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Re: CONSERVATION OF ENERGY



I'd like to suggest that much of the confusion here is the result
of a failure to appreciate that

kinetic friction is not a heating process.

I think this common confusion has to do with the fact that both
may be considered to involve distributed, microscopic works done
at the interface between two systems. Heating, however, is a
*statistical net result* of the two systems having different
temperatures; the higher temperature system loses some amount of
internal energy while the lower temperature system gains the
*same* amount. In contrast, kinetic friction involves microscopic
works that are *organized* by the macroscopically observable
directions of relative motion between the surfaces; both systems
generally gain internal energy in amounts that are *not*
necessarily the same and which depend on the details of the
surface interactions.

Perhaps we need carefully to distinguish between the concepts of
"heating" (i.e., thermally transferring energy) and "warming"
(i.e., causing the temperature to increase). Although kinetic
friction does generally "warm" the two systems as a result of
"dissipation" (a marvelously apt word for the process by which
visible, bulk forms of energy are "redistributed" into hidden,
microscopic degrees of freedom) and although it is often the
proximate cause of a *subsequent* or even *concurrent* heating
process as that dissipated energy tries to redistribute itself in
accordance with equipartition, it is itself fundamentally a *work*
process.

Note also that heating can be done reversibly while kinetic
friction is always irreversible. This is why, in order to
determine the temperature rise that accompanies kinetic friction,
we often construct an *alternate* path between initial and final
states that involves a heating process with an "equivalent" heat
transfer. (Perhaps if we were more explicit about this "alternate
path" construction process, we would be less apt to think of
kinetic friction as *really* involving heat.)

Ultimately, our mental models of these processes are critical to
appreciating the difference between them:

In heating we envision elastic collisions between molecules at the
interface. These collisions have a tendency to equalize the
kinetic energies of the colliding molecules. It is precisely this
*tendency* that the second law is talking about. The result is a
statistically mandated flow of energy from the hot system to the
cold system.

In kinetic friction we envision "high points" coming into contact,
being forced to deform in the direction of motion of the other
surface, and then "breaking loose" only to start over again and
again. Both systems now see themselves yielding to external forces
in the same direction that those forces are applied. As a result
organized and generally positive microscopic works are done on
both systems relative to the rest frames of the systems
themselves. The previously referenced AJP paper by Sherwood and
Bernard (sorry, I don't have the reference with me here on the
Island) is an essential read in order to fully appreciate the
ramifications of this model.

John
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A. John Mallinckrodt http://www.intranet.csupomona.edu/~ajm
Professor of Physics mailto:ajmallinckro@csupomona.edu
Physics Department voice:909-869-4054
Cal Poly Pomona fax:909-869-5090
Pomona, CA 91768-4031 office:Building 8, Room 223