What Is the Coefficient of Friction?

Friction is the heat producing resistive force generated by the motion of two contacting surfaces against each other. It is indirectly the product of one of the four known fundamental forces. The friction of a system is impossible to predetermine strictly from theoretical first principles. Mathematically, the expression for friction includes a single constant that incorporates all causative factors — a coefficient of friction (COF), symbolized by the Greek letter, μ. The equation is simply written f_x = μ_xF, where f_x defines the form and measure of friction, while F is the perpendicular or "normal" force exerted by both surfaces, one upon the other.

All coefficients of friction are dimensionless, scalar quantities; individual contributing factors resist complete explanation or quantification. The fundamental force responsible for most friction is also the one that enables the formation of chemical bonds — the electrostatic force. On initial consideration, it might seem that gravity is the source of friction, since the downward force due to gravity is the source of the variable F. Actually, though, the coefficient is a measure of the "stickiness" between the two surfaces, and that is determined at the microscopic level by the electrical charges tending to prevent motion by “binding” them together. Such binding is a characteristic of adhesives used to cement two surfaces together.

That this is the case is well illustrated by the modern polymer, polytetrafluoroethylene (PTFE). Best known under its DuPont™ brand name, Teflon®, PTFE exhibits only the very weakly attractive London dispersion electrostatic forces. This gives PTFE a coefficient of friction among the "top three" known — approximately 0.05-0.10. If the coefficient of friction was the product of gravity, the chemistry of the surfaces would not matter, and such substances as would not be as economically important as they are.

There are ways of lowering friction without, in some sense, changing the materials from which the surfaces are made. Coefficient of friction for a system may be effectively lessened by providing a thin layer of lubricant. Alternatively, it is often possible to lower friction by inserting a blanket of gas between the surfaces, which lessens the apparent weight of the surface on top and eliminates manufacturing flaws, such as surface roughness. The change in effective weight lowers the normal force, while the lack of flaws changes the coefficient of friction; both mathematically lower the resultant force of friction. Engineers have utilized the gas-layer phenomenon to develop hovercraft for travel across both land and water surfaces.