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[Phys-L] Re: collision question (revisited) (again)

--- "John S. Denker" <jsd@AV8N.COM> wrote in part:
SNIP

On 02/25/05 09:43, John Barrer wrote:

It would thus appear
that these non-zero instantaneous
vibrating-particle
momenta could not have resulted from a transfer of
CoM
momenta, but rather from the transfer of some of
the
CoM KE (but NO CoM p) to internal and external
vibrations, the results of which are time-varying
values of both instantaneous non-CoM KE and p. Is
this
mental model correct/reasonable?

JD's initial reply follows:

I'm not 100% sure I follow that statement, but
if it means what I think it means, then yes, there
is an important (indeed beautiful) physics idea
here.

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.

SNIP

In JD's example, p and KE are transferred into the
interior of the system (the trapdoor truck) via mass
transfer. No such mass transfer occurred in my
original question. So, the original question
(speculation?) remains: In the lab cart collision, is
it correct to say that some CoM KE is transferred to
the carts' interiors without any simultaneous transfer
of CoM p?

Also, with the trapdoor truck (a very nice Gedanken
expt IMO), JD posits internal collisions "ad
infinitum". I think a closer analogy to the colliding
lab cart situation I described would be internal
collisions that are only partially elastic. Thus, each
successive "round trip" collision with the F&R walls
of the truck would (I think) deliver a diminishing net
forward impulse to the truck. When the motion of the
ball in the truck RF finally ceases, the net result of
all the internal collisions initiated by the "mass
injection" would be a small forward impulse plus
heating of the ball and the truck. Having thought on
this a bit more, I'm still stuck on the question
stated at the end of the preceding paragraph.

SNIP

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.

SNIP

Would be GREAT for AP students, but for all others,
I'd be happy if just a few of them spent some mental
energy wrestling with the conceptual issues.

SNIP




Of course, this
would lead to another question: Why can CoM KE be
transferred to internal vibrations but CoM p
cannot?

JD response follows:

Well, yes and no. I'd say p _can_ be transferred,
within limits.

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.

SNIP

If I interpret this correctly, JD seems to be saying
that CoM p IS transferred to internal vibrations (and
therefore internal p), but that it ultimately
reappears as CoM p. But consider that some of the
(colliding lab carts) system KE immediately escapes to
the environment as sound. Since any CoM p that went
along for this "ride" cannot reappear at a later time
as CoM p, does this not argue by analogy for the
proposition that ONLY KE is transferred to the carts'
interiors?

John Barrere University HS Frersno, CA