 
the normal force acting between the two surfaces. 
(?? ?? ) ? ?? 
(?? ?? )
max
= ?? s
N f
s
= Limiting friction ; ?? s
= coefficient of static friction  
KINETIC FRICTION 
?  Kinetic friction comes into picture when relative slipping occurs. 
? It acts in direction opposite to relative velocity. 
? Its value is constant. 
Laws of kinetic friction: 
?? st 
 law: Kinetic friction acting between two surfaces in contact does not depend on area 
of contact. 
2nd law: The value of kinetic friction force is directly proportional to the normal force 
acting between the two surfaces in contact. 
?? ?? ? ?? ?? ?? = ?? ?? ?? ?? ?? = coefficient of kinetic friction 
 
FEW IMPORTANT POINTS 
(1) The value of ?? k
 is always less than ?? s
(?? k
< ?? s
) from experimental observation. 
(2) If only the coefficient of friction (?? ) is given by a problem then ?? ?? - ?? ?? = ?? 
(assumption for) 
(3) The value of ?? ?? and ?? ?? is independent of surface area it depends only on surface 
properties of the contact surface. 
(4) ?? k
 is independent of relative speed. 
(5) ?? s
&?? k
 are properties of a given pair of surfaces i.e. for wood-to-wood combination ?? 1
, 
then for wood-iron ?? 2,
 and so on. 
Example. A block of mass 1 kg is at rest on a rough horizontal surface, where 
coefficients of static and kinetic friction are 0.2 and 0.15. Find the frictional forces if a 
horizontal force (?? = 9.8 m/s
2
) 
 
 
(a) F = 1 N 
(b) F = 1.96 N 
(c) F = 2.5 N is applied on a block 
Solution: Maximum force of friction is the timing friction f
sm
= 0.2 × 1 × 9.8 N = 1.96 N 
(a) For F = 1 N, F < f
sm
 
So, the body is at rest means static friction is present, and hence  f
s
= F = 1 N 
(b) For ?? = 1.96 N,  F = f
cm
= 1.96 N. The block is about to slide, therefore f = 1.96 N 
(c) For = 2.5 N, So F > f
sm
 
Now the body is sliding and kinetic friction acts 
Therefore f = f
k
= ?? k
N = ?? k
mg= 0.15 × 1 × 9.8 = 1.47 N 
Example. Find unit vector in the direction of friction force acting on the block 
?? ?
?? = 7??ˆ - 2??ˆ, ?? ?
?? = 3??ˆ + ??ˆ 
Solution: ?? ?
?? /?? = 3??ˆ + ??ˆ - (7??ˆ - 2??ˆ) 
 
On ???? /?? of ?? ?? ˆ
?? = -?? ˆ
?? /?? = -
4
5
??ˆ +
3
5
??ˆ 
Objective: Kinetic friction opposes relative velocity. 
Example. ?
5mg/s
 Im 
 
After what time will it stop? if ?? s
= 0.5, ?? k
= 0.4 
Solution: ?? = 20 
 ? f
k
= ?? k
× N
f
k
= 0.4 × 20
f
k
= 8 N
 ? a = -4 m/s
2
 ? ?? = 0, ?? = -4, ?? = 5
0 = 5 - 4?? ?? =
5
4
 sec. 
 
 
Example. ?
6 N
2 kg 
 
Starting from rest ?? s
= 0.5, ?? k
= 0.4, find friction acting on the block? 
Solution: 
 
N = 20
 ? (f
s
)
max.
= 0.5 × 20 = 10
 ? f = 6 N [Friction force acts only according to requirement] 
 
Example. ?
F
 ??? 
vkg 
Starting from rest ?? s
= 0.5, ?? k
= 0.4 
Solution: 
 
(f
s
)
max.
= 10 N 
f
k
= 8 N 
F Initial velocity f type f value acceleration 
At rest 
6 N 0 Static 6 0 
9 N 0 Static 9 0 
12 N 0 Kinetic 8 2 m/s
2
 
Started moving 
6 N +(? 0) Kinetic 8 -1 m/s
2
 
9 N 0 Static 9 0 
10 N 0 Static 10 0 
 
 
 
 
Example.