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Re: Work/Energy Theorem



I wonder if I could step back in here -- just to help my thinking -- not to
referee:

Bob Sciamanda said -
The word "work" is defined as the left hand side of the Work-Energy
theorem (at least for me).

Yes, Bob, but John says "Which forces?" and "Which path?" If the system
is a particle, life is straightforward, but, if the system is a gob of goo,
it ain't obvious which forces should be used so John considers all the
possibilities he can think of.

But, John, I am like many in this discus sun -- if I throw this gob of goo
at a wall, I want to think of work stopping it. And I don't want to talk
about confusing things like pseudoforces. You want to say that no external
applied work is done to the gob in this case. But in your papers you
consider that work is done by internal forces as the gob of goo deforms. Do
I have this right?

Bob says:
I think you mis-read me, John. The Work Energy theorem is a numerical
equality which speaks of previously defined quantities (F,m dr,. .).

Bob, I don't think it is that easy. John posted a summary of his seven
"works" and six results contained in his paper. I am still wading through
this somewhat opaque paper, but, before the ideas that John espouses are
discounted, one should read the paper -- "All about work" AJP Apr 1992
p356ff and the follow up paper "Stopping objects with zero work: Mechanics
meets thermodynamics" AJP Feb 1993 p 121ff (This one is about two gobs of
goo colliding)

Bob says:
I think that is why we have the First Law of Thermodynamics
IN ADDITION TO the W.E. theorem.

This question seems to be in John's mind in these two papers: The final
paragraph of "All about work" contains the following:

"The results of this paper have led us indirectly and incompletely to the
concept of heat. Roughly, conductive heat transfer can be viewed as
external work performed at the system interface via "collisions" with the
elements of neighboring systems."

Now THIS warms my heart and may sound very familiar to some on the list but
I am not sure why the authors put "collisions" in quotes. This is *exactly*
the correct view! In the second paper external forces act on each gob, but
only at the interface and as the interface does not move (in the paper's
example) no external work is done -- but *internal* forces do work during
any deformation -- and *this* work increases the internal KE which is the
thermodynamic "internal energy", dU. The suggestion is that for a hot body
abutting a cold one, the hot molecules collide with and do *work" on the
cold ones thereby increasing their KE and thus the internal energy of the
system.

But, John, this paper goes on to say the following:

"The work energy holds in _pure_ mechanics and applies only to point
particles ... It requires modification in problems where bulk mechanical
(kinetic or potential) energy transformed into nonmechanical _internal_
energy associated with the molecules of macroscopic bodies. This
nonmechanical energy is present even in objects at rest ..."

and

"... [omitted material] conforms with the assumed symmetry and has the
pleasing interpretation that the original kinetic energy of the two
[colliding] bodies is transformed completely into internal energy during the
collision."

Now Leigh will find this language just fine, but I find myself wondering
why, in a paper about the W/E theorem that contemplates that "heat" is
"work", the idea of energy flowing rears it's head.

The paper wants to consider an "Extended work-energy theorem which says

W(ext)=dKE+dU [except for some reson the paper uses deltas]


I would much rather that one said that two "works" were done during the
collision of the two bodies -- one to stop the bodies and one (well many
really) to speed the molecules inside.

I am still much more comfortable saying that there can be a dKE *only* if
there is an applied "work".

But I am still studying the two papers.

Somebody tutor me here.


Jim Green
JMGreen@sisna.com