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Re: CONSERVATION OF ENERGY



I am currently entertaining a visiting theoretician and I have not
followed the discussion. I would like to catch up because I think Ludwik
has asked a question which can be used to shatter some misconceptions. I
believe the question must be reformulated before it can be answered (at
least it must be before I will be able to answer it) and I will detail
my requirements for reformulation. I'm sorry to be such a laggard, but
the question certainly has merit. Please excuse me if I'm turning over
a furrow that's been turned over before.

An iron cube whose mass is m slides horizontally over a long iron plate.
The mass of the plate M is much larger than m. The plate is a rest while
the cube has an initial kinetic energy K. Friction brings the cube to
rest before its base reaches the plate's boundary. Everything is in the
vacuum and the thermal energy, dU, added to both pieces of iron is not
radiated. [In principle, dU can be calculated from the observed change of
temperature but no thermometer is available.] Which of the following is
correct and why?

I have been unable to see how the assumption M >> m can be usefully
employed in this problem, as seems to be implied in its statement.
As the poser of the question doesn't know the answer, can we neglect
instead this particular "simplification"?

1. The thermal energy change, dU, is equal to K.

=46Irst let us examine the term "thermal energy". This term is not in my
lexicon, nor should it be in that of any physics teacher. It is a source
of confusion and is frequently found to be a barrier to conceptual grasp.
If you will define the term as a function of the parameters which describe
the state of the system (energy is a state function) I will then be able
to do two things. I will be able to suggest the appropriate conventional
term and I will be able to discuss and probably answer the question. Note
that I am not asking for a semantic clarification here; I'm asking for a
physical relation.

2. Only part of K goes into dU, the rest is used to do work W=3DR*x, where
R is the force of kinetic friction and x is the distance the cube
slides before comming to rest.

The concept of work should not be confounded with that of energy. That
seems to be implicit here. The confusion arises because both quantities
are expressed in the same units. Work is a classification into which
some energy transfer processes can be subsumed. There is a work-energy
theorem by means of which the two quantities may be seen to be related,
much as the height of a water column is related to the pressure at its
base. Height and pressure are not the same thing, however, even if the
latter is expressed in the units of the former, a common practice.

3. Neither of the above is correct.

That is likely.

I am really confused in this situation. My frame of reference (for K and x)
is attached to the plate.

Why have you chosen an accelerated frame of reference? The problem was
really quite a bit better as originally stated. I don't think I would
want to use that frame of reference.

I would prefer to adopt instead the frame of reference in which the
initial conditions are given, i.e. that in which the large iron plate
is initially at rest.

Make sure I understand you.

That is the challenge we all face as teachers. It goes without saying.
The Germans have a great word for it: "selbstverst=E4ndlich"!

Leigh

Leigh Hunt Palmer Phone: 604 291 4844
Department of Physics FAX: 604 291 3592
Simon Fraser University Home: 604 299 3731
Burnaby, BC V5A 1S6 email: palmer@sfu.ca
CANADA 122d58m W 49d17m N