Amontons and Coulombs Law

Amontons law is purely empirical and results from the interplay of complex processes that we have only recently begun to understand. At first sight, Amontons finding that the friction force is independent of the surface area is quite surprising. 

1) Leonardo da Vinci, 1452-1519. Italian scientist, inventor, and artist. 

tc is the yield stress during shear, that is, the maximum lateral stress the contact can bear. Bowden and Tabor assumed that this is equal to the shear strength of the material itself The true contact area Areai depends on the compliance of the materials. For soft, rubberlike materials, the real contact area will be larger than that for hard 

With these methods, it was found that the friction force is, in fact, proportional to the actual contact area. This implies that the true contact area must increase linearly with load. To illustrate how this is possible, we consider two extreme cases. In the first 

The true contact area is independent of the apparent contact area and increases linearly with increasing load. Typical values for the yield stress of metals are 10 -10 Pa. Thus, for a 10 kg cubic block of a metal, the true area of contact expected from this model is of the order of (0.3-1 mm).  

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