# Frictional force and Normal force

## Main Question or Discussion Point

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)

Related Classical Physics News on Phys.org
arildno
Homework Helper
Gold Member
Dearly Missed
Yes. bundles of it, experimentwise.

It is an empirical relationship

arildno
Homework Helper
Gold Member
Dearly Missed
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
Homework Helper
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
Homework Helper
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: