Applications of the theory of Solid, Static and Kinetic Friction

** Static Friction**

When a person walks along a road, he or she is prevented from slipping by the force of friction at the ground. In the absence of friction, for example on an icy surface, the person’s shoe would slip when placed on the ground. The friction force always opposes the motion of the shoe.

The Frictional force between the surface of a table and a block of wood A can be investigated by attaching one end of a string to A and the other to a scale-pan S,. The string passes over a fixed grooved wheel B. when small weights are added to S, the block does not move. The frictional force between the block and table is thus equal to the total weight on S together with the weight of S. when more weights are added, A does not move, showing that the frictional force has increased, but as the weight is increased further, A suddenly begins to slip. The friction force now present between the surfaces is called the limiting frictional force, and we are said to have reached limiting friction. The limiting frictional force is the maximum frictional force between the surfaces.

** Coefficient of Static Friction**

The normal reaction, R, of the table on A is equal to the weight of A. by placing various weights on A to alter the magnitude of R, we can find how the limiting frictional force F varies with R by the experiment just described. The results show that, approximately,

and µ is known as the coefficient of static friction between the two surfaces. The magnitude of µ depends on the nature of the two surface; for example, it is about 0.2 to 0.5 for wood on wood, and about 0.2 to 0.6 for wood on metals. Experiment also shows that the limiting frictional force is the same if the block A in Fig **** is turned on one side so that its surface area of contact with the table decreases, and thus the limiting frictional force is independent of the area of contact when the normal reaction is the same.

The coefficient of static friction, µ can also be found by placing the block A on the surface S, and then gently tilting S until A on the point of slipping down the plane, fig **** The static frictional force F is then equal to mg sin o where o is the angle of inclination of the plane to the horizontal, the normal reaction R is equal to mg cos0

**Kinetic Friction. Coefficient of Kinetic (Dynamic) Friction**

When brakes are applied to a bicycle, a frictional force is exerted between the moving wheels and brake blocks. In contrast to the case of static friction, when one of the objects is just on the point of slipping, the frictional force between the moving wheel and brake blocks is called a kinetic (or dynamic) frictional force. Kinetic friction thus occurs between two surfaces which have relative motion. The coefficient of kinetic (dynamic) friction, µ, between two surfaces is defined by the relation

Where F’ is the frictional force when the object moves with a uniform velocity and R’ is the normal reaction between the surfaces. Weights are added to the scale-pan, and each time A is given a slight push. At one stage A continues to move with a constant velocity, and the kinetic frictional force F is then equal to the total weight in the scale-pan together with the latter’s weight. On dividing F by the weight of A, the coefficient can be calculated. Experiment shows that, when weights are placed on A to vary the normal reaction R, the magnitude of the ratio F’/R is approximately constant. Results also show that the coefficient of kinetic friction between two given surfaces is less than the coefficient of static friction between the same surfaces, and that the coefficient of kinetic friction between two given surfaces is approximately independent of their relative velocity.

** Laws of Solid Friction**

Experimental results on solid friction are summarized in the laws of friction, which state:

- The frictional force between two surfaces opposes their relative motion.
- The frictional force is independent of the area of contact of the given surfaces when the normal reaction is constant.
- The limiting frictional force is proportional to the9 normal reaction for the case of static friction. The frictional force is proportional to the normal reaction for the case of kinetic (dynamic) friction, and is independent of the relative velocity of the surfaces.

** Theory of Solid Friction**

The laws of solid friction were known hundreds of years ago, but they have been explained only in comparatively recent years, mainly by F. P. Bowden and collaborators. Sensitive methods, based on electrical conductivity measurements, reveal that the true area of contact between two surfaces is extremely small, perhaps one ten thousandth of the area actually placed together for steel surfaces. This is explained by photographs which show that some of the atoms of a metal project slightly above the surface, making a number of crests or humps’. As Bowden has stated: ‘The finest mirror, which is flat to a millionth of a centimeter, would to anyone of atomic size look rather like the South Downs – valley and rolling hills a hundred or more atoms high.’ Two metal surfaces thus rest on each others projections when placed one on the other.

Since the area of actual contact is extremely small, the pressures at the points of contact are very high, perhaps 100 million kgf per m^{2} for steel surfaces. The projections merge a little under the high pressure, producing adhesion or ‘welding’ at the points, and a force which opposes motion is therefore obtained. This explains Law 1 of the laws of solid friction. When one of the objects is turned over, so that a smaller or larger surface is presented to the other object, measurements show that the small area of actual contact remains constant. Thus the frictional force is independent of the area of the surfaces, which explains Law 2. When the load increases the tiny projections are further squeezed by the enormous pressures until the new area of contact becomes big enough to support the load. The greater the load, the greater is the area of actual contact, and the frictional force is thus approximately proportional to the load, which explains Law 3.

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