# Is friction a function of surface area? What is the microscopic workings of friction?

I know the friction is given by the following equation $$\mu F_N=F_f$$

which tells me friction is independent of surface area, but how do I characterize it as such if I want to add surface area into my equation what would the equation be?

We all know friction is a function of the normal reaction exerted on the body and the coefficient of friction. How is this coefficient derived, any equation? Or is it all experimental? Any quantum mechanical explanation for friction?

• Friction laws depend very much on the system you are dealing with. There are no general formulas and the experimental reality of it is messy and hard to reproduce because even thin deposits on surfaces can greatly change friction properties (which is why lubrication works so well). The simple area independent law is more of a high school fiction about friction than a useful way of dealing with the problem in a technical setting. – CuriousOne Sep 21 '15 at 6:34
• But it doesn't answer the question? what ARE the microscopic laws governing friction and its equation if any? – Russell Yang Sep 21 '15 at 6:54
• I like the word that CuriousOne used: "messy". If you want to get into the details of friction, it really gets messy and can involve details about surface impurity or oxide layers, the surface smoothness or morphology, air humidity, etc. And it really depends a lot on the particular materials you're considering. If you really want to delve into the nitty-gritty details of friction, you should probably be consulting a materials science discussion forum rather than a physics forum. As for the equation that you presented, I believe that it is basically an empirical approximation. No deep physics. – user93237 Sep 21 '15 at 7:08
• @SamuelWeir I see that helps alot, at least now I know the topics I am delving into. – Russell Yang Sep 21 '15 at 7:15
• @RussellYang: I understand your frustration. I can only tell you that I was taught about as much in my university classes in physics about fraction as I had to learn for my high school physics exam, and that was the very formula that you are citing. Friction is not a big topic for physicists because there is no general theory that one can teach. It lives at a very ugly crossroads of molecular dynamics, thermodynamics and chemistry and one can spend a lifetime on it without getting much traction. Samuel got it right, the material scientists might be a better resource. – CuriousOne Sep 21 '15 at 7:53

The most common model for dry friction is the Coulomb Friction, which results in the friction equation you give.

The model is based on considering the asperities (roughness) of the two surfaces and the force required to lift asperities on one surface over the other. If assume that the contact points/area is approximately constant why find that the fiction is independent of the contact area as the increase in contact area is countered by a decrease in the load each point must lift (assuming constant total mass).

Also note that $\mu$ is an experimental value for two particular surfaces. Coulomb friction is a fairly macroscopic model and does not consider the real interaction between the surfaces, which would be very difficult to measure over a large area.

In many cases Coulomb's model doesn't hold and friction is proportional to contact area. This is particularly true for lubricated contacts and sometimes when there is significant deformation of the surface.

• Thank you for your answer! However may I ask what other mathematical or descriptive models are there of friction? – Russell Yang Sep 21 '15 at 22:22
• sorry didnt tag u @nivag – Russell Yang Sep 22 '15 at 2:18
• I'm not really an expert in friction modelling, but there are various models that account for lubrication depending on the pressure involved and how well lubricated the surface is. For dry friction there are more advanced models that account for things like stick-slip and hysteresis effects. Some review type papers can be found here and here. I suspect there are also models for plowing and other deformation, but I don't really know about these. – nivag Sep 22 '15 at 8:41
• thanks for the articles, I am only interested between dry friction of the slipping of paper that account for pressure. Any other inputs will definitely be helpful, especially on other dry friction models – Russell Yang Sep 22 '15 at 8:43

Friction coefficients are experimental... For a friendly discussion of microscopic friction, I refer you to chapter 12 section 1,2,3 of Feynman Lectures on Physics. Here is a link:

http://www.feynmanlectures.caltech.edu/I_12.html#Ch12-S2

Hope that helps