Re: Energy, etc

["JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>]

Robert-
        Congratulations on your making a simple model that makes the
skater discussion more precise!  Simplify it a bit more by detaching
the block from the spring, so that when the block moves away from the
wall, it does not carry the spring with it.  Attach the other end of
the spring to the wall.
        Move the block to compress the spring, giving it an energy
E.  Now let go.  The free end of the spring moves as it pushes against
the block.  Integrate Fdx and find that the work done by the spring is
just E.  That work is now transformed into the kinetic energy of the block.
The wall did not move, so it did no work.  So what is the issue?  I say
that if you play the game strictly by the rules, there is nothing left
to wonder about.
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   Perhaps the following problem illustrates what I mean.  A block is on a
frictionless surface and attached to a horizontal spring (note: it doesn't
have to be horizontal and frictionless but it simplifies the problem). The
spring is attached to a immovable wall.  If the spring is initially
compressed, then as the spring extends, the block on the end speeds up.

Question #1: As the block speeds up, is any work done on the block?

Question #2: As the spring/block system speeds up, is any work done on the
spring/block system?

The former is typical of standard textbook problems that illustrate the
"work-kinetic energy theorem".  The latter is analogous to the skater
pushing against the wall.  My attempt was to restate the latter question
in terms of the former.  In other words, although it may be misguided to
ask if any work is done on skater (arm/body system), it is helpful (at
least to me) to see that the wall/arm is doing work on the body of the
skater in much the same way as the wall/spring is doing work on the block.
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                                Regards,
                                        Jack

        "I scored the next great triumph for science myself,
to wit, how the milk gets into the cow.  Both of us
had marveled over that mystery a long time.  We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
                Mark Twain, Extract from Eve's
                Autobiography