# Frictional force is independent of the area of contact

1. Aug 9, 2009

### monty37

one of the laws of friction states that the frictional
force is independent of the area of contact,and velocity,how true is this?
my book says this particular law is only approximately true.

2. Aug 9, 2009

### Pupil

Re: friction

As far as I know, when one says friction does not depend on the area of contact, they do it by looking at the equation for the force of friction.

$$F = \mu F_n$$

So the force of friction depends only on the unit-less constant Mu and normal force. Neither of these things depends on the area, so we say the force of friction doesn't depend on area.

Someone might be able to give a deeper understanding of why, but that's how I've always thought of it.

3. Aug 9, 2009

### dx

Re: friction

It's possible to understand roughly in this way: Divide the surface area of the floor into small pieces. Now, the number of these tiny pieces that are pushing the block is proportional to A, the contact area, but the force that each of these little pieces applies to the object is proportional to the pressure exerted on the floor at that point, i.e. to N/A (where N is the normal force), so the total friction force is proportional to A(N/A) = N.

4. Aug 9, 2009

### Staff: Mentor

Re: friction

Another way of looking at it: all of the properties of the contact patch, including its area, are contained in the friction coefficient.

5. Aug 9, 2009

### rcgldr

Re: friction

The book is correct, it's just an approximation that doesn't apply in real life, especially if the objects get reasonably small. This is discussed and demonstrated as an off topic subject in the second half of video #2 in this series on gyroscopes:

http://www.gyroscopes.org/1974lecture.asp

In that video, the smaller but otherwise identical (same density) "cubes" have a much higher static coefficient of friction.

In the case of tires, load sensitivity causes coefficient of friction to decrease with load, so larger tires are better until weight, drag, or other factors become an issue. (Larger tires also allow for more heat dissapation in race car).

6. Aug 10, 2009

### J_Cervini

Re: friction

The way I remember it ('88 grad) - you have two types of friction:
Static - this is related to the force necessary to get a stationary object to move from rest.
Dynamic - this is related to the force necessary to sustain a moving object at a constant velocity. Does the question pertain to both phases of friction or just one?

7. Aug 11, 2009

### Shooting Star

Re: friction

That would imply that the co-efficient of friction between the same pair of materials would vary with the area of contact, which is not the case.

This makes good sense.

8. Aug 11, 2009

### KLoux

Re: friction

Actually, this is the case. It probably varies with materials, but one example is car tires on asphalt. High performance cars have wider tires to increase the size of the contact patch and in turn the coefficient of friction. Maybe this is a different case since the rubber is compliant and can be squeezed into the surface of the not-perfectly-smooth asphalt, but my college physics book also states that the coefficient of friction takes into account the area (and other factors, like whether or not one material is compliant and can squeeze into cracks of the other material). If your area of contact changes, you might need a new coefficient of friction, depending on the materials, allowable error, etc.

-Kerry

9. Aug 11, 2009

### Pupil

Re: friction

This is something that bothered me a bit (like your tire example). How is Mu calculated between material A and A'? Testing it would be an easy method. Suppose A and A' are made of the same materials, but A' is twice the length and width of A. Would A''s coefficient of friction be larger than A's in the real world? If so, then Mu is dependent on the area, and thus the force of friction does as well.

10. Aug 11, 2009

### Nabeshin

Re: friction

These kind of experiments are common in a first year mechanics course, and show that the coefficient of friction is not correlated with the area of contact. Of course, when I performed the experiments it was in a crumby little lab and any small effects would have been completely surpassed by experimental error, so at most I can say is that there is a very loose correlation if at all.

The example of a racecar's tires was explained to me to have to due with things other than just normal sliding friction. It was explained to me that because the tires got so hot from friction, the rubber became, in a sense, sticky, which gave rise to a different force which is correlated with contact area.

11. Aug 11, 2009

### Shooting Star

Re: friction

No, it is not the case in the regime where the laws of static and dynamic friction are valid -- otherwise those laws woudn't exist. I was not consideiing rolling friction, so the tire scenario is not very pertinent to my point..

This point is well exemplified by Pupil in post #9.

12. Aug 11, 2009

### rcgldr

Re: friction

They're not laws, but instead simplifications of a real life situation, similar to Bernoulli equation being a simplified case of the more accurate Navier-Stokes equations. Please watch the 2nd half of the video #2:

http://www.gyroscopes.org/1974lecture.asp

A clean flat plate with 4 solid blocks of varying sizes is angled upwards, and the larger blocks begin sliding well before the smaller blocks. The smaller blocks exhitbit a higher coefficient of friction with the flat plate, demonstrating some form of load senstitivy (the smaller blocks exert a smaller force per unit area).

From wiki:

though in general the relationship between normal force and frictional force is not exactly linear :

http://en.wikipedia.org/wiki/Friction

13. Aug 11, 2009

### Staff: Mentor

Re: friction

The tire scenario is a static friction scenario. Yes, it is usually true that static friction does not vary with contact area, but the OP said:
...and static friction in tires is one example where it is not true.

I suppose there is no single set of equations that people generally refer to for friction, but one could write one with separate terms for how friction force varies with area. In cases where it doesn't those terms would simply cancel out, similar to the way Bernouli's equation is used.

14. Aug 12, 2009

### monty37

Re: friction

when the area of contact becomes lesser,pressure increases and then the law does not
hold true,and is this not the case for all kinds of friction:rolling,sliding,static,dynamic?

15. Aug 18, 2009

### Shooting Star

Re: friction

(Sorry for the delayed post.)
I believe that applies to all the laws of science. The point was that the equation for static fiction holds quite true within a narrow regime. Or does it? The video was most illuminating.
Yes, my oversight. I was thinking of something else.
Could you give a simple example where the area is explicitly involved and which would reduce to an area-independent equation for simple cases?