Question

according to law of friction it is said that friction force between to object doesnt depends on area of contact but according to modern theory of friction it is said that friction force is due to adhessive force between the surfaces. so more the area of contact more will be the friction force. so what do you think does friction force depends on area of contact?

Answer 1

According to me,
We know
Frictional force = (mu)(normal Force) and only these two two factors should be held accountable for frictional force.

Answer 2

Actually, friction can depend on a variety of things, ranging from the relative speeds the bodies are movies from, the roughness or smoothness, the nature of the bodies, temperature, etc. Apart from the groves and ridges, friction does depend on the adhesive force between molecules. Try rubbing two magnets against one another. Even if their surfaces are smooth, you'll see that friction is quite strong there. Polished metals with clean surfaces put together create enormous amounts of friction. Metallic bond orbitals quickly overlap between there surfaces causing relative motion quite difficult. Molecules of my sneakers however don't seem the create bonds with a smooth marble floor in a posh office building. You could just slide away and never stop if you started. So all surfaces don't "click" that way.

For your question however, let us consider a rectangular block of dimensions L,L,2L. You will recall that the friction depends on normal reaction, i.e, how hard it presses into the ground. Let us consider it being put on the ground on the L,L surface first and then on the L,2L surface next. Both positions experience equal normal force, which is their weight.

In the first case, the area in contact is half the second case, so friction is half the value. But the pressure is double as it is resting on a smaller area. So net friction: 1/2*2*friction=friction.

In the second case, area of contact is double but the pressure is only half as it is resting on a larger area. So net friction is again: 2*1/2*friction=friction.

As you can see, greater area contributes to greater friction, but the pressure exerted on the ground is smaller by the same factor. So, on the whole, it does not depend on area.

There is an exception though. It is independent of area when the surface it is placed on isn't altered in any way. While your weight doesn't change when your wear those spiked boots for football, they do give you better grip on the ground because the spikes being sharp, dig into the ground, thereby increasing friction.

Hope that helps.