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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 $F=\mu N$?

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marked as duplicate by sammy gerbil, Qmechanic Apr 14 '17 at 20:49

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    $\begingroup$ I am surprised at your statement that the dependence on Normal Force is NOT intuitive. To me, it is entirely intuitive. If you imagine at the microscopic level of detail of the two mating surfaces you can visualize bumps of uneven surface. As the pieces slide against each other, they have to lift up over a bump here and there and this is in the direction of the Normal force. Also note that this frictional force ($F$ in your equation) is negative in that it opposes the force to accelerate and move the sliding objects. $\endgroup$ – K7PEH Apr 14 '17 at 14:43
  • $\begingroup$ Possible duplicate of How is frictional force dependent on normal reaction? $\endgroup$ – sammy gerbil Apr 14 '17 at 15:30
  • $\begingroup$ See also Why is the equation for friction so simple? $\endgroup$ – sammy gerbil Apr 14 '17 at 15:31

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