The Laws of Static Friction

Abstract

The relation F = aRn between the frictional force and normal reaction is found to hold for fibers, and it is proposed to replace Amontons' law by this form. The friction index, n, is found to lie between 0.80 and unity. The significance of this relation is discussed in terms of the cohesion theory of friction. A satisfactory interpretation can be given if it is assumed that the areas of contact are determined by the visco-elastic properties of the surfaces. A compari son of this relation with that of Gralén's is made. Two important consequences arise from the adoption of this friction law: the frictional force is no longer independent of the apparent area of contact; and, in the case of friction of a string or fiber wrapped around a cylinder, the so- called "coefficient of friction" depends upon the initial tension and also upon the cylinder radius.