How to find the coefficient of kinetic friction?

Learn and understand the equation used to find the coefficient of friction. The magnitude of the force of kinetic friction is f (k) = u (k) N, where N is the normal force. The coefficient therefore is f (k) / N. It is a dimensionless number, and its value depends upon the surface. Smooth surfaces have lower values than rougher ones. For example, for a glass-upon-glass surface, it may be 0.6, and for ice-on-ice it may be 0.03. These numbers are approximate depending on whether the surfaces are clean, wet or sanded, for example. 2 Use the equation given in Step 1 to find the coefficient if you have a problem where you are given f (k) and N. Plug in the values and solve directly for u (k). If you are not given the frictional and normal forces, proceed to Step 33. Calculate f (k) and N by using Newton's second law F = ma. Find the sum of all of the forces acting upon the moving object. Remember that for no acceleration, the net forces will be equal to zero. Remember also that f (k) opposes movement, and so will be opposite in sign to the force making the object move. 4 Draw a free body diagram to find the horizontal and vertical components of the forces acting upon the object in Step 3. A standard example is a box being pulled by a rope or a person pulling another person on a sled. Practice Steps 3 and 4 by studying the diagram to the left, and writing out the appropriate equations. Shown is a pulling force, F, along with a frictional force, f (k), a normal force, N, and a gravitational force, mg. There is no acceleration. The sum of all the forces: F + N + f (k) + mg = 0.

The sum of all the horizontal forces: Fh - - f (k) = 0 (there is no acceleration).

The sum of all of the vertical forces: Fv + N - - mg = 0 (the object is not moving up or down).

Use f = u (k) N, Fv = Fsin (theta), and Fh = Fcos (theta) to solve the second and third equations simultaneously to find the coefficient of friction u (k). The answer is u (k) = Fcos (theta) / (mg - - Fsin (theta)).