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

["Folkerts, Timothy J" <FolkertsT@bartonccc.edu>]

I'm not sure the analogy is extremely wonderful to start with, but let's try one more time.
 
Heavy cart => earth
light cart => spacecraft 
spring => gravity
 
> When dealing with gravity, it's not the same force, it's the same acceleration.
It IS the same magnitude of force when comparing "the gravitaional force of the earth on the spacecraft" to "the graviational force of the spacecraft on the earth".  Thus it is a very different acceleration for the spacecraft compared to the earth.

 
If the spacecraft is simply "dropped", it will accelerate at some relatively large amount ( 10 m/s^2) because it has a relatively small mass.  The earth will accelerate at some relatively small amount because it has a large mass.  If the spacecraft is held a fixed distance above the earth by firing rockets, the entire earth-spacecraft system will move upward.  Conservation of momentum assures us that the downward gain of momentum by the exhaust is equal to the upward gain in momentum of the earth-spacecraft system.
 
By making the relative difference in mass less, the spring/cart analogy exaggerates the effects
 
Now there are a couple of problems with the spring analogy mainly that it increases with distance and a different spring would be needed to model gravity for different mass "rockets", but that is really seconadry to the general analogy.  The other big weakness with the analogy is that the earth "catches" the exhaust, rather than just letting it fly off into the "room".  In my opinion, this is the real weakenss of the analogy.
 
Tim 

 
________________________________

From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Jack Uretsky
Sent: Wed 7/26/2006 11:57 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Rocket Hovering and Conservation of Momentum



That's one trouble with analogies, they often mis-state the problem.  When
dealing with gravity, it's not the same force, it's the same acceleration
- quite a different matter.  You are, in effect -if I understand you-
saying that a heavier body will fall more slowly than a light body.  Even
Aristotle would blush!
                        Regards,
                                Jack

On Tue, 25 Jul 2006, Folkerts, Timothy J wrote:

> > Hi Timothy-
> >        Are you saying that heavy bodies fall faster than light bodies?
> > Aristotle, you've finally been vindicated!
> >                                                Regards,
> >                                                        Jack
>
> Um...  No, Jack, I'm not saying that at all.  You must have misunderstood my analogy (or perhaps the earlier analogy that I was modifying).
>
> I'm saying that when the same magnitude of force (ie from the spring) is applied to two objects (ie low friction carts of different mass on a horizontal track), the smaller mass will have a larger acceleration, and hence move faster and farther than the heavy cart.  I think that is all in accordance with Newtonian Mechanics.
>
> Tim F
>
>
> On Tue, 25 Jul 2006, Folkerts, Timothy J wrote:
>
> > I think a better example would be one very light cart connected by the spring to a very heavy cart.  If you let go, they will both move toward each other, but the light cart will move more.
> >
> > If a rocket is connected to the light cart to maintain a constant distance from the heavy cart, then the whole system will slowly accelerate (the same as if a solid bar connected the two while the rocket fired).
> >
> > To make a better analogy with the earth, you might want to consider a large plastic bag surrounding the carts to contain the air.  That complicates the system, but makes a fairly tight analogy.
> >
> >
> > > 2.  Consider two aircarts connected by a spring.  The track runs from
> > > left to right and the spring is initially stretched so the carts would
> > > pull toward each other.  If one holds the left cart so that it is
> > > stationary in the lab frame, the right cart accelerates toward it.  Now
> > > replace the person holding the left cart with a rocket that keeps the
> > > left cart stationary in the lab frame. (This would require a controller
> > > on the rocket the adjusts the thrust constantly.) The right cart
> > > accelerates to the left and thus gains momentum, balancing the
> > > conservation of momentum equation.

--
"Trust me.  I have a lot of experience at this."
                General Custer's unremembered message to his men,
                just before leading them into the Little Big Horn Valley



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