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The cleanest version of the idea is as follows:
Imagine a box-car of mass M, with a trap door
on the back side. For simplicity, assume it
is initially at rest. We shoot it from behind
with a ball of mass m. The ball goes freely
in through the trap door and goes all the way
to the front wall of the box, where it bounces
elastically. It then travels back to the back
of the box, where it cannot get out the trap
door, so it bounces elastically, returns to
the front, et cetera ad infinitum.
This makes a great homework problem: Find the
*average* velocity of the M+m system.
For good students, you should not be explicit
about what you mean by "average". Make them
figure out what should be meant, and make
them tell you. This is good practice for
solving real-world ("Letter to Garcia")
problems. But for the dimmer bulbs, you'll
have to tell them what average you want.
Anyway, among other things, this gives a nice
unforgettable mental model of dissipation. If
you draw the world-line of the system in enough
detail, there is no dissipation. But if you
average over a moderately-long timescale, you
see only the average behavior, which is what
we call the dissipative case.
The point is that the transferred p cannot be
hidden -- not for long anyway -- not in a closed
system. You can hide some of the momentum some
of the time, but there's a strict upper bound
(tx) on how long you can hide it, and averaging
over any longer timescale will reveal the "hidden"
momentum, forcing it to contribute to the black-
box CoM motion.
For homework, find tx explicitly in terms of m,
M, and the size of the box.