If two objects are in contact and at rest and a force applied to one object does not cause motion, then this force must be balanced by an opposing and equal size frictional force so that the resultant force is zero.

If the applied force is increased a point is reached when motion just starts. When this occurs there must be a resultant force acting on the object and thus the applied force must have become greater than the frictional force.

The value of the frictional force that has to be overcome before motion starts is called the limiting frictional force. The following are the basic laws of friction:

# Law 1. The frictional force is always in such a direction as to oppose relative motion and is always tangential to the surfaces in contact.

# Law 2. The frictional force is independent of the apparent areas of the surfaces in contact.

# Law 3. The frictional force depends on the surfaces in contact and its limiting value is directly proportional to the normal reaction between the surfaces.

The coefficient of static friction Us is the ratio of the limiting frictional force F to the normal reaction N:

Us = F/N

The coefficient of kinetic friction Uk is the ratio of the kinetic frictional force F to the normal reaction N:

Uk = F/N

Typical values for steel sliding on steel are 0.7 for the static coefficient and 0.6 for the kinetic coefficient.

If a block of steel of mass 2 kg rests on a horizontal surface, the coefficient of static friction being 0.6, what horizontal force is needed to start the block in horizontal motion? Take g to be 9.8 m/s2.

The normal reaction force N = mg. The maximum, i.e. limiting, frictional force is F = uN = 0.6 × 2 × 9.8 = 11.8 N. Any larger force will give a resultant force on the block and cause it to accelerate while a smaller force will be cancelled out by the frictional force and give no resultant force and hence no acceleration. Thus the force which will just be on the point of starting the block in motion is 11.8 N.

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