Re: [Phys-l] Rocket Hovering and Conservation of Momentum

[Leigh Palmer <palmer@sfu.ca>]

On 26-Jul-06, I wrote:

> On 25-Jul-06, at 9:00 Zeke Kossover wrote:
>
> > Howdy-
> >
> > A student asked me this question recently, and I am not
> > sure about my answer.
> >
> > He asked, "Imagine a rocket hovering off the ground,
> > applying a thrust equal to the rocket's weight. Gas is
> > moving downwards getting downwards momentum. What is
> > getting upwards momentum?"
>
> I haven't read any of the ensuing discussion, ...
>
>  [deletia]
>
> I will not extend this already prolix note farther because there is  
> no need to. Do the analysis!

I have now read the contributions to this thread through Thursday's  
Digest and I don't like any of them except, perhaps, Jack Uretsky's.  
I feel that I must do the very simple analysis explicitly, though any  
of the respondents could have done it for themselves.

First, in order to apply the principle of conservation of  
translational momentum to this system one must define an applicable  
system. Such a system must be isolated, which in the case of  
translational momentum conservation means it must be closed and free  
of net external force. In order to be closed, no momentum carrying  
entities, like masses, neutrinos or photons, may cross the system's  
boundary in the interval during which we mean to apply the principle.  
Of course we may approximate appropriately, neglecting what is  
justifiably negligible.

With these requirements clearly in mind, the simplest system I can  
imagine to which the principle of conservation of linear momentum can  
be applied in Zeke Kossover's student's problem is one which contains  
the rocket and the Earth*. In the simplest calculation I can do the  
translational momentum of this system is exactly zero in the center  
of momentum frame. This momentum may be considered to be  
compartmentalized into subsystems, but the exhaust gas subsystem is  
not an isolated system because it is neither closed nor free of  
external forces. If we choose instead to calculate the translational  
momentum of the [exhaust gas plus rocket fuel] subsystem, we find it  
is both closed and free of net external force. However it is  
difficult to dot all the necessary i's and cross the necessary t's -  
this system is not sufficiently simple to use in teaching! For  
example, I have to modify my model by eliminating Earth's atmosphere  
and digging a hole below the rocket deep enough to accommodate all  
the exhaust generated in the period of interest. In this case the  
[exhaust plus fuel] system will have some constant net downward  
momentum in the previously established frame, and the [Earth plus  
rocket] subsystem will have an equal and oppositely directed  
translational momentum in that frame.

I see that many more comments have come in this morning's Digest, so  
back to reading.

Leigh

*The KISS principle also applies.