# Frictional force and Normal force

when a body is slided or move in a horizontal floor, the Frictional force is directly proportional to the Normal force acting on the body. Is there is any proof (emperically or Theoretically)

arildno
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Gold Member
Dearly Missed
Yes. bundles of it, experimentwise.

It is an empirical relationship

arildno
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Gold Member
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To be specific, the local frictional force has been establish to be proportional to the local point pressure.

This point pressure, roughly equals N/A, where N is normal force, A is area, so that the frictional FORCE equals k*(N/A)*A=kN, for k constant of proportionality.

HallsofIvy
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In fact, like most simple physics laws, it is a "first order" approximation. Any "reasonable" (analytic) function can be written as a power series, f(x)= a+ bx+ cx^2+ .... Obviously, if there were NO normal force holding object to surface, there is no friction so a= 0. Approximating the function by its linear approximation, f(x)= bx so f is proportional to x to the first order in x.

rcgldr
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In fact, like most simple physics laws, it is a "first order" approximation.
In the case of tires, there's a load sensitivity factor, reducing the coefficient of friction as the load increases. Wiki artcile, although this is for static friction: