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Re: positive and negative work



On Sun, 11 Nov 2001, John S. Denker wrote:

John Mallinckrodt wrote:

1. With respect to what will you measure your ds's? An inertial
frame, the frame of the system CM, an arbitrary frame?

Anything of physical significance can be calculated in a frame-independent
way. Usually it may _also_ be calculated in innumerably many frame-dependent
ways also, but that doesn't change the physics. Introducing a new reference
frame doesn't introduce a new concept; it is just a new representation of the
same old concept. It does not require a new mental model, and it does not
require conjuring up six or seven idiosyncratic names as if new concepts had
been created.

For example, any measurement of kinetic energy (plain old kinetic energy) will
depend on the reference frame, since some frames may be moving relative to
others. But this does not change the physics of what happens on the pool
table, or anything else. It doesn't require introducing a new concept of
kinetic energy, or a new name.

In an elementary course, do everything in the lab frame and don't worry about
it. In a second course, pick a frame (any one frame) and stick to it. The
third time around, figure out how to compare one frame's measurements with
another's.

None of this seems controversial, but it ducks my question.

As I understand it, you want to promote a single definition of
work. For that definition to be useful, we need to know what to do
wih it after we calculate it. That would seem to me to require
knowing how it is related to the change in some independently
calculable energy of the system. To determine that we need to
know the answers to my two questions.

The answer to this first question will, for instance, determine
whether or not work is related to changes in the bulk
translational kinetic energy of an object. Lots of people think
it is, but there are times when we use a different convention.
Consider for instance the result of pushing gently on an otherwise
freely floating balloon and doing a *thermodynamic* analysis of
its contents. In a case like this, we generally say that no work
has been done on the gas even though its bulk translational
kinetic energy changes.

2. Which forces will you consider on each particle? Both external
and internal forces? Only the external ones? Only the internal
ones?

If we decompose the system into pointlike elements with no internal degrees of
freedom, as seemed to be the consensus a moment ago, then such questions do
not arise. By definition the pointlike elements cannot have any internal
forces.

Here you have simply misunderstood me. Recall that you made the
excellent (IMO) suggestion that we decompose the composite system
into a collection of point particles. My question is about what
forces you will consider on each of those point particles when you
calculate "the" work done on the system. Will you use the net
force on each particle? Just the forces from outside the system
(the external forces)? Or just the forces from other particles
inside the system (the internal forces)? Or something else?

Again, the answer matters if we want to be able to *use* "the"
definition of work in solving problems because that answer
determines the relationship of "work" to independently calculable
energy changes--a source of endless disputes in these threads.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm