static friction : dependence on area and normal force

In section 10.10 on page 248 it says:

Measurements show that the angle θ_max at which objects begin to slide [...] does not depend on the contact area.

Also, emphatically:

**The maximum force of static friction [...] is proportional to the force [...] and does not depend on the contact area.***

Some things in this world are more complicated than they appear. Friction is in this category. The simple models are not good, and the good models are not simple. Experts consider friction to be a "challenge" and a "topic of current research" ... which is a polite way of saying that nobody fully understands it.

Here are some basic, approximate facts:

Scenario 1: For some materials under some conditions, we observe that the maximum magnitude of the static friction is approximately proportional to the normal force. This applies mainly to relatively hard solid substances, in situations where the normal force is not too large. In this scenario, the remarkable thing is that the maximum magnitude of the static friction is approximately independent of the nominal macroscopic area of contact. We can explain this (or at least make it plausible) by saying that because the surfaces are hard and uneven, the area of actual molecule-to-molecule microscopic contact is quite small compared to the nominal macroscopic area. The normal force deforms the objects and increases the microscopic contact area, as shown in figure 10.40. This idea of microscopic deformation is consistent with other things we know, such as the fact that under some conditions, the electrical conductivity of the junction between two blocks of metal is proportional to the normal force.

Scenario 2: Under other conditions, the maximum magnitude of the frictional force is proportional to area, and not proportional to the normal force. This applies when one of the objects (or both) is relatively soft and the normal force is large; think of sandpaper clamped to rubber.

Scenario 3: Oddly enough, there are situations where having more area gives you less static friction, for any fixed amount of normal force. A notorious example involves the quasi-static rolling friction between a tire and wet pavement, in situations where hydroplaning might occur.

  Martin H. Müser, Ludgar Wenning, and Mark O. Robbins
  "Simple Microscopic Theory of Amontons's Laws for Static Friction"
  Phys. Rev. Lett. 86, 1295 (12 February 2001)
  http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.86.1295
  http://arxiv.org/pdf/cond-mat/0004494

  Mark O. Robbins, Martin H. Müser
  "Computer Simulations of Friction, Lubrication and Wear"
  http://arxiv.org/abs/cond-mat/0001056
  Review chapter for the Handbook of Modern Tribology (2000) edited by Bharat Bhushan

Also:

Scenario 4: There exist Johansson blocks aka Jo blocks aka gauge blocks. These are metal or ceramic blocks with exceedingly flat, parallel faces. The distance between faces is known to high precision, so the blocks are used as secondary standards for calibrating measuring instruments and machine tools.

If you put two such blocks together and wring them to remove most of the remaining air and lubricants, you find that the coefficient of static friction is more than infinity. That is, the blocks will stick together, even if the normal force component is zero or negative. If you're not careful, the blocks will cold-weld and you'll never get them apart again.

Scenario 5: Outright adhesion. If you try to slide a piece of adhesive tape across a clean, flat surface, you see something that looks a lot like static friction, with an eeeeenormous coefficient of friction.

Arguably there is a fine line between static friction and outright adhesion, but in many cases it's just an imaginary line. As a corollary, this is one of the many reasons why there will never be a simple theory of friction.

ericmazur / PnPbook

static friction : dependence on area and normal force #115