Properties of Friction
❑ It resists tendency of motion Friction
or relative motion.
❑ It can adjust it’s direction. Limiting
❑ It can adjust it’s magnitude Friction
also. Kinetic
❑ Kinetic Friction is generally Friction
less than maximum value of
Static Friction i.e. Limiting
Friction.
Applied Force
Is Friction Unwanted?
We cannot always say so. Sometimes, it’s unwanted like in
machine elements friction causes loss of power and thus a
decreased efficiency. However, without existence of Friction,
it would be impossible to walk or drive vehicles etc. You may
slip while walking on ice because of less friction. A rider is
highly likely to slip on wet road because of lesser friction.
Types of Friction
Static Friction
❑ It is the Friction acting between bodies when there is no
slipping between them.
❑ It acts so as to oppose the tendency of motion.
❑ It can adjust it’s magnitude upto a certain limit.
❑ Friction depends on smoothness of surfaces but there is
sudden increment of friction when both bodies are very
smooth. Like friction between glass and glass is
approximately double that between glass and wood.
Types of Friction
Limiting Friction
❑ It is the maximum limit of Static Friction. If the applied force is
increased beyond Limiting Friction, the body will start slipping.
❑ It’s magnitude depends on material or roughness of bodies in
contact & is proportional to Normal Reaction between surfaces
under consideration.
❑ It does not depend on contact area of surfaces.
❑ fL = μSN where μs is Coefficient of Static Friction
and N is Normal Reaction.
❑ Also, fS ≤ fL ⇒ fS ≤ μSN
Types of Friction
Kinetic/Dynamic Friction
❑ It is the friction which acts when there is relative slipping
between the bodies & tries to stop it.
❑ It’s magnitude depends on material or roughness of bodies in
contact & is proportional to Normal Reaction between surfaces
under consideration.
❑ It does not depend on contact area of surfaces.
❑ fK = μKN. Also generally, fK < fL i.e. μK < μS
❑ If not mentioned we generally assume μ = μK = μS
❑ μK & μS can also be greater than 1. Like between dry copper & dry
copper is 1.6.
Deciding direction of Friction
To decide direction of friction, we will assume friction to be
absent. We will then try to predict the motion of body or
bodies. Friction will now act so as to oppose the relative
motion or to produce motion as predicted.
Direction of
Acceleration F
Deciding direction of Friction
Rear Wheel Drive Car a
Angle of Friction
Reaction
Normal
Friction
Angle of Repose
θ
Q) Can you accelerate a car on a frictionless horizontal road
by putting more petrol in the engine? Can you stop a car
going on a frictionless horizontal road by applying brakes?
Ans : No. No.
Q) Two cars of unequal mass use similar tyres. If they are
moving at the same initial speed, the minimum stopping
distance
a) is smaller for the heavier car.
b) is smaller for the lighter car.
c) is same for both cars.
d) depends on the size of car.
Q) A car starts from rest on a half kilometer long bridge. The
coefficient of friction between the tires and the road is 1.
Show that it is not possible for the car to cross the bridge in
less than 10 seconds.
Q) A body of mass ‘M’ is kept on a rough horizontal surface
(friction coefficient = ). A person is trying to pull the body
by applying a horizontal force but the body is not moving.
The net force by the surface on the body is ‘F’ where
a) F = Mg b) F = Mg
c) Mg F Mg 𝟏 + 𝛍𝟐 d) Mg F Mg 𝟏 + 𝛍𝟐
Q) The coefficient of static friction between a block of mass
2 kg and an incline is S = 4/3.
i) What can be the maximum angle ‘’ of the incline with
horizontal so that the block does not slip on the incline?
ii) If the incline makes an angle of 370 with the horizontal,
find the frictional force acting on the block.
Q) When a horizontal force of 15 N is applied on a block of
mass 2.5 kg kept on horizontal surface, it is about to slide.
Also it is found that if force is increased to 20 N, it takes 2
seconds to slide through 6 meters, starting from rest.
Determine the coefficients of friction.
Q) Assuming strings and pulley
to be light, for the 10 kg block,
find: 10 kg
i) acceleration
ii) frictional force acting on it 𝛍 = 0.5
iii) tension in the connected
string
5 kg
Q) A body of mass 2 kg is lying on a rough inclined plane of
inclination 370. Coefficient of static friction between body
and incline is 1. Find the minimum magnitude of force
needed to move the block
i) up the incline ii) down the incline
Q) A small block of mass 0.1 kg lies on a fixed inclined plane
PQ which makes an angle ‘’ with the horizontal. A
horizontal force of 1 N acts on the block as shown in figure.
The block remains stationary if: Q
a) = 450 without friction in play.
b) > 450 & a frictional force acts on
block towards ‘P’. 1N
c) > 450 & friction acts towards ‘Q’.
d) < 450 & friction acts towards ‘Q’.
O P
HW Ans : a, c
Q) A block of mass ‘m’ placed on a horizontal surface is being
pushed by a force ‘F’ making an angle ‘’ with the vertical. If
the friction coefficient is ‘’, how much force is needed to get
the block about to move. Discuss the situation for tan < .
Q) Find the maximum value of M/m in the situation shown in
figure so that the system remains at rest. Friction coefficient
at both contacts is ‘’ and angle of incline with horizontal is
‘’. Discuss the situation for tan < .
𝛍
HW Ans :
𝐬𝐢𝐧𝛉−𝛍𝐜𝐨𝐬𝛉
The system will remain at
rest for all M/m values.
Q) A block of mass ‘m’ is placed on a surface with a vertical
cross section given by y = x3/6. If the coefficient of friction
between the block and the surface is 0.5, the maximum
height ‘y’ above the ground at which the block can be placed
without slipping is:
a) 1/6 m b) 2/3 m c) 1/3 m d) 1/2 m
Q) The friction coefficient between the board and the floor
shown in figure is ‘𝛍’. Find the maximum force that the man
(of mass M) can exert on the rope so that the board (of mass
m) does not slip on the floor.
Q) A block of mass 2 kg is pushed against a rough vertical
wall with a force of 40 N. The coefficient of static friction
between block and wall is 0.5. Another horizontal force of
15 N, parallel to the wall, is applied on this block. Will the
block move? If yes, in which direction? If no, what is the
frictional force exerted by the wall on the block?
Q) Consider the situation shown in figure. The string
connecting the 1 kg blocks is free from tension initially.
Consider the hanger to be massless. If a mass ‘m’ is placed in
hanger, what will be the tension in the string connecting the
1 kg blocks for i) m = 0.5 kg ii) m = 0.3 kg iii) m = 0.1 kg
1 kg 1 kg
𝛍 = 0.2 𝛍 = 0.2
Hanger
1 kg 1 kg
𝛍 = 0.2 𝛍 = 0.2
Hanger
1 kg 1 kg
𝛍 = 0.2 𝛍 = 0.2
Hanger
1 kg 1 kg
𝛍 = 0.2 𝛍 = 0.2
Hanger
Q) A block is kept on a rough inclined plane of inclination
370. Coefficient of static friction between the block and
incline is 0.5. What should be the range of horizontal
acceleration of the incline for the block to not slip on the
incline? Take g = 10 m/s2.
HW Ans :
20/11 m/s2
to 20 m/s2
Q) A block of mass ‘m’ is kept on a rough horizontal surface.
The coefficient of static friction between the block and the
surface is ‘𝛍’. The block is to be slid by applying minimum
force on it. What should be the magnitude of force on it?
Q) Consider the situation shown
in figure. The horizontal surface m
below the bigger block is
smooth. The coefficient of F
friction between the blocks is M m
‘’. Find the minimum and
maximum value of applied
horizontal force ‘F’ such that the
smaller blocks remain at rest
relative to the bigger block.
m
F
M m
m
F
M m
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.5 whereas the ground is smooth. If a
horizontal force of 12 N is applied on 4 kg block, then find
the acceleration of both blocks.
2 kg
12 N
4 kg
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.1 whereas the ground is smooth. If a
horizontal force of 12 N is applied on 4 kg block, then find
the acceleration of both blocks.
2 kg
12 N
4 kg
HW Ans : a2 = 1 m/s2 right and a4 = 2.5 m/s2 right
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.3 and between 4 kg block and ground is 0.4. If
a horizontal force of 18 N is applied on 4 kg block, then find
the acceleration of both blocks.
2 kg
18 N
4 kg
HW Ans : a2 = a4 = 0
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.3 and between 4 kg block and ground is 0.1. If
a horizontal force of 18 N is applied on 4 kg block, then find
the acceleration of both blocks.
2 kg
18 N
4 kg
HW Ans : a2 = a4 = 2 m/s2 right
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between all
surfaces in contact is 0.1. If a horizontal force of 18 N is
applied on 4 kg block, then find the acceleration of both
blocks.
