Re: CONSERTVATION OF ENERGY, eureka !

[LUDWIK KOWALSKI <kowalskil@alpha.montclair.edu>]

On Sat, 26 Jul 1997  Bob Sciamanda <Sciamanda@worldnet.att.net> wrote:

> This clearly illustrates (harking back to an old thread) the confusion 
> that results when the Work-Energy Theorem of Newtonian Mechanics is 
> confused with the First Law of Thermodynamics.  Given the situation 
> (as I read you): R is the constant net force on the object as it "loses" 
> K (kinetic energy) over a displacement x (in the direction of R), then K 
> and R*x are numerically equal - and rigorously so, by Newton's laws of 
> motion. This is a purely mechanical (dynamics) question, and stands
> quite apart from any conservation of energy postulate or thermodynamic
> considerations.

And he did not want to embarass me by saying that the described experiment
was a waste of time, unless one wanted to verify another prediction of
Newtonian mechanics. I now agree entirely with this observation. The
relation K=R*x remains valid no matter what subsequently happens to K.
R*x is not a form of energy into which K, which is a form of energy, can
be converted. Sharing the same unit, joule, does not make them convertible
into each other; I think it was Leigh who was pointing out to this. In the 
case of sliding cubes most of the K is likely to be found in thermal energy. 
Thus [c*(M+m)*dT] should have been expected to be essentially the same as 
[R*x], as emphasized earlier by Al.

In the case of the lunar collision the depth of the meteor penetration 
would be equal to K/R even if much less that 100% of K "went" into non-
thermal forms of energy, such as the "chemical" energy of compounds formed 
in the lave, gravitational potential energy of piles of rocks around the
crater, etc. Working and heating are processes through which internal energy 
can be changed by [R*x] or [c*(M+m)*dT] joules, repectively. The quantities 
in square brackets refer to changes in "forms of energy", they are not forms 
of energy themselves. 

A tricky linguistic nuance? Yes. Here is an analogy. A transaction whose 
value is $10 dollars is a process of buying or selling, it is not the same 
thing as the dollar amount of milk, bread, and sugar. How to make sure that
students (I was not pretending of being confused) do not fall into linguistic 
traps? Inventing Martian words may help but this should not be up to each 
teacher. We should be pedagogically creative but in certain areas, such as 
words and units, the coordinated approach is essential. A topic for another 
thread? 

The initial discussion between teachers A and B, and a decision to resolve
the issue in an experiment, was based on the "deeply rooted" misconception, 
still very common, that heat and work are forms of energy. Heat and work
are "path dependant" while forms of energy (kinetic, potential, chemical, 
nuclear, electric, thermal, and so on) are state functions. For example, 
a change in electrostatic energy of two charges, when their separation is 
increased, does not depend on the path along which one charge was moved 
with respect to another. Likewise, a change in kinetic energy of a particle, 
equal to force*distance, does not depend on the direction of the displacement. 
Atomic energy (joules of light) "liberated" in a direct transition between 
two levels is exactly the same as in transitions in several photons are
emitted in cascades. The same is true for photons from nuclear or molecular 
transformations. Am I falling into another liguistic trap, the word level?

Without realizing it, the teachers whose converstion lead to this debate
were thinking that part of K is used to do work and another part is used to 
increase the thermal energy of sliding blocks. What would be interesting to 
measure, and Joule was an expert in this, is dT. How much K goes into thermal 
energy is not predetermined by F=m*a. And the laws of thermodynamics, I would 
say, have nothing to do with this. All depends on what is behind the word 
friction. One dissipative process can be very different from another, in 
that respect, even whan "frictional forces" are identical. Oh yes, there is 
a lot of depth behind nearly everything we teach. Some people know about 
nuances, others not.

It was a very long thread. Was I the only one who learned so much from it? 
Thanks to all who bother to contribute. 
                                                    Ludwik Kowalski