How can friction work that way?
Ok, so you're willing to believe that the scientists and engineers who work with friction probably know what they're talking about. They've been saying for over 300 years that friction does not increase with increased contact area. If it isn't true then there's a Nobel prize waiting for the person who can show that they've been wrong for the last 300 years. They're probably not wrong, so how can this be true?In what follows, keep in mind that I'm not a tribologist (a scientist who works in the field of friction) or an engineer in the field. Most of what's here comes from the article "Friction at the Atomic Scale" by Jacqueline Krim in the October 1996 issue of Scientific American magazine.
To recap, the classic first law of friction is that friction between two surfaces is proportional to the force pressing those surfaces together. (This is called the "normal" force, using the mathematicians' definition of normal, meaning perpendicular.) The second is that the force is independent of the apparent area of contact. Finally, the friction is independent of the speed of motion; once sliding starts, the friction is the same whether the two surfaces are sliding quickly or slowly relative to one another. The only one of these which gives serious heartburn to us laymen is the second.
Friction is dependent on contact area!
You were right all along: The force of friction is indeed dependent on the actual area of contact. The catch is that the actual area is not even close to the apparent area. Take a small piece of steel, with an area of 1 square unit, and put it on another larger piece of steel. What's the area of contact? One square unit? Not so. At the microscopic level, those seemingly flat pieces of steel are heavily ridged and pitted. The true area of contact is where the ridges meet, leaving a gap between much of the two pieces. Naturally, those areas not actually in contact do not contribute to the friction.Now we can see that if you take another small piece of steel, half the thickness and twice the area (hence the same weight) as the first one, it'll have the same actual area of contact because it's still only the highest ridges which meet on the two pieces. Hence the friction won't change because the actual area of contact hasn't changed. To get more friction you have to increase the real contact area. One way to do that is to press the pieces harder so that more ridges meet. And indeed, that results in the first law: Increasing the pressure increases the friction.
The difference between true and apparent area of contact is at the heart of our disbelief in the second law, that friction doesn't depend on (apparent) area of contact. So if that's all you wanted to know, rejoice and go back to where you came from. You were right all along, friction depends on the (actual) area of contact; it's just that you were fooled by the subleties of the microscopic surfaces involved. But if you want to know more about the atomic origins of friction, stick around for more of what Ms. Krim has to say.
False Reasons for Friction
The model of bumps and ridges of surfaces coming into contact suggests a possible reason for the origin of friction: It's caused by galling, the deformation of the ridges as they're dragged along one another. Promising as that was, it didn't work out. Ms. Krim's article states: "By the mid-1950s, surface roughness had been ruled out as a viable mechanism for most everyday friction. Automobile makers and others had found, surprisingly, that the friction between two surfaces is sometimes less if one of the surfaces is rougher than the other [see “Friction,” by Frederic Palmer; Scientific American, February 1951]."That gives me another idea. How about adhesion between the two areas in contact? Sorta like cold-welding. This may have a role, but it isn't complete. Krim again: "It simply could not explain the fact that substantial friction exists even in cases in which wear is negligible."