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My understanding about conservative force is a force that its work is independent of path such that we can construct another form of the work called potential to make our life easier.

For friction, if I start from microscopic point of view, it should be the macroscopic effect of the electric force or gravity which are both conservative force.

Why do we initially have description by conservative forces (electric/gravity force) but end up with a macroscopic description of nonconservative force(friction)?

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Related: – Qmechanic Jul 14 '12 at 16:54
Thanks for the link, my question is more like how to start from microscopic model which contain only conservative forces to derive the macroscopic description of the system. I am not quite sure whether this approach is possible or not. For friction, naively, I would expect some kind of two-dimensional disorder system, but I am not quite sure whether it is possible or not to think along this line...I believe it is related to statistical mechanics though...but I have no idea how to do this kind of coarse-graining. – Yi-Ping Huang Jul 14 '12 at 17:07
Friction is not due to electrostatics or to gravity. It is due to Pauli-force, the force from Pauli exclusion, acting between things in contact, together with some electrostatic mediated electron sharing between atoms at contact points. – Ron Maimon Jul 14 '12 at 21:32

Coming at the problem from a philosophical level (rather than a detailed look at the micro-physics), I like to note that the"non-conservative" forces you encounter in day-to-day life don't break the conservation of energy in general: then only break the conservation of a-few-specified-types-of-energy-that-we've-studied-in-class-so-far.

That is to say that the energy "lost" during a physics 101 laboratory on friction ends up as heat (and sometimes sound) which we generally haven't addressed at that point in the course.

The origin of this kind of non-conservativeness is physics happening on a scale (in distance or time) that we are ignoring. To a large degree this comes down to thermodynamics and in particular that pesky second law.

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That sounds reasonable, I think Stein mention similar idea that some portion of the force contribute to lattice vibration instead of the translation motion. Base on this picture, for two rigid body, even though they never exist, the "friction" between them will be conservative force. If I assume a rigid "table" and a rigid "block" on it, since the friction is a conservative force, I can write down some potential to describe it. The block either can move forever or it will stick on the table forever. That sounds like some frictionless surface... – Yi-Ping Huang Jul 14 '12 at 21:07
I kind of feel it is weird, maybe I think it wrong. If I release the condition a little bit, for some material that is similar a rigid body, the friction suppose to be smaller since the heat created around surface will be reduced. Since for harder material, the gap less phonon mode is stiffer. if I assume no phonon-phonon interaction, I can approximate the distribution as classical Maxwell one. Stiffer dispersion should reduce the energy that goes into phonon modes. If I assume the surface is perfectly flat, I should have a conclusion that the harder the material,the smaller the friction is. – Yi-Ping Huang Jul 14 '12 at 21:19

Not all forces on the microscopic scale add up to a force on the macroscopic scale. Some create motion on a microscopic scale, which we see as temperature on a macroscopic scale. So thermal energy is "lost" and the force is nonconservative.

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