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Originally Posted by Pat Roche
Paul, the kinematical physics say that surface area does not matter. A wheel and a track will slip once the coefficient of friction is broken regardless of surface area.
-Pat
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Yes, but that is assuming ideal conditions. As others have said, you can have materials like Velcro, or rubber, that will "stick" to the surface. If you were to measure mu between rubber and asphalt, and used two blocks with the same weight but a different surface area, you'd get a slightly different result for mu (would it be linear with area?). Try it with Velcro and carpet and the difference would be huge.
For instance, extrapolate and loctite a block to a table. Loctite 158184 will hold 1300 N per square centimeter. Take a 1x1x1 (cm) block that weighs 100 g and pull it till you manage to rip it apart from the table. Would you consider your mu to be 1300 (Force/Normal)? Obviously not, because friction is not the only issue here. Same with the situations I discussed above.
Now I have two questions I'm not sure of the answer:
a) If surface area really doesn't matter, why is it much harder for a treaded robot to turn on a dime than it is for a robot with wheels? Also, why does it get much easier if you add an idler pulley? (I haven't put a lot of thought into this one yet, but I think it's not entirely dependent on the surface area, but also because the treads dig into the carpet and you have to overcome the fibers in order to skid laterally)
and
b) (not that it really makes much difference, but...) We all know that a rolling wheel has v=0 on the contacting point and v=2wr at the diametrically opposed point. Now, do we have static of dynamic friction?
I would say static, considering if you "break traction" the force you apply to the floor will be reduced, and as the wheel won't be translating anymore, the relationship I mentioned above won't hold true.