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

[John Barrer <forcejb@YAHOO.COM>]

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

> On 02/26/05 09:14, John Barrer wrote:
> > .... 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?
>
> I've read that question (and its context) several
> times
> and I fear I still don't understand it.

Perhaps if I throw in some numbers my question will be
better stated. All vector quantities are expressed in
the lab frame. Let's assume the inelastic collision
occurs in a vacuum chamber so there are no air
molecules present to carry away some of the system KE.
The system consists of two carts (a=.25kg, b=1.0kg) on
a "frictionless" surface. At time
0-delta t, Va=0.5m/s, Vb=0.0m/s so that before the
collision, system KE=.03125J and system p=.125kgm/s
with 100% of both "resident" in the CoM motion of cart
a. At time 0+delta t, Va=Vb=0.1m/s which gives the
following:
Cart a: p=.025kgm/s, KE=.00125J
Cart b: p=.1kgm/s, KE=.005J
Conservation of p, 80% dissipation of CoM KE.

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?

My mental model of the momentum and energy transfer is
as follows. During the collision, the velocities of
both carts VERY quickly change to 0.1m/s; internal
vibrations and deformations of both carts account for
.025J of energy but 0.0kgm/s of momentum while .00625J
and .125kgm/s are evident in the motion of the carts
in the lab frame.

I realize that I am ignoring the period during which
both carts (as well as internal particles) accelerate
from their "pre-collison" conditions and that this
could well cause some problems with this model.
Nonetheless, it seems reasonable overall. If correct,
this would mean that the irreversible transfer of
energy to internal vibrations and deformations is NOT
accompanied by a simultaneous but temporary and
reversible transfer of ANY momentum to these internal
particles. Also, the non-zero diminishing
instantaneous momenta of the internal vibrating
particles did NOT "come from" (and is not in a
temporary "holding account" of) the original .125kgm/s
system momentum.

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.

John Barrere  University HS, Fresno,CA
_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu
https://www.physics.buffalo.edu/mailman/listinfo/phys-l