Frictional force and Normal force

[manimaran1605]

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]

Yes. bundles of it, experimentwise.

 

[dauto]

It is an empirical relationship

 

[arildno]

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]

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]

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:

https://en.wikipedia.org/wiki/Tire_load_sensitivity