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W-->E-->Q-->U, at my level of teaching



I also would like to thank both John's for helping us see
nontrivial nuances. And I hope that each of them values
the substance higher than the form. Please try to improve
the form, and above all, please continue.

I would like to return to John_M's collision of 2 kg and
1kg bodies moving toward each other with identical speeds
of 1 m/s. The initial KE of these two bodies is 1.5 J. The
final KE was postulated as 0.5 J. (By saying that the 2 kg
body does not move after the collision; the total linear
momentum must be conserved.) Thus the amount of KE
lost is 1 J. Where does it "go"?

It depends. Brian used cotton to stop the larger pendulum
bob. Different "brakes" can also be visualized. For example,
mechanisms with little wheels inside of each body. The
wheels are at rest before the collision but start spinning
during the collision. The masses of braking mechanisms,
like the masses of cotton layers, contribute to the initially
given 2 kg and 1 kg.

So where does the lost KE go? I think this question was
answered by John_D to everybody's satisfaction. On a
long time scales the lost energy is thermalized, but on a
shorter scale part of the lost translational KE, in this
example, is used to create rotational KE. For another
"braking device" a fraction of the lost KE may be found
in the form of PE of compressed springs inside the two
block. This would happen if additional (previously
compressed) springs, were used to immobilize main
springs at some moment.

Thus the question of how much of the lost KE -->"heat"
and how much --> "work" can not be answered in general.
The answer depends on the collision mechanisms involved
and on the acceptable time scale. A collision mechanism of
some kind is always present and the W/Q question can not
be answered without examining its details. Even in cotton
some threads behave as "compressed springs".

There was also a disagreement about the term "internal
energy". Should the KE of rotating wheels (inside the
blocks after the collision) be counted as internal energy or
not? I would also call it internal but not thermal energy of
each block. The time scale for thermalizing this part of KE
is likely to be much longer than the "collision time". A
distinction between internal and thermal energies is
necessary, if we want to avoid another linguistic trap.
Internal means being inside, thermal means contributing
to the temperature.

What is heat? It is thermal energy which is transferred
spontaneously from one body to another. What is work?
It is F*x, or the integral of F(x)*dx, to be more general.
To keep things simple, I am referring to a force acting on
a rigid body and passing through its center of mass along
the x axis. Where am I wrong? Many teachers and authors
were saying all this for a long time.
Ludwik Kowalski