# Friction force and contact area [duplicate]

It's usually stated that the friction force is independent of the area of contact (Amontons' Second Law).

I've always thought that this shouldn't be true, because the atraction between molecules would be higher and there would be more peaks.

I've read that this is important for rubber surfaces. Is it important for nonelastic materials, like wood? Are there any quantitave studies of this phenomenon?

• It is only true in certain limits. Limited distortions, no permanent distortions of either material and the like. Commented May 27, 2013 at 23:46
• Possible duplicates: physics.stackexchange.com/q/16213/2451 and links therein. Commented May 28, 2013 at 8:32
• @Qmechanic I was also asking for numerical results and how good is Amontons model compared to reality, but it seems that it's not very studied. Commented May 29, 2013 at 13:10

Because surfaces aren't smooth on the atomic scale, when you touch two surfaces together only the high points (asperities) on the surfaces make contact so the real area of contact is much smaller than the apparent area of contact. I'm guessing you know this, hence your comment in your second paragraph:

and there would be more peaks

The reason why the force is approximately independant of area is that as you increase the force you get elastic deformation of the asperities and the real area of contact per asperity increases. If you increase the area you increase the number of points of contact but you also decrease the force per point of contact so the asperities deform less and the real area of contact per asperity goes down.

The real area per asperity is roughly proportional to pressure, i.e. $F/A$, and the number of asperties in contact is proportional to area $A$. So when you multiply these together you find the real area of contact, and hence the friction, is just proportional to the applied force.

For relatively soft materials like rubber the approximation doesn't hold, and their frictional behaviour is a lot more complex.

• Nice explanaion ! Can you please add the explanation for rubbers ?
– user174490
Commented Jan 31, 2018 at 7:46
• Forgive me for commenting on such an old answer but I am very confused about one thing. what about the case where the normal contact force and surface area are increased in proportion? According to the “laws” of friction, which mention nothing of pressure, the friction should still increase, Even though the pressure is unchanged Commented Jul 1, 2020 at 13:33