Law of friction

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.Learn more with VidyaBharti Educational Institutions.

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3. 3
Law of friction
Properties of frictional force
1. act along the surface between two bodiessurface between two bodies
2. act in a direction so as to oppose relative oppose relative
motionmotion of the surfaces.

4. 4
Limiting friction
If the block remains at rest,
f = F
A
The frictional force to be
overcome before it moves
is called limiting friction.
Frictional
force f
Applied
force F
A

5. 5
Limiting friction
Frictional
force f
Applied
force F
A
F
A
/ N f / N
0 0
1 1
2 2
3 3
4 3
5 3
Limiting friction = 3 NLimiting friction = 3 N

6. 6
Limiting friction
Frictional
force f
Applied
force F
A
Limiting friction = 3 NLimiting friction = 3 N
F
A
/ N
f / N
0 1 2 3 4 5
1
2
33
At rest Moving
Static Kinetic
friction friction

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Limiting friction
F
A
/ N
f / N
0 1 2 3 4 5
1
2
33
At rest Moving
Static Kinetic
friction friction
•Kinetic / Dynamic friction is
the frictional force acting on
an object when it is moving.
•Static friction is the frictional
force when the object is
stationary.

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From experiment, limiting
friction f is slightly greater
than kinetic friction f’.
i.e. f > f’

Suppose f = 3.1 N, f’ = 3N
A force of 3.1 N is required to
make the block move.
But once the block is moving,
a force of 3 N only is required
to keep the block moving.
Friction f
Applied force F
Static frictionKinetic friction
f’
f
For simplicity, take f = f’

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Law of friction
1. The limiting frictional force f is directly proportional to
the normal reaction N exerted by the surface.
i.e. f
∝
N or f = mN where m is a constant called
coefficient of limiting friction.
2. The kinetic frictional force f is directly proportional to
the normal reaction N exerted by the surface.
i.e. f’ ∝ N or f’ = m’N where m is a constant called
coefficient of kinetic friction.
Frictional force f
Applied
force F
A
Normal
reaction N
For simplicity, take f = f’ = mN and m = m’

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If the surface is smooth, m = 0 ⇒ f = 0 N
Coefficient of friction depends on the two
contacting materials.
For simplicity, take f = f’ = mN and m = m’
Rubber Concrete (Dry) m = 0.6 – 0.85
Rubber Concrete (Wet) m = 0.45 – 0.75
Frictional force does not depend on the
area of contact of the surfaces.

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A block of mass 2 kg starts from rest, sliding down a
rough inclined plane making an angle of 30
o
with the
horizontal. Length of plane is 8 m. It takes 4 seconds to
reach the bottom. Find the coefficient of kinetic
friction.
Solution:Solution:
t = 4 s, s = 8 m, u = 0 ms
-1
By s = ut + ½ at
2
8 = 0(4) + ½ a(4)
2
a = 1 ms
-2
mg sin 30
o
– f = ma
(2)(10)sin 30
o
– f = (2)(1)
f = 8 N
R = mg cos 30
o
= 17.32 N
By f = mR
8 = m(17.32)
m = 0.462
30
o
8 m
R
mg
f a

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For the following situation, find the least coefficient of
friction between the ground and the ladder.
N = 250 Newton
Take moment about A,
S x 4 sin 60
o
= 250 x 2 cos 60
o
S = 72.17 Newton
f = S = 72.17 Newton
The ladder is about to slip,
f = mN
72.17 = m x 250
m = 0.289
60
o
250 N
4

m
s
m
o
o
t
h
S
N
fA

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How to find coefficient of limiting friction? p 22
The coefficient of limiting friction, m, can be found by
placing the block on a surface and tilting the latter to an
angle q at which the block is just about to slip.
 Along the plane:
f = mg sin q --- (1)
 Perpendicular to the plane:
N = mg cos q --- (2)
 Since the block is just about to slip,
f = mN --- (3)
 Sub (3) into (1):
mN = mg sin q --- (4)
 (4)/(2):
m = tan q
q
mg
f
N
Hence, the coefficient of limiting friction is just tan q.

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