Re: Physics Answer to a Question...

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

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.  Yours
would result in a relative velocity of V + dv.  It makes little difference
here because m is as good as infinitesimal, but only my formula works in
the case that m is *not* infinitesimal.  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.

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

John
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