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Re: why pseudowork (NOT)



On Fri, 29 Oct 1999, John Denker wrote:

At 08:53 PM 10/28/99 -0800, John Mallinckrodt wrote:

you seem here to be
talking about a rigid block, one with no internal degrees of
freedom.

No, I'm just recognizing the distinction between macroscopic and
microscopic degrees of freedom.

This is the distinction recognized by every physicist who ever described
the temperature of a baseball and then separately described its
center-of-mass motion without giving an ultramicroscopic description of the
thermal motions.

I beg your pardon for being out of the loop inhabited by "every
physicist". Perhaps you can tell me how "every physicist" deals with the
general motion of a slinky? I am sorry for my tone here, but I object to
your implication that the answer is obvious and general. I respect your
usual insistence that arguments that are not general, that apply only to
special cases, are not particularly useful.

...
Does this mean you agree that it is unphysical to claim that the block and
the table undergo equal and opposite work? Then we are basically in agreement.

I would have thought that by now you would understand that I recognize the
usefulness of *many* different definitions of work. Using some of them
the works are equal and opposite; using others they are not. Let me be
exceedingly clear: I have no quarrel with your apparent desire to have the
works be independent of each other. If it is important to you to use one
and only one definition of work, one that allows this to be the case, then
please be my guest. But I will insist that you not change your definition
midstream and pretend that you didn't.

Here's where things stand AFAICT:

1) For friction mediated by a lubricant, the claim that the block and the
table undergo equal and opposite work is indefensible.

I've never addressed this problem, but I can't imagine it being otherwise.
After all, there are three systems one of which is between the other two.

2) For friction without lubricants, e.g. friction mediated by wiggly
asperities attached to the block and/or table, there are multiple viewpoints:
a) According to one viewpoint, *all* the energy transferred to the table
is transferred by reversible conservative forces (and is therefore called
work) and is immediately thereafter thermalized.
b) According to another viewpoint, some of the energy transferred to the
table is thermalized before transfer. The transfer of thermal energy
should not be called work.
c) According to yet another viewpoint, *all* of the energy that the table
gets is thermalized before it becomes part of "the table".

I assert that (2a) does not describe the typical sliding block and applies
only to an extreme limiting case.

I assert that 2a fails to be a candidate because of its ridiculous
implication that work can only be done by conservative forces.

I recognize that (2c) is also an extreme case. It can be made less extreme
by revising it, such as:
c') ... *all* of the energy that the main part of the table gets is
thermalized before it becomes part of "the main part of the table".

I find that word "before" to be kind of weird, but if you find that you
can do physics that way I have no objection.

I choose to define things so that the wiggly asperities attached to the
tabletop do not belong to the *main* part of the table. I define the
asperities to be part of the "frictional mechanism" in analogy to the
lubricant. This definition is arbitrary but not unreasonable.

I think this is even weirder, but I won't claim to speak for "every
physicist."

I recognize that this distinction between the frictional mechanism and the
rest of the table involves some approximations. For example, real friction
includes processes such as the following: Scraping radiates sound into the
main part of the table. This is initially nonthermal. After some time
(possibly a very long time by microscopic standards) it becomes
thermalized. But this example is tangential to the present thread, because
sound doesn't do a lot of net "F dot dx" work.

If we are going to discuss processes that convert nonthermal energy to
thermal energy, we must somewhere draw the line between macroscopic and
microscopic. The place I have drawn the line is arbitary but not
unreasonable. It is in fact quite conventional, as evidenced by the
textbooks that handle these issues the same way.

This is why I don't like the phrase "thermal energy." In my view there is
only "internal energy" and bulk translational kinetic energy. Internal
energy includes everything but the three translational degrees of freedom.
Again I think about the slinky and choose not to attempt to say which
degrees are microscopic and which are macroscopic.

To summarize:
--) The claim that the sliding block and the stationary table undergo
equal and opposite work is not true for the typical sliding block.

Again, that depends on your definition of work.

--) The claim that friction does zero work on the table (while doing
negative work on the block) must be softened to something more like this:
Friction does zero work on the main part of the stationary table, while
doing negative work on the main part of the sliding block.

"Main part"? Whatever.

... where as always I take "work" to mean "net 'F dot dx' work" in problems
of this sort.

As do I. But there are lots of ways of deciding which F's to include, how
to measure the dx's, and whether to sum forces first or works later.
Until you have unambiguously settled those questions (as Harvey Leff and I
do in seven different ways in our paper), you can't calculate anything.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm