Introduction:

Between metals, minute welds form and break as one piece slides over the other. But it is hard to see how this can explain friction between dissimilar surfaces. Surprisingly, for some surfaces, the more smooth they are, the more friction. The polishing of the surfaces allows more contact. For fluids, the frictional force varies with speed and is often proportional to a power of the speed. Friction is partially physical and partially chemical and is the subject of much research.

Because of the complexity, elementary physics texts describe friction empirically. Since frictional forces are approximately proportional to the force pressing the surfaces together (the normal force), we call the proportionality constant the coefficient of friction. Since there is a considerable difference between the force required to start an object moving (against friction) and the force to keep it moving, we distinguish between the static and kinetic frictional forces:

The proportionality constants are usually less than one, but some tires have been manufactured which have coefficients greater than one. The static frictional force is less than, or equal to, the product on the right because there can be many static frictional forces. Consider these cases for a 5 kg wood block on a horizontal surface for which is 0.73 and is 0.55 . The normal force is (5)(9.8) = 49 N and a horizontal force F_app is applied to the block:

Case 1: F_app = 0. There is no frictional force.
Case 2: F_app = 2 N. The frictional force is 2 N, just enough to keep the block from moving
Case 3: F_app = 15 N. The frictional force is 15 N.

Case 4: F_app = 35.77 N. The frictional force is 35.77 N, and could have been computed using the coefficient of friction times the normal force. The block is on the verge of motion, which is the only time the equation for static friction can be used.
 

Case 5: F_app = 45 N. The block moves, and the frictional force decreases to the kineticvalue. The kinetic equation can be used since the surfaces are in relative motion. The frictional force is (0.55)(49) = 26.95 N. The net force is 45 - 26.95 and the block accelerates. The kinetic equation can always be used if there is relative motion between the surfaces.

Even this simple description of friction makes problems much more complex. Often, you cannot easily decide if a body moves, or even which way if it does. Examples are the best way to learn to solve problems, provided you do the examples - don't just read them!

Example 1: A block sliding on a table

Example 2: Two blocks on two inclines

Example 3: A strange cart revisited

Here are some rather simple problems for which I have supplied the answers.  Can you get the answers?