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Re: Physics Answer to a Question...



On Sun, 9 Feb 1997, John Mallinckrodt wrote:

On Mon, 10 Feb 1997, A. R. Marlow wrote:

Here is where the problem lies -- you are using V - v - dv as the speed
of the ejected tobacco after the spit. But by definition V is the
difference between the speed of the rocket (old man) and the speed of
the ejected material in the given frame, and so the correct expression
for the speed of the ejected material in your formula above is simply
V-v. (See, for example, Marion & Thornton, Classical Dynamics of
Particles and Systems, Fourth Edition, Saunders, 1995, p. 89). By
including the extra dv you get a cancelation of the earlier mdv term, but
that cancelation in fact does not actually occur. In the standard
derivations of the rocket formula, the mdv term is dropped because it
is a product of two infinitesimals (specifically noted in the text of
Marion & Thornton cited above), but we cannot argue that here, and
hence the term remains and contributes to the motion of the old man.

Again, I must demur. You'll note that my formula gives a relative
velocity of V between the old man and his most recent projectile. ...

You don't want that relative velocity, since it introduces the new
accelerated frame of the old man -- you want V to give the relative
velocity of the ejecta wrt the same inertial frame you started with.
Again I can only ask you to check the existing standard treatments of
the rocket problem (for example, Marion & Thornton) and see if you
agree with them. If you do not, but think they are erroneous, then
you should publish that -- it would be an important contribution
and correction to the existing literature.


... Using your formula the added velocity turns out to be

dv = mV/(M-m)

So, for the fun of it, I just tried this in my spreadsheet. Not
surprisingly--and, again, since m is *as good as* infinitesimal--the
result is still 9064 spits.
...

Isn't m = .001 kg ?? That gives m/(M-m) as about 2 x 10-5. Even
using your 9064 spits that builds up to give a dv = .9 m/s. (With V =
5m/s)
If you are adding in the "rocket formula" term as well, you must be
doing something wrong to be still getting 9064 spits. The two terms
produce about equal effects, so together they require only about
5000 spits.

Am I going to have to pull out my "Always Right Card"? ;-)

John

Only after you prove the standard textbook derivations of the rocket
equation wrong. Please do so.



A. R. Marlow E-MAIL: marlow@beta.loyno.edu
Department of Physics, Box 124 PHONE: (504) 865 3647 (Office)
Loyola University 865 2245 (Home)
New Orleans, LA 70118 FAX: (504) 865 2453