Surely, if you have 2 surfaces interlocking then a horizontal force would also result affect the force of friction. It seems unintuitive that friction is only proportional to normal force.  Is there an intuitive proof of $F=\mu N$?
It is a general concept that horizontal forces can only influence physical quantities along horizontal direction; similarly vertical force can produce acceleration etc. only along vertical direction. This is the same concept that helps us study projectile motion as a combination of two independent motions. If this relation is universally true, how come, then friction depend on a force which normal to it?
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