2 kg
18 N
4 kg
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.6 and between 4 kg block and ground is 0.5. If
a horizontal force of 24 N is applied on 2 kg block, then find
the acceleration of both blocks.
24 N
2 kg
4 kg
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 1.4 and between 4 kg block and ground is 0.5. If
a horizontal force of 24 N is applied on 2 kg block, then find
the acceleration of both blocks.
24 N
2 kg
4 kg
HW Ans : a2 = a4 = 0
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 1.4 and between 4 kg block and ground is 0.2. If
a horizontal force of 24 N is applied on 2 kg block, then find
the acceleration of both blocks.
24 N
2 kg
4 kg
HW Ans : a2 = a4 = 2 m/s2 right
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.8 and between 4 kg block and ground is 0.2. If
a horizontal force of 24 N is applied on 2 kg block, then find
the acceleration of both blocks.
24 N
2 kg
4 kg
HW Ans : a2 = 4 m/s2 right and a4 = 1 m/s2 right
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.8 and between 4 kg block and ground is 0.3. If
a horizontal force of 12 N (towards right) is applied on 2 kg
block and 24 N (towards left) on 4 kg block as shown in
figure, then find the acceleration of both blocks.
12 N
2 kg
24 N
4 kg
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 1.0 and between 4 kg block and ground is 0.1. If
a horizontal force of 12 N (towards right) is applied on 2 kg
block and 24 N (towards left) on 4 kg block as shown in
figure, then find the acceleration of both blocks.
12 N
2 kg
24 N
4 kg
HW Ans : a2 = a4 = 1 m/s2 left
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.6 and between 4 kg block and ground is 0.1. If
a horizontal force of 12 N (towards right) is applied on 2 kg
block and 24 N (towards left) on 4 kg block as shown in
figure, then find the acceleration of both blocks.
12 N
2 kg
24 N
4 kg
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.4 and between 4 kg block and ground is 0.3. If
a horizontal force of 12 N (towards right) is applied on 2 kg
block and 24 N (towards left) on 4 kg block as shown in
figure, then find the acceleration of both blocks.
12 N
2 kg
24 N
4 kg
HW Ans : a2 = 2 m/s2 right and a4 = 0
Q) Two blocks of masses 2 kg and 4 kg are placed one over
another as shown in figure. Coefficient of friction between
the blocks is 0.4 and between 4 kg block and ground is 0.1. If
a horizontal force of 12 N (towards right) is applied on 2 kg
block and 24 N (towards left) on 4 kg block as shown in
figure, then find the acceleration of both blocks.
12 N
2 kg
24 N
4 kg
HW Ans : a2 = 2 m/s2 right and a4 = 2.5 m/s2 left
Q) Figure shows two blocks in contact sliding down an
inclined surface of inclination 300. The friction coefficient
between the block of mass 2 kg and incline is ‘1’ and that
between 4 kg block and incline is ‘2’. Find the acceleration
of 2 kg block if (Take g = 10 m/s2):
i) 1 = 0.2 and 2 = 0.3
ii) 1 = 0.4 and 2 = 0.3
300
300 300
300 300
Q) A classroom demonstration of Newton’s First Law is as
follows. A glass is covered with a plastic card and a coin is
placed on the card. The card is given a quick strike and the
coin falls in the glass.
i) Should the friction coefficient between the card and the
coin be small or large?
ii) Should the coin be light or heavy?
iii) Why does the experiment fail if the card is gently
pushed?
Q) Consider the situation shown in figure. The wall is smooth
but the surfaces ‘A’ and ‘B’ in contact are rough. The friction
on ‘B’ due to ‘A’ in equilibrium is
a) upward b) downward c) zero
d) the system can’t remain in equilibrium.
F
HW Ans : (d) A B
Q) Suppose all the surfaces in the previous question are
rough. The direction of friction on ‘B’ due to ‘A’
a) is upward b) is downward c) is zero
d) depends on masses of ‘A’ and ‘B’.
HW Ans : (a)
Q) A circular disc with a groove
along it’s diameter is placed
horizontally on a rough surface.
A block of mass 1 kg is placed
as shown in figure. The
coefficient of friction between
block and all surfaces of groove 25 m/s2
in contact is 0.4. The disc has an
acceleration of 25 m/s2 left.
Find the acceleration of block
with respect to the disc.
Given = 370. HW Ans : 10 m/s2
