Law of friction

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

2. Applied force FA Frictional force f Limiting friction • If the block remains at rest, f = FA • The frictional force to be overcome before it moves is called limiting friction.

3. Limiting friction Applied force FA Frictional force f Limiting friction = 3 N

4. At rest Moving Static Kinetic friction friction Limiting friction Applied force FA f / N 3 2 Frictional force f 1 0 1 2 3 4 5 FA / N Limiting friction = 3 N

5. f / N At rest Moving 3 2 1 0 1 2 3 4 5 FA / N Static Kinetic friction friction Limiting 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. Friction f Staticfriction Kinetic friction f f’ Applied force F • 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. For simplicity, take f = f’

7. Normal reaction N Law of friction Applied force FA 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 For simplicity, take f = f’ = mN andm = m’

8. For simplicity, take f = f’ = mN andm = m’ • If the surface is smooth, m = 0 ⇒ f = 0 N • Coefficient of friction depends on the two contacting materials. • Frictional force does not depend on the area of contact of the surfaces.

9. R f a mg 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: • 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 = mR 8 = m(17.32) m = 0.462 8 m 30o

10. S N f 250 N 60o 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 = mN 72.17 = m x 250 m = 0.289 smooth 4 m A

11. N f q mg 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 Hence, the coefficient of limiting friction is just tan q.