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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: μ_s and μ_k. It is always the case that μ_s > μ_k.

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 F_applied. The frictional force f_s matches F_applied up to the frictional force's maximum value, f_{s; max} = μ_s N = 392 N. After that the frictional force dramatically decreases, the block accelerates, and the frictional force becomes the kinetic friction of motion, f_k = μ_k N.

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

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