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Bob,
You have a serious word wrap problem.
. . .
OK then. What is the conventionally accepted definition of work?
Whose convention are you following? Please; I really have no idea
what your definition of work might be.
To summarize, by the WE theorem I refer to the usual (dot product)
integration
of F=ma over the trajectory of the CM of a system of one or more
particles.
(F= the vector sum of all external forces acting on the particle
system.)
Does this mean that a couple applied to the system does no work?
I'm sure you don't mean that, but that is a logical consequence
of your definition, if I read it correctly. I don't like that
very much.
I have six textbooks which are devoted to classical mechanics onI have been looking for Hestenes book. It's out of print. Do you know a
my shelf here at home: French, Davis, Synge & Griffith, Goldstein,
Fowles & Cassiday, and an excellent book, "New Foundations for
Classical Mechanics" by David Hestenes. Of these only the last has
an index entry for anything like the work energy theorem. Hestenes'
book gives two versions, one which includes the internal kinetic
energies of the particles and one which does not. He calls the
first version (which allows for nonconservative internal forces)
the general work energy theorem. A version which constrains the
internal forces to be conservative is also derived. Thus the only
text I have that even mentions the theorem does not make it unique,
and neither agrees with either your version or mine.
I have one elementary textbook on my shelf here at home, Fishbane,
Gasiorowicz and Thornton. (I'm teaching from this text now. I did
not select it and I would not advise others to do so.) It has
several index entries for the work energy theorem, one of which
(called "the work-energy theorem") deals with a single "object"
(which I take to be a particle) and equates the change in kinetic
energy of the particle with the work done on it by all external
forces. I have no problem with that result, but I judge it to be
so trivial as to be unworthy of being singled out for its own
designation. F, G & T go on to define "the work-energy theorem for
rotations". Unsurprisingly this one allows couples to do work
(perhaps because that's the only way they can make it today).
. . .
Nothing more than F=ma and mathematical logic is required to show a
numerical
equality between this "work integral" and the change in the CM kinetic
energy
of the particle system. If energy conservation were abandoned this WE
theorem
would still be valid. It is simply a re-statement of F=ma; it applies
to all
forces, frictional included; it says nothing about universal energy
conservation;
it knows about no other kinds of energy than kinetic- and this only as a
convenient numerical quantity as expressed in the theorem.
It implies nothing about a transfer of energy from the agents of F to
the particle
system. The term dw in the first law of thermodynamics is a different
animal,
both conceptually and numerically except in some carefully contrived
circumstances
(I suggest that dw in the FLT not be called work, call it adiabatic (or
non-thermal?)
energy transfer.)
Well, that sure clears up a lot, doesn't it? Are you aware that
conventionally the terms W & Q in the first law of thermodynamics are
called, respectively, heat and work?
. . .Your example illustrates how the WET can evaluate the change in the CM
Finally, let me illustrate the application of these versions in a
simple example. Consider a particle of mass m to which is affixed
a massless Hooke spring of spring constant k. Starting at time t=0
I pull on the spring with a force F=Ct, where C is a constant. The
system is initally at rest.
. . .