Friction

• Let us consider the example, a body of mass m at rest on a horizontal table. The force of gravity (mg) is cancelled by the normal reaction force (N) of the table. Now, assume a force F is applied horizontally to the body, if the applied force is small it may not be enough to move the body. But, if the applied force F is the only external force on the body, it must move with acceleration , however small.

• Clearly, the body remains at rest because some other force comes into play in the horizontal direction and opposes the applied force F, resulting in zero net force on the body. This force  parallel to the surface of the body in contact with the table is known as frictional force, or simply friction (below fig. (a)).

Static and sliding friction:
(a) Impending motion of the body is opposed by static friction. When external force exceeds the maximum limit of static friction, the body begins to move.
(b) Once the body is in motion, it is subject to sliding or kinetic friction which opposes relative motion between the two surfaces in contact. Kinetic friction is usually less than the maximum value of static friction.

• The subscript stands for static friction to distinguish it from kinetic friction  (above fig. (b)). Note that static friction does not exist by itself. When there is no applied force, there is no static friction. It comes into play the moment there is an applied force. As the applied force F increases,  also increases, remaining equal and opposite to the applied force (up to a certain limit), keeping the body at rest. Hence, it is called static friction.

• Static friction opposes impending motion. The term impending motion means motion that would take place (but does not actually take place) under the applied force, if friction were absent.

• As the applied force exceeds a certain limit, the body begins to move. It is found experimentally that the limiting value of static friction is independent of the area of contact and varies with the normal force(N) approximately as :

------ (1)

where  is a constant of proportionality depending only on the nature of the surfaces in contact. The constant  is called the coefficient of static friction. The law of static friction may thus be written as

------ (2)

• If the applied force F exceeds  the body begins to slide on the surface. It is found experimentally that when relative motion has started, the frictional force decreases from the static maximum value . Frictional force that opposes relative motion between surfaces in contact is called kinetic or sliding friction and is denoted by . Kinetic friction, like static friction, is found to be independent of the area of contact. Further, it is nearly independent of the velocity. It satisfies a law similar to that for static friction:

------ (3)

where  the coefficient of kinetic friction, depends only on the surfaces in contact. As mentioned above, experiments show that  is less than . When relative motion has begun, the acceleration of the body according to the Second Law is  . For a body moving with constant velocity, . If the applied force on the body is removed, its acceleration is and it eventually comes to a stop.

• The laws of friction given above do not have the status of fundamental laws like those for gravitational, electric and magnetic forces. They are empirical relations that are only approximately true. Yet they are very useful in practical calculations in mechanics.

• Thus, when two bodies are in contact, each experiences a contact force by the other. Friction, by definition, is the component of the contact force parallel to the surfaces in contact, which opposes impending or actual relative motion between the two surfaces. Note that it is not motion, but relative motion that the frictional force opposes.

Rolling friction:

• A body like a ring or a sphere rolling without slipping over a horizontal plane will suffer no friction, in principle. At every instant, there is just one point of contact between the body and the plane and this point has no motion relative to the plane. In this ideal situation, kinetic or static friction is zero and the body should continue to roll with constant velocity.

• In practice, this will not happen and some resistance to motion (rolling friction) does occur, i.e. to keep the body rolling, some applied force is needed. For the same weight, rolling friction is much smaller (even by 2 or 3 orders of magnitude) than static or sliding friction. This is the reason why discovery of the wheel has been a major milestone in human history.

• Rolling friction again has a complex origin, though somewhat different from that of static and sliding friction. During rolling, the surfaces in contact get momentarily deformed a little, and this results in a finite area (not a point) of the body being in contact with the surface. The net effect is that the component of the contact force parallel to the surface opposes motion.

• We often regard friction as something undesirable. In many situations, like in a machine with different moving parts, friction does have a negative role. It opposes relative motion and thereby dissipates power in the form of heat, etc.

• Lubricants are a way of reducing kinetic friction in a machine. Another way is to use ball bearings between two moving parts of a machine (below fig. (a)). Since the rolling friction between ball bearings and the surfaces in contact is very small, power dissipation is reduced. A thin cushion of air maintained between solid surfaces in relative motion is another effective way of reducing friction (below fig. (b)).

Some ways of reducing friction.
(a) Ball bearings placed between moving parts of a machine.
(b) Compressed cushion of air between surfaces in relative motion.

In many practical situations, however, friction is critically needed. Kinetic friction that dissipates power is nevertheless important for quickly stopping relative motion. It is made use of by brakes in machines and automobiles.

Similarly, static friction is important in daily life. We are able to walk because of friction. It is impossible for a car to move on a very slippery road. On an ordinary road, the friction between the tyres and the road provides the necessary external force to accelerate the car.