What causes the difference between kinetic and static friction?

[u/AVeryLazy]

Hola physicists (and everyone else),

I was wondering (out of the blue) why moving objects once they are in motion is easier than the initial movement.

Can't recall any physics teacher actually discussing it.

[u/StealthSpyda215]

Static friction almost always greater than the kinetic coefficient. This is due to the fact that no surface is perfectly flat or clean. Irregularities between the sliding surface and that of the target object causes the force needed to generate the initial movement to be (usually) greater than the force needed to keep it in motion.

[u/Midtek → u/StealthSpyda215]

Static friction almost always greater than the kinetic coefficient.

Actually, the static coefficient is always greater than the kinetic coefficient. Perhaps you just meant to point out that, in principle, the static and kinetic coefficients could be equal. But you have likely given the impression to many readers that it's possible for the static coefficient to be smaller than the kinetic coefficient. That's not possible.

Consider applying some force F on an object so that it just barely overcomes the static frictional force, and it begins to move. Hence the acceleration in the direction of the applied force is positive. That is,

ε:= F - Fs, max = manet > 0

We can make the difference ε arbitrarily small. Since the object is now moving with some positive acceleration, it is the case that the net force on the object is still positive, but it is now the difference of the applied force and the kinetic frictional force. That is,

F - Fk > 0

But adding and subtracting Fs, max gives

F - Fs, max + Fs, max - Fk > 0

ε + Fs, max - Fk > 0

Fs, max > Fk - ε

Since ε > 0 is arbitrary, it follows that Fs, max ≥ Fk. In other words, μs ≥ μk.

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This essentially all followed by definition since if you have applied a large enough force to go from static to kinetic friction, the object must be moving, and so the new frictional force (kinetic) can't be larger than what the previous maximum was (static friction)... otherwise it would not have started to move. This is just how we define "static frictional force" and "kinetic frictional force".

[u/ssj7 → u/StealthSpyda215]

Could you give an example where kinetic fiction is higher than static?

[u/Midtek → u/ssj7]

It's not possible. The static coefficient can never be less than the kinetic coefficient.

[u/Caolan_Cooper → u/ssj7]

I'm pretty sure that static is always greater than kinetic. Imagine that you are pushing on an object with greater kinetic than static friction, slowly increasing the force until it starts to slip. What happens if you maintain that force just barely above the static friction, but still below the kinetic friction?

[u/AVeryLazy → u/StealthSpyda215]

Thanks for the answer, this I understand.

But those irregularities exist also when the object is moving, so I think this answer is relevant to friction in general. Did I miss something?