Why friction is independent of surface area?

Question

Every book says that friction is independent of surface area in contact. It is pretty obvious that equation for our friction doesn't have any "area term" in it.

But in some cases it seems counterintuitive. The definition of friction states that it is resisitive force emerged from attractive forces between molecules of the objects. Now lets imagine a cube made from say $1\times 1\,\,m^2$ plates. Now we place it on a rough surface. Only molecules which are on surface of the plate in contact, participate in creating friction (static or kinetic). Now we disassemble the cube in individual plates, and we make $3\times 2\,\,m^2$ rectangle out of it. Now all plates molecules in attration with the surface, so it seems that friction should be dependent on area, but it is not. Nearly all books I read dont give any satisfying explanation for it. So, my doubt is that why friction is independent of surface area, and would like explanation with my cube's context.

Answer 1

Every book says that friction is independent of surface area in contact. It is pretty obvious that equation for our friction doesn't have any "area term" in it.

The "area term" is built into the value of the normal (perpendicular) force, $N$, between the contacting surfaces. Think about $N$ being the pressure (force per unit area) on the surface times the contact area.

Therefore, if we increase the contact area for a given force (e.g., a given weight), the pressure on the contact area decreases so that the product of pressure and contact area, $N$, remains the same. Likewise, for a given force if we decrease the contact area the pressure increases so that the product, $N$, remains the same.

Hope this helps.

Answer 2

The reason is that the weight of the cube is now spread over a larger area of contact, so each part of every plate is now pressed more lightly in contact with the surface.

Answer 3

Friction does depend on the normal force. As the area gets bigger, the normal force per unit area and the friction per unit area get smaller: f = (f/A)A = [μ(N/A)]A = μN.