Re: Ohne die Arbeit, part 3 (Long & wordy)

[Bob Sciamanda <sciamanda@worldnet.att.net>]

John Mallinckrodt wrote:
> On Sat, 15 Nov 1997, Bob Sciamanda wrote:
>
> > The use of potential energy functions will usually be restricted to
> > . . .
> > As a very useful example consider the
> > dumbbell system of two masses interacting through a central force
> > F(|R|); R is the vector locating mass 1 from mass 2 and F(|R|) depends
> > only on its magnitude.  This could be the model for a variety of
> > physical systems, from a hydrogen molecule to a binary star system.  We
> > are interested in the time behavior of the vector R, ie.; the motion of
> > M1 relative to M2, assuming the dumbbell system is isolated from other
> > forces.
> >
> >                 R2                            R1
> >
> > M2<-----------------------CM----------------------------------------------------->M1
> >
> > ------------------------------------------------------------------------------->
> >                                       R
> > The difficulty is that if we define M1 as our system, the force on it
> > depends not only on its location, but also on the location of M2, which
> > will not stand still for us. However:
> > . . .
> > Using Eq#2,  m*R'' = F(|R|) * R / |R| , where m = (M1*M2)/(M1+M2), the
> > "reduced" mass.  (Eq #4)
> >
> > Eq (4) describes the behavior of the vector R, which locates M1 from
> > (the moving) M2, and says that its behavior is the same as that of a
> > particle of mass m under the influence of the central force F(|R|) of a
> > FIXED source.  Obviously, the MET can use a potential energy function to
> > describe the behavior of R in Eq #4.
>
> Bob,
>
> All of the above is true, of course; it follows the exposition found in
> any intermediate level textbook on mechanics. But I don't agree with the
> conclusion in your last sentence because I don't see what it has to do
> with the MET (or, as it is more commonly known, the "pseudowork-energy
> theorem," PET.)  The MET/PET talks *only* about the effects of *external*
> forces on the motion of the *CM* of a system.  Of course, the extremely
> restricted case of an isolated system of two point particles interacting
> only via a separation-dependent attractive or repulsive force is
> isomorphic to the equally restricted case of a single particle subject
> only to a radius-dependent central force.  And since the latter case *is*
> restricted enough to be usefully described by your extended MET (EMET),
> one can use the results from the EMET analysis to describe the former
> case. But when the MET/PET *itself* is applied to the two body system what
> one finds is no "pseudowork" and no change in CMKE--i.e., 0 = 0, hardly an
> illuminating result.
> . . .

Read more carefully, John. You are correct that the MET exploits the 
(pseudo)work of only external forces.  But in this example, I have
chosen 
my system as only the mass M1, so that F(|R|) is an external force.
I am not interested in the motion of the CM of the dumbell, only in the
behavior 
of R(t), the motion of M1 relative to M2.

I realize that your work explicitly breaches the defined system and
exploits the 
work done by all forces (including internals).  I praise this as a very
useful 
work, however at least for the present it is inaccessible to, and
beyond, 
an introductory course. I am illustrating what can be done with the MET 
(which gets along without taking any cognizance of internal forces), a
statement 
(under other names or nameless) already at home (but misunderstood)in
introductory 
courses, at least as applied to a particle.

(Your article abhors potential function representations of external
forces because 
of a (subconscious) reification of potential energy and the subsequent
concern about 
where it is to be located; Cf your footnote #14.) 

> John
> -----------------------------------------------------------------
>  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

-- 
-Bob

Bob Sciamanda				sciamanda@edinboro.edu
Dept of Physics				sciamanda@worldnet.att.net
Edinboro Univ of PA			http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA				(814)838-7185