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



On 02/27/05 11:45, John Barrer wrote:

[cart collision scenario]

OK, the new wording of the question is clear.
Thanks.

My question boils down to this: In the time interval
from 0-delta t to 0+delta t, how were the original
system momentum and system KE distributed?

I am 100% confident that this question has no unique
answer. The scenario is underdetermined.

It is one of the miracles of physics that the
_long_-time behavior can be described by a mere
handful of macroscopic parameters: overall
momentum, overall mass, temperature, et cetera.

In contrast, in the moments immediately after a
collision, the system is far from equilibrium
and there's nothing simple about it. There are
not just a handful of parameters, but in principle
maybe 10^23 different things going on. Bouncing,
wiggling, jiggling, et cetera. Maybe not all
10^23 are important, but there could easily be
dozens and dozens that are important.

To figure out what really happens would require
a a detailed analysis, starting from a detailed
description of the internal structure of the carts.

There are folks who do this for a living. Consider
for example designing an airplane to withstand
the stress of landing, turbulence, et cetera.
There's nothing simple about it. They used
finite-element modelling with thousands or even
millions of elements.

All of the above is to try to convince myself that,
just as momentum transfer w/o energy transfer is quite
possible, the reverse is true as well. Thanks to all
for your patience.

If that's what you want, the following scenario
might be of interest:

Cart B starts at rest and remains at rest always.

Cart A is small and drives right underneath car
B, like a car going through a car-wash, maintaining
constant velocity always.

There is negligible transfer of momentum, but the
two carts can exchange energy via black-body
radiation.

As an issue of terminology, I suspect many people
would hesitate to call this interaction a "collision"
but whatever you call it, it is some kind of
interaction that exchanges lots of energy and little
(if any) momentum.
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