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Re: ENERGY WITH Q



Tom W wrote:

The words "A block slides along a table" are insufficient to
understand what the problem is.

I agree.

"Carl E. Mungan" wrote:

What's unclear? Let me try again another way:

A block slides to rest along a level rough table. The only net force
on the block is kinetic friction. The table is clamped to the floor
and hence to the earth. We approximate the earth as being an inertial
system. The observer is at rest with respect to the table. I hope
this is clear. Now for the question:

HOW MUCH WORK DID THE BLOCK DO ON THE TABLE?

Since I only read the digest, I may as well provide a grading key
right now. If your answer was zero, congratulations, you are a
believer in pseudowork. If your answer was positive, you are
consistent in your use of thermodynamic work. A new text you may like
is Halliday, Resnick, and Krane 5th ed. (See the top left hand column
on page 283.)

My answer is that we don't know what the work is, because the problem is
severely underspecified. As discussed below, we can't make progress
unless we impose additional assumptions, resulting in a whole family of
inequivalent answers.

In particular, consider the following assumptions:
a) The block can be described in macroscopic terms.
b) The table can be described in macroscopic terms
c) Friction occurs.

You can't have all three. Since the statement of the question demands
(c), we must choose either (a) or (b) or neither, but not both.

Work is the integral of F dot ds. The step (ds) is well-defined (and
hence work is well defined) if and only if we are dealing with objects
that are pointlike (no internal structure). There is no sensible way to
calculate the "overall" work in terms of the "overall" motion and the
"average" force. For more on this see
http://www.monmouth.com/~jsd/physics/thermo-laws.htm#sec-define-w-q
which I recently revised.

There exists a special case in which assumption (b) holds. Imagine an
ideal macroscopic table with no internal degrees of freedom. Imagine
that the friction occurs because of tiny wheels on the bottom of the
block, connected to tiny disc brakes. As the block slides across the
table, zero work is done on the table (its F dot ds is zero). Whatever
work and/or heating occurs is entirely within the block.

One can equally well imagine the other extreme, where assumption (a)
holds. Imagine an ideal macroscopic block; all the frictional
mechanisms and processes are attributed to the table. In this case, the
work done on the table is distinctly nonzero.

In general neither (a) nor (b) holds. The value of F dot ds is
anybody's guess.

Please do not alter the spirit of the question. You may *not* try to
put both the block and table in the system. The system is the table
(plus earth). You may *not* instead tell me about heat; my question
is only about the work. You may *not* answer by invoking a special
magical formula; the whole point of this question is to illuminate
how you think about work in general--the specifics of this example
are just there to give us something concrete to discuss.

I think I followed these instructions; if not, please clarify.

Only three people that I know about are allowed to choose both
answers: they are John M, Joel R, and Gene M. John D has lots of
support here:
* all of the industrial researchers he polled - say 15 people
* all other active PHYS-L members interested in this thread - say 50 people
* the remainder of my dept - 35 faculty
So not only are industrial researchers unwilling to use pseudowork,
so are academic scholars. From this limited survey, we can say that
about 97% of all physicists are *hostile* to pseudowork. I chose the
highlighted word purposefully. As I have gone around my dept here at
the Academy for example, my colleagues tell me they not only don't
teach pseudowork, they believe it's a confusing, heretical term in
league with cold fusion, astrology, and such ilk. Here's a sample
quote of just this kind from the list:

Hey don't get me involved with a spurious thing called "pseudowork". I
disavow ever using the term out loud. There is enough nonsense in physics
teaching without introducing yet more.

Hear, hear.