Re: why pseudowork?

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Thu, 28 Oct 1999, Ludwik Kowalski wrote:

> My question is this. Why should the renaming affect elementary
> courses rather than more advanced courses, such as thermodynamic?
> The "pseudo" part implies that the F*d is less good than the "real
> work". Why should we distract novices with "pseudo" when we are
> not ready to make it meaningful? Keeping things as simple as possible
> is importnat, complications should be introduced gradually and our
> terminology should promote this.

Ludwik,

I understand your point and have some sympathy for it.  I don't really
have strong feelings one way or the other about what to call the various
forms of work, but one advantage of the term "pseudowork" is that it makes
clear that we are using a definition that is distinctly at odds with that
used for calculating work in thermodynamics.  When we integrate p dV we
are doing what I consider to be more like a traditional work calculation,
that is, looking at the external forces applied at each point, integrating
them over the motions of those points of application, and then adding 'em
up.

More generally, if we want to find the work done on a system of particles,
I just think it makes more sense to define that work as the sum of the
elementary works done on the individual particles rather than to add the
forces and integrate them over the motion of the center of mass.

But let me be very clear, alternate definitions are exceedingly useful in
different situations.  The problem is that people don't seem to be
generally aware that they use different definitions in different
situations.  The result of that is that they make mistakes in determining
which kind of system energy change is associated with which work.

Here is a sketchy summary of three of the most commonly used definitions
and what they turn out to be equal to:

Integral of net force over the motion of the center of mass
   = change in bulk translational kinetic energy
(This is what I call the "pseudowork-kinetic energy theorem."  It is most
readily derived as a single, simple integration of Newton's Second Law.)

Sum of integrals of all external forces over the motions of the points of
application calculated in an inertial frame
   = change in total energy (bulk translational + internal)
(This is what I call the "frame specific external work-total energy
theorem."  It is the one that I consider the best candidate for being
called "the" work-energy theorem, but nobody has to agree with me!)

Sum of integrals of all external forces over the motions of the points of
application calculated in the system CM frame (possibly noninertial)
   = change in internal energy
(This is what I call the "system specific external work-internal energy
theorem."  It is the one generally--but not always--used in
thermodynamics.)

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