QUIZRR 1
FRICTION
3
3 .1 . CON T A CT FORCE
When two bodies are kept in contact, electromagnetic forces act between the charged particles at the
surfaces of the bodies. As a result, each body exerts a contact force on the other.
3 .2 . FRICT I ON
The perpendicular component of the contact force is called the normal contact force and the parallel
component is called friction.
Friction is not a fundamental force, as it is derived from electromagnetic force between charged
particles, including electrons, protons, atoms and molecules and so cannot be calculated from first
principles, but instead must be found empirically. When contacting surfaces move relative to each other,
the friction between the two surfaces converts kinetic energy into thermal energy or heat.
Contrary to earlier explanation, kinetic friction is now understood not to be caused by surface
roughness but by chemical bonding between the surfaces.
Surface roughness and contact area, however, do affect kinetic friction for micro-and nano-scale
objects where surface area forces dominate inertial forces.
3 .3 T Y PES OF FRICT I ON
Fj = Force of friction
F
W
Ff = øN
N
1. Kinetic friction
2. Static friction
Co e f f i c i e n t o f f r ic t i o n
The coefficient of friction (COF), also known as a frictional coefficient or friction coefficient, symbolized
by the Greek letter ø, is a dimensionless scalar value which describes the ratio of the force of friction
between two bodies and the force pressing them together.
The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient
of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from
near zero to greater than oneăunder good conditions, a tire on concrete may have a coefficient of friction
of 1.7.
FRICTION
,2 QUIZRR
3 .4 L A WS OF FRICT I ON
1. If the bodies slip over each other, the force of friction is given by
k kN
Where
k is the force of friction
N is the normal contact force
øk is the coefficient of friction between the surfaces
2. The direction of kinetic friction on a body is opposite to the velocity of this body with respect
to the body applying the force of friction.
3. If the bodies do not slip over each other, the force of friction is given by
s = øsN
(Causing Movement)
Static Friction Dynamic Friction
Net Force
e
orc
F
et
N
f = Friction force Fapp = Applied force
Applied Force (Fapp ) = ø.N
Friction Force
Fr
ic
tio
n
Fo
rc
e
N = Normal force between object and surface
=
A
pp
lie
d
Fo
rc
e
Fs =øsN fd =ødN
where
Fs = static force of friction
øs = coefficient of static friction between the bodies
N = normal force between them
The direction and magnitude of static friction are such that the condition of no slipping between
the bodies is ensured.
If the applied force is small, the friction force will be equal to it. As the applied force is
increased friction force also increases to a maximum limit and if additional force is applied the
bodies start slipping.
4. The frictional force fk or fs does not depend on the areas of contact. It depend on normal
contact force only.
3 .5 T H E N ORM A L FORCE
Block on a ramp (top) and corresponding free body diagram of just the block (bottom).
The normal force is defined as the net force compressing two parallel surfaces together, and its
FRICTION
, QUIZRR 3
direction is perpendicular to the surfaces. In the simple case of a mass resting on a horizontal surface,
the only component of the normal force is the force due to gravity, where. In this case, the magnitude
of the friction force is the product of the mass of the object, the acceleration due to gravity, and the
coefficient of friction. However, the coefficient of friction is not a function of mass or volume; it depends
on the material. For instance, a large aluminium block has the same coefficient of friction as a small
aluminium block. However, the magnitude of the friction force itself depends on the normal force, and
hence the mass of the block.
If an object is on a level surface and the force tending to cause it to slide is horizontal, the normal
force between the object and the surface is just its weight, which is equal to its mass multiplied by the
acceleration due to earthÊs gravity, g. If the object is on a tilted surface such as an inclined plane, the
normal force is less, because less of the force of gravity is perpendicular to the face of the plane.
Therefore, the normal force, and ultimately the frictional force, is determined using vector analysis,
usually via a free body diagram. Depending on the situation, the calculation of the normal force may
include forces other than gravity.
A block on a ramp
m
Free body diagram
of just the block
j
i
Ff
N
Ex a m p l e 1
Find the minimum force which needs to applied to the Y
incline of mass M having a cube of mass m placed on its
rough surface with ø = (2 tan ). So that the block m starts
to slide. m
F
X
O
M
Z
FRICTION
, 4 QUIZRR
Solution :
Let us first Calculate the acceleration
F
When the blocks are not sliding against each other, a
m M
Pseudo force = m a (ă i) {on block m}
mF
= i 90ă
m M
mgsin
Parallel forces to the plane are mg
mF
mg sin and
M
m a
mF
2 N
(Resultant Force) Fr mg sin 2 ma
m M mgcos
for just sliding Fr = fs (max)
mg
2 mgsin
mF
mg cos
2
(mg sin )2 +
m M
mg cos 2 mg sin 2 m M 2
F Ans.
m2
Ex a m p l e 2
Find :
(a) acceleration of each block.
(b) tension with string T. m 2m
A B
(c) friction forces.
øA = 2/3 øB = 1/3
45Ĉ 45Ĉ
Solution :
Concept : The block starts sliding down the plane if
2 mg sin 45Ĉ > fs (max)B + fs (max)A + mg sin 45Ĉ
OR component weights along the inertia > maximum static friction.
Net pulling force > Net retarding force
First frictional force balance the component of wt. down the plane if it cannot, then tension is
provided by string.
Concept : First frictional force balances the component of weight down the plane, if it
cannot, then tension is provided by string
In this case
FRICTION
FRICTION
3
3 .1 . CON T A CT FORCE
When two bodies are kept in contact, electromagnetic forces act between the charged particles at the
surfaces of the bodies. As a result, each body exerts a contact force on the other.
3 .2 . FRICT I ON
The perpendicular component of the contact force is called the normal contact force and the parallel
component is called friction.
Friction is not a fundamental force, as it is derived from electromagnetic force between charged
particles, including electrons, protons, atoms and molecules and so cannot be calculated from first
principles, but instead must be found empirically. When contacting surfaces move relative to each other,
the friction between the two surfaces converts kinetic energy into thermal energy or heat.
Contrary to earlier explanation, kinetic friction is now understood not to be caused by surface
roughness but by chemical bonding between the surfaces.
Surface roughness and contact area, however, do affect kinetic friction for micro-and nano-scale
objects where surface area forces dominate inertial forces.
3 .3 T Y PES OF FRICT I ON
Fj = Force of friction
F
W
Ff = øN
N
1. Kinetic friction
2. Static friction
Co e f f i c i e n t o f f r ic t i o n
The coefficient of friction (COF), also known as a frictional coefficient or friction coefficient, symbolized
by the Greek letter ø, is a dimensionless scalar value which describes the ratio of the force of friction
between two bodies and the force pressing them together.
The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient
of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from
near zero to greater than oneăunder good conditions, a tire on concrete may have a coefficient of friction
of 1.7.
FRICTION
,2 QUIZRR
3 .4 L A WS OF FRICT I ON
1. If the bodies slip over each other, the force of friction is given by
k kN
Where
k is the force of friction
N is the normal contact force
øk is the coefficient of friction between the surfaces
2. The direction of kinetic friction on a body is opposite to the velocity of this body with respect
to the body applying the force of friction.
3. If the bodies do not slip over each other, the force of friction is given by
s = øsN
(Causing Movement)
Static Friction Dynamic Friction
Net Force
e
orc
F
et
N
f = Friction force Fapp = Applied force
Applied Force (Fapp ) = ø.N
Friction Force
Fr
ic
tio
n
Fo
rc
e
N = Normal force between object and surface
=
A
pp
lie
d
Fo
rc
e
Fs =øsN fd =ødN
where
Fs = static force of friction
øs = coefficient of static friction between the bodies
N = normal force between them
The direction and magnitude of static friction are such that the condition of no slipping between
the bodies is ensured.
If the applied force is small, the friction force will be equal to it. As the applied force is
increased friction force also increases to a maximum limit and if additional force is applied the
bodies start slipping.
4. The frictional force fk or fs does not depend on the areas of contact. It depend on normal
contact force only.
3 .5 T H E N ORM A L FORCE
Block on a ramp (top) and corresponding free body diagram of just the block (bottom).
The normal force is defined as the net force compressing two parallel surfaces together, and its
FRICTION
, QUIZRR 3
direction is perpendicular to the surfaces. In the simple case of a mass resting on a horizontal surface,
the only component of the normal force is the force due to gravity, where. In this case, the magnitude
of the friction force is the product of the mass of the object, the acceleration due to gravity, and the
coefficient of friction. However, the coefficient of friction is not a function of mass or volume; it depends
on the material. For instance, a large aluminium block has the same coefficient of friction as a small
aluminium block. However, the magnitude of the friction force itself depends on the normal force, and
hence the mass of the block.
If an object is on a level surface and the force tending to cause it to slide is horizontal, the normal
force between the object and the surface is just its weight, which is equal to its mass multiplied by the
acceleration due to earthÊs gravity, g. If the object is on a tilted surface such as an inclined plane, the
normal force is less, because less of the force of gravity is perpendicular to the face of the plane.
Therefore, the normal force, and ultimately the frictional force, is determined using vector analysis,
usually via a free body diagram. Depending on the situation, the calculation of the normal force may
include forces other than gravity.
A block on a ramp
m
Free body diagram
of just the block
j
i
Ff
N
Ex a m p l e 1
Find the minimum force which needs to applied to the Y
incline of mass M having a cube of mass m placed on its
rough surface with ø = (2 tan ). So that the block m starts
to slide. m
F
X
O
M
Z
FRICTION
, 4 QUIZRR
Solution :
Let us first Calculate the acceleration
F
When the blocks are not sliding against each other, a
m M
Pseudo force = m a (ă i) {on block m}
mF
= i 90ă
m M
mgsin
Parallel forces to the plane are mg
mF
mg sin and
M
m a
mF
2 N
(Resultant Force) Fr mg sin 2 ma
m M mgcos
for just sliding Fr = fs (max)
mg
2 mgsin
mF
mg cos
2
(mg sin )2 +
m M
mg cos 2 mg sin 2 m M 2
F Ans.
m2
Ex a m p l e 2
Find :
(a) acceleration of each block.
(b) tension with string T. m 2m
A B
(c) friction forces.
øA = 2/3 øB = 1/3
45Ĉ 45Ĉ
Solution :
Concept : The block starts sliding down the plane if
2 mg sin 45Ĉ > fs (max)B + fs (max)A + mg sin 45Ĉ
OR component weights along the inertia > maximum static friction.
Net pulling force > Net retarding force
First frictional force balance the component of wt. down the plane if it cannot, then tension is
provided by string.
Concept : First frictional force balances the component of weight down the plane, if it
cannot, then tension is provided by string
In this case
FRICTION
