<P> The Coulomb approximation mathematically follows from the assumptions that surfaces are in atomically close contact only over a small fraction of their overall area, that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact), and that the frictional force is proportional to the applied normal force, independently of the contact area (you can see the experiments on friction from Leonardo da Vinci). Such reasoning aside, however, the approximation is fundamentally an empirical construct . It is a rule of thumb describing the approximate outcome of an extremely complicated physical interaction . The strength of the approximation is its simplicity and versatility . Though in general the relationship between normal force and frictional force is not exactly linear (and so the frictional force is not entirely independent of the contact area of the surfaces), the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems . </P> <P> When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example, adhesive tape resists sliding even when there is no normal force, or a negative normal force). In this case, the frictional force may depend strongly on the area of contact . Some drag racing tires are adhesive for this reason . However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications . </P> <P> As of 2012, a single study has demonstrated the potential for an effectively negative coefficient of friction in the low - load regime, meaning that a decrease in normal force leads to an increase in friction . This contradicts everyday experience in which an increase in normal force leads to an increase in friction . This was reported in the journal Nature in October 2012 and involved the friction encountered by an atomic force microscope stylus when dragged across a graphene sheet in the presence of graphene - adsorbed oxygen . </P> <P> Despite being a simplified model of friction, the Coulomb model is useful in many numerical simulation applications such as multibody systems and granular material . Even its most simple expression encapsulates the fundamental effects of sticking and sliding which are required in many applied cases, although specific algorithms have to be designed in order to efficiently numerically integrate mechanical systems with Coulomb friction and bilateral or unilateral contact . Some quite nonlinear effects, such as the so - called Painlevé paradoxes, may be encountered with Coulomb friction . </P>

Why are the coefficients of static and kinetic friction different