2.5 Friction

In the previous example, the frictional force was given in the problem’s information. Often, though, the frictional force must be calculated. An empirical formula exists for calculating the force of kinetic (or sliding) friction, which occurs when one object slides on another:

where m k (the Greek "mu sub k") is called the coefficient of kinetic friction, and N is the normal force. A similar equation describes the static frictional force, or the force parallel to two touching surfaces which exists when relative motion does not occur:

where m s is the coefficient of static friction. The coefficients of friction between two surfaces are unique to the surfaces, and calculated experimentally. Table 2.1 lists the approximate coefficients of friction for some common materials.

Table 2.1: Approximate Coefficients of Friction

 Surface Static Friction (m s) Kinetic Friction (m k) wood/wood 0.4 0.2 ice/ice 0.1 0.03 steel/steel (lubricated) 0.15 0.07 steel/steel (unlubricated) 0.7 0.6 rubber/dry concrete 1.0 0.8 rubber/wet concrete 0.7 0.5 rubber/other solid surfaces 1-4 1 teflon/teflon in air 0.04 0.04 teflon/steel in air 0.04 0.04 lubricated ball bearings < 0.01 < 0.01 synovial joints (in human limbs) 0.01 0.01

Notice that the kinetic frictional force is generally less than or equal to the static frictional force.