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Re: Rocket action

But if the exhaust gases that were emitted at first are still moving
(at high speed relative to the initial point of firing) they are a
long way from the cm by this time and thus provide the
"counterbalance" that can keep the cm fixed. I haven't tried this
calculation, so my impression may be wrong, but it seems to me that
this fact could account for the possibility of the final velocity of
the rocket (rel. to the original starting point) can be faster than
its exhaust velocity (rel. to the rocket). This also may lead to the
condition that the mass of the fuel must be greater than a certain
multiple of the empty rocket mass that someone mentioned early in
this thread. In other words, the "system" is the now fuel depleted
rocket, and a stream of exhaust gas spread out over space. The gas
farthest from the rocket is moving fastest relative to the original
position of the rocket, with that closest to the rocket moving at a
speed which, while equal to the specified exhaust speed relative to
the rocket, may well be moving in the opposite direction from the
earliest emitted exhaust gas, in other words, the rocket is moving
faster than its (originally emitted) exhaust gas.

This makes sense to me, but it certainly is no "proof" that the
rocket can go faster than the first gas exhausted when the rocket was
just starting to move. I leave it to others more well versed in this
type of math than I to show whether I am right or wrong. Maybe next
year, when I'm retired, I'll have time to do the complete calculation.

Hugh

Let me elaborate on the meaning of my message so that Brian can respond.

I was just commenting on what to me seems less than an obvious situation.
We know that in this situation momentum is conserved (at zero) since there
are no external forces. This is equivalent to saying that the center of
mass remains fixed.

But now consider the rocket--moving to the left from an initial position P0.
At first it is not hard to see that a small mass of fuel/exhaust is expelled
and is moving to the right of P0 with a large velocity while the rocket and
remaining fuel moves off to the left with a much lower velocity--conserving
momentum and leaving the CM fixed. But now if the engine IS NOT throttled
such that the velocity of the exhaust relative to the engine remains fixed,
the velocity of the exhaust relative to P0 is constantly decreasing in the
rightwards direction and eventually (with enough fuel/thrust) the exhaust
gasses expelled at some later time will actually have a velocity towards the
left of P0. It is at this point that I don't have a good intuitive feel for
how the CM remains fixed. I"m sure I can do the math, I just have trouble
'seeing' it. Thus my comment was aimed only at the fact (at least for me)
that the rocket problem is non-trivial, and non-intuitive. I have no
problem when I consider the motion from a force/acceleration point of
view--but from the momentum, CM point of view, it gets more hazy. ;-)

Rick

----- Original Message -----
From: "Robert A Cohen" <bbq@ESU.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, December 10, 1999 1:22 PM
Subject: Re: Rocket action


> On Thu, 9 Dec 1999, brian whatcott wrote:
>
> > At 15:53 12/9/99 -0500, Robert Cohen wrote:
> > >On Fri, 3 Dec 1999, brian whatcott wrote:
> > >
> > >> At 08:52 12/2/99 -0500, Rick Tarara wrote:
> > >>
> > >> >It is easy to 'see' that the rocket can continue to accelerate under
a
> > >> >sustained thrust, but less obvious how the center of mass (rocket
starting
> > >> >in space, originally at rest) remains fixed and at rest, especially
> > >> >once the
> > >> >speed of the rocket exceeds the speed of the exhaust. ;-)
> > >> >///
> > >> >Richard W. Tarara
> > >>
> > >> I believe Rick would want to reconsider this mind experiment.
> > >>
> > >> brian whatcott <inet@intellisys.net>
> > >> Altus OK
> > >>
> > >
> > >Why reconsider it? Is something wrong with it?
> > >
> >
> > I have written up my objection to the list two or three
> > times by now. Is the objection not intelligible?
> >
> > The idea of a time progression until a rocket outraces its
> > exhaust is a physics textbook fairy tale in essence, if you
> > consider that its exhaust can be throttled to low velocity
> > at some indefinitely early stage.
>
> I'm sorry but you've lost me. What is it, specifically, about Rick's mind
> experiment that you object to? Is it his statement that the center of
> mass remains fixed? It seems reasonable to me and I'd like a clear
> explanation for why it is wrong. By the way, I've only been a member of
> this list for a short while and so I may have missed your earlier posts
> (although I checked the archive and couldn't come up with anything).
>
> ----------------------------------------------------------
> | Robert Cohen Department of Physics |
> | East Stroudsburg University |
> | bbq@esu.edu East Stroudsburg, PA 18301 |
> | http://www.esu.edu/~bbq/ (570) 422-3428 |
> ----------------------------------------------------------
>


Hugh Haskell
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
have to..
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