# Why does friction does not depend upon area of contact? [duplicate]

Why does friction does not depend upon area of contact ? Now we know that friction=(coefficient of friction)*Normal.So also is, why does friction arise.Is it because of the irregularities of a surface or because of the electrostatic forces in between the surfaces?

## marked as duplicate by sammy gerbil, Jon Custer, heather, AccidentalFourierTransform, user12029 Feb 2 '17 at 2:30

I will quote Klepnner here ,

It may seem strange that friction is independent of the area of contact.The reason is that the actual area of contact on an atomic scale is a minute fraction of the total surface area.Friction occures because of the interatomic forces at these minute regions of atomic contact.The fraction of the geometric area in atomic contact is proportional to the normal force devided by the geometric area.If the normal force is doubled ,the area of atomic contact is doubled and the friction is twice as large .However ,if the geometric area is doubled while the normal force remains the same ,the fraction of area in atomic contact is halved and the actual area in atomic contact hence the fiction force remains constant.

• That's one interpretation that hinges on a linear model. But realistically frictional force is very complex and nonlinear to the point it cannot be accurately predicted except under very controlled conditions that force a more linear relationship. Friction also depends on other parameters such as temperature and other intervening materials such as lubricants. There are regimes of friction: static and dynamic equally difficult to model and almost impossible to model in the transition. – docscience Jan 27 '17 at 15:24
• @docscience Regarding linearity, there is indeed a very accurate linearity between friction and normal force for small normal forces/pressures - which is the most usual situation. Few models are fitting in the entire range, and this is one of them - nothing wrong in stating linearity, because we assume everyday cases as long as nothing else is mentioned in the question. – Steeven Jan 27 '17 at 15:37
• @Steeven I agree linear models in general get you linearized answers over small displacements, forces, etc. But in the real world nothing polices scale of motion. I guess the point I failed to include in my last comment. If you consider the realistic nonlinear behavior of frictional forces, those forces indeed do depend on contact area. – docscience Jan 27 '17 at 15:43

Why does friction does not depend upon area of contact ?

Because, even though surface gripping would scale with contact area, so does other parameters that are in the friction formula. Area therefore appears more times in the expression and turns out to cancel out completely, leaving the formula as $f=\mu n$.

For low normal forces, one would expect friction to be proportional to contact area $A$ and also to the pressure $q$ that presses the surfaces together (the normal pressure):

$$f \propto Aq$$

Normal pressure is normal force over area, $q=n/A$, so plugging this in causes $A$ to cancel out.

why does friction arise.Is it because of the irregularities of a surface or because of the electrostatic forces in between the surfaces?

Both. You can both have mechanical interlocking - as velcro - but also adhesion of one material onto the other - like glue - which tries to prevent sideways sliding. Friction is then the force needed to rip this adhesion free again.

I find it useful to think of the surfaces as very rough with "stickey" peaks and valleys. Peaks can grip into valleys and when pressed together like that they don't want to slide