## Illustration 5.1: Static and Kinetic Friction

Fapplied = N | m = kg

How does friction change our analysis? Well, friction is due to the fact that objects, even smooth ones, are actually very bumpy on a microscopic level. Because of this, atoms from each surface are in such close contact that they form chemical bonds with each other. These bonds need to be broken in order for motion to occur. Restart.

The direction of the frictional force is opposite to the direction of motion, and the magnitude of the frictional force is proportional to the magnitude of the normal force, N. There are two kinds of frictional forces: static and kinetic friction.

Static friction is the force when there is no relative motion between surfaces in contact. Conversely, kinetic friction is the force when there is relative motion between surfaces in contact. We represent the coefficient of friction by the Greek letter μ, and use subscripts corresponding to static and kinetic friction, respectively: μs and μk. It is always the case that μs > μk.

Consider what happens when you pull on a stationary block up to the point where there is still no motion. Set the mass to 100 kg and vary Fapplied. The frictional force fs matches Fapplied up to the frictional force's maximum value, fs; max = μs N = 392 N. After that the frictional force dramatically decreases, the block accelerates, and the frictional force becomes the kinetic friction of motion, fk = μk N.

So what are μs and μk? Well, given that there is no motion until when Fapplied = 392 N, fs; max is approximately 392 N. Therefore, given that the normal force is 980 N, μs = 0.4. Now there is an acceleration when Fapplied = 392 N. Since the change in v = 9.8 m/s in 5 seconds, a = 1.96 m/s2. Given this, ma = Fapplied - fk = Fapplied - μk N. Therefore, after some algebra, μk = 0.2.

Illustration authored by Mario Belloni.
Script authored by Steve Mellema and Chuck Niederriter and modified by Mario Belloni.

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