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Re: positive and negative work

On Sun, 11 Nov 2001, John S. Denker wrote:

John Mallinckrodt wrote:

Work (in any of its
many forms) is conventionally *defined* as a product of some force
with some distance (or, more generally, as a sum of integrals of
infinitesimal such products.)

I would have said that work is conventionally defined to be the integral
of F dot ds, where ds is well-defined (and therefore work is
well-defined) if and !!only!! if we are dealing with pointlike particles
(i.e. no internal structure).

This *is* certainly one way to go and it *would* eliminate all
ambiguity. But it would also eliminate our ability to talk about
work done on non-pointlike systems of particles like gases, cars,
skaters, etc. This would require the elimination or at least a
pretty radical alteration of "Chapter 7" in most intro texts. I
wonder how many of us think that would be a good idea?

Recommendation: When in doubt, decompose the system into pointlike
elements and apply F dot ds to each element separately. If you do
anything else, you're strictly on your own -- you shouldn't call it
"work", and whatever you call it you will have to explain what it is and
why we should care.

This is, of course, precisely what is done in the paper you claim
to have read and not to have been persuaded by (and I am curious
what you found to be so unpersuasive.) But as soon as you do
this, there are at least two questions that arise:

1. With respect to what will you measure your ds's? An inertial
frame, the frame of the system CM, an arbitrary frame?

2. Which forces will you consider on each particle? Both external
and internal forces? Only the external ones? Only the internal
ones?

It is precisely the answers to these questions that distinguish
six useful forms of work. I'd be interested in knowing which
answers you intend to stick with.

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