Smooth surfaces are defined by the properties that when they are in contact, the surfaces is always perpendicular to their common tangent plane. It can, however, be verified experimentally that no surfaces are perfectly smooth and that whenever there is a tendency for two bodies which are in contact to move relative to each other, a force known as the force of friction tends to prevent the relative motion. The mathematical discussion of the force of friction depends on certain assumptions which are embodied in the so called laws of friction and are found to be in close agreement with experiments.

Law 1 When two bodies are in contact the direction of the forces of Friction on one of them at it's point of contact, is opposite to the the direction in which the point of contact tends to move relative to the other.

Law 2 If the bodies are in equilibrium, the force of Friction is just sufficient to prevent friction and may therefore be determined by applying the conditions of equilibrium of all the forces acting on the body.The amount of Friction that can be exerted between two surfaces is limited and if the forces acting on the body are made sufficiently great, motion will occur. Hence, we define limiting friction as the friction which is exerted when equilibrium is on the point of being broken by one body sliding on another. The magnitude of limiting friction is given by the following three laws.

Law 3 The ratio of the limiting friction to the Normal reaction between two surfaces depends on the substances of which the surfaces are composed and not on the magnitude of the Normal reaction.This ratio is usually denoted by .Thus if the Normal reaction is R, the limiting friction is For given materials polished to the same standard is found to be constant and independent of R. is called The Coefficient of friction

Law 4 The amount of limiting friction is independent of the area of contact between the two surfaces and of the shape of the surfaces, provided that the Normal reaction is unaltered.

Law 5 When motion takes place the direction of friction is opposite to the direction of relative motion and independent of velocity. The magnitude of the force of friction is in a constant ratio to the Normal reaction but this ratio may be slightly less than when the body is just on the point of moving.

It should be stressed that the above laws are experimental and are accepted as the basis for the mathematical treatment of friction. Modern theory suggests that the force of friction is in fact due to the non - rigidity of bodies. When one body rests on another, there is always an area of contact, which is much smaller than the apparent area and also depends on the the normal pressure between the bodies. Friction is considered to be due to the fusion of materials (of which the bodies are composed) over the area of contact. Therefore friction would be proportional to the area of contact and therefore proportional to the normal pressure as assumed in the above laws.

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