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Re: Why work before energy in texts



What the many respected authors are doing are defining potential energy in
terms of work. I.e. they are committing the "even bigger blunder".

I quote from section 14-3, Feynman, end of second paragraph and the
beginning of third paragraph.

" . . . Now the work done in going from position P to a particular position
in space is a function of that position in space. Of course it really
depends on P also, but we hold the arbitrary point P fixed permanently for
the analysis. If that is done, then the work done in going from point P to
point 2 is some function of the final position of 2. It depends upon where
2 is; if we go to some other point we get a different answer.
We shall call this function of position -- U(x,y,z), . . ."

and just after equation (14.1)

" . . . and we call U the potential energy."

About as clear a statement of defining potential energy in terms of work as
I can imagine.




Another oft used author, Marion page 79 4th ed.; commits the same blunder
where he states

"We may define the potential energy of a particle in terms of the work (done
by the force *F*)."

Yet another clear statement of defining potential energy in terms of work.

(see interleaved comments below)

-----Original Message-----
From: John S. Denker [mailto:jsd@MONMOUTH.COM]
Sent: Monday, October 15, 2001 2:33 PM
To: PHYS-L@lists.nau.edu
Subject: Re: Why work before energy in texts


I wrote:

"BOTTOM LINE: Defining work in terms of potential energy is a
blunder. Defining potential energy in terms of work is an
even bigger
blunder."

Then Joel Rauber wrote:
Many respected authors do this of course,
(define potential energy in terms of work)

E.g.
Feynman chapters 13 and 14 Vol. 1
Goldstein page 4, 3rd ed.
Arnold page 15
Marion 4th ed., page 79

. . . ad nauseum

Huh?

When I look at Feynman volume I page 13-3, a few lines below equation
13.9, it seems absolutely clear that work is being _defined_ in terms
of F dot ds.


huh? (see opening paragraph for clarification.)

I may have missed it, but I don't see the words "potential energy" at all on
page 13-3. Consequently this objection seems irrelevant to the assertion
clarified by the parenthetical "(define potential energy in terms of work)".
I also might add that page 13-3 is dealing with one specific example, force
of gravity, something that is eschewed below.

There may be _examples_ where some sort of calculation shows a
relationship between work and potential energy, but an example is not
the same thing as a definition. Not by a long shot.


Huh? The authors are stating that one may define potential energy in terms
of work, they aren't just listing examples.

I stand by my assertion: Defining work in terms of potential energy
would be a blunder. Defining potential energy in terms of work would
be an even bigger blunder.


I stand by the assertion that many respected authors define potential energy
in terms of work. I even agree that it is reasonable for those authors to
do so (a new assertion on my part.)

Joel R.