The last time I entered this discussion I was accused of speaking ex
cathedra. I don't quite understand how I got that label; nonetheless, I was
indeed not speaking directly to the issue at hand.
John Denker has finally stated, probably exactly, where I am on this issue.
So my position is clear, I have included three of Denker's paragraphs below.
These paragraphs strike me as quite good.
An additional point I would make is the following. This discussion, as can
be surmised from the title, got started over the +/- sign convention for
work. If work is defined as integral of F dot ds (which is the way I teach
it, and all the calculus-based textbooks on my shelf define it) then there
is no question about the sign.
But I also explain to my students there is a big sign problem when we try to
use the "work-energy theorem" because the work-energy theorem itself does
not specify whether the agent doing the work done and the thing changing
energy are the same. So, when I write the work-energy theorem I simply
write W = +/- delta-E and tell the students they have to figure out which
sign is appropriate on a case-by-case basis.
Conclusion, I believe there is a firm sign convention for what I consider
the formal definition of work (integral force dot ds). But there is no
formal convention for the sign used in the work-energy theorem because the
theorem does not specify whether both sides of the equation are referring to
the same body/agent or not.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817
J. Denker said (with some parts snipped out)
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).
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.
Recommendation: Fixating on work is a blunder. Work is of secondary
importance at best. Energy is primary and fundamental. Pay attention
to the energy. If "work" helps you keep track of the energy, fine --
otherwise forget about "work".