1

Law of friction

Properties of frictional force

1. act along the surface between two bodiessurface between two bodies2. act in a direction so as to oppose relative oppose relative motionmotion of the surfaces.

2

Limiting friction

If the block remains at rest,

f = FA

The frictional force to be overcome before it moves is called limiting friction. Frictional

force f

Applied force FA

3

Limiting friction

Frictional force f

Applied force FA

FA / N f / N

0 0

1 1

2 2

3 3

4 3

5 3Limiting friction = 3 NLimiting friction = 3 N

4

Limiting friction

Frictional force f

Applied force FA

Limiting friction = 3 NLimiting friction = 3 NFA / N

f / N

0 1 2 3 4 5

1

2

33

At rest Moving

Static Kineticfriction friction

5

Limiting friction

FA / N

f / N

0 1 2 3 4 5

1

2

33

At rest Moving

Static Kineticfriction 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.

6

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 friction Kinetic friction

f’f

For simplicity, take f = f’

7

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 = N where is a constant called co

efficient 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’ = ’N where is a constant called co

efficient of kinetic friction.

Frictional force f

Applied force FA

Normal reaction N

For simplicity, take f = f’ = N and = ’

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If the surface is smooth, = 0 ⇒ f = 0 N Coefficient of friction depends on the two

contacting materials.

For simplicity, take f = f’ = N and = ’

Rubber Concrete (Dry) 0.6 – 0.85

Rubber Concrete (Wet) 0.45 – 0.75

Frictional force does not depend on the area of contact of the surfaces.

9

A block of mass 2 kg starts from rest, sliding down a rough inclined plane making an angle of 30o 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 at2

8 = 0(4) + ½ a(4)2

a = 1 ms-2

mg sin 30o – f = ma(2)(10)sin 30o – f = (2)(1)f = 8 N

R = mg cos 30o = 17.32 N By f = R

8 = (17.32) = 0.462

30o

8 m

R

mg

f a

10

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 60o = 250 x 2 cos 60o

S = 72.17 Newton f = S = 72.17 Newton The ladder is about to slip,

f = N72.17 = x 250 = 0.289

60o

250 N

4 m

smoo

th

S

N

f A

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How to find coefficient of limiting friction? p 22 The coefficient of limiting friction, , can be found by

placing the block on a surface and tilting the latter to an angle at which the block is just about to slip.

Along the plane:

f = mg sin --- (1) Perpendicular to the plane:

N = mg cos --- (2) Since the block is just about to slip,

f = N --- (3) Sub (3) into (1):

N = mg sin --- (4) (4)/(2):

= tan

mg

f

N

Hence, the coefficient of limiting friction is just tan .