Bob Sciamanda's extension of his MET (or what others have called
the pseudowork-energy theorem, PET?) to include the concept of
potential energy is certainly correct. It follows the usual
course of 1) "discovering" that the "work-like" line integral for
certain well-behaved forces is a function only of the endpoints of
the integral, 2) defining a position-dependent function--the
potential energy--that gives the value of the integral as a simple
(negative) change in the potential energy, and 3) throwing it all
over to the other side of the equation where the sign changes.
I'd like to point out, however, that it is rarely very fruitful to
extend the MET/PET to include potential energy in this manner. As
Bob was careful to note, this can be done only when one or more of
the external forces is a function only of the system CM position.
I can think of only two situations in which this can be the case:
1) the system is a point particle or a rigid, non-rotating body
that behaves like a point particle (in which case the extended
MET/PET reduces to its most elementary form) or 2) the force is
constant.
Using the extended MET/PET we can do roller coaster problems (as
long as we can ignore the minor up and down motions of the earth
that result from its interaction with the roller coaster), but we
cannot perform any significant analysis of the interaction of two
or more large gravitating masses. We can analyze the motion of a
single body attached to a spring, but *only* if the other end is
fixed in an inertial frame *and* we perform the analysis *in* that
frame.
This is a good example why it is much more fruitful to define work
more generally as the line integral over the displacement of the
point at which the force acts rather than that of the system CM.
Doing so we see that potential energy in its most general form
actually arises from the work done by *internal forces* and we can
fruitfully use the concept to analyze extended systems including
springs, molecules, and arbitrarily large conglomerations of
gravitating bodies from arbitrary (even noninertial) reference
frames.
John
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A. John Mallinckrodt http://www.intranet.csupomona.edu/~ajm
Professor of Physics mailto:ajmallinckro@csupomona.edu
Physics Department voice:909-869-4054
Cal Poly Pomona fax:909-869-5090
Pomona, CA 91768-4031 office:Building 8, Room 223