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I would like to know why dry frictional force does not depend on speed(assuming that the heat generated by friction is small so it does not alter the coefficient of friction).

Let me explain how I think about dry friction. When I slide one object on another than their small irregularities on surfaces are bashing to each another and this causes the friction. If I higher the sliding speed than those irregularities will bash to each other more frequently so it seams to me that the friction should rise. But Coulomb's friction force says that the force does not depend on speed.

So can anybody give me intuitive explanation why is that?

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I don't know extremely much about tribology, but here my two cents:

"If I higher the sliding speed than those irregularities will bash to each other more frequently so it seams to me that the friction should rise. "

Yes, more frequently, but the interaction time is also shorter. If you move your object on a surface from point $a$ to $b$, the number of molecular encounters which sum up to the resistance will not depend on how fast after each other they are. It will only depend on how long the way is you take.

If you'd want to argue that the friction should depend on the velocity, you should argue why the effect of the collision would be different for different speeds of the colliding molecules.

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