Originally Posted By: paul

the individual masses that are being accelerated in the rail gun will reach the turnaround slightly faster than the individual masses that are floating to the other turnaround.

It's crucial to quantify that in case 'slightly' is actually 'too much'.

- The pipe starts with momentum
pp = 0
- An accelerated mass starts with momentum p1.
- After acceleration at force F for time t it ends up with momentum p1+F*t. The reaction has the opposite effect on the pipe,
pp = 0-F*t
- After turning around 180deg, its momentum in the free-floating stage is -(p1+F*t). This is a change in momentum of -2*(p1+F*t), so the reaction on pipe causes the opposite change in momentum. The pipe gains 2*(p1+F*t),
pp = 0-F*t+2(p1+F*t)
- But at the same time a free-floater is turning around at the other end, imparting momentum -2*p1 onto the pipe.
pp = 0-F*t+2(p1+F*t)-2*p1
Then that just-turned-around free-floater starts to accelerate, imparting -F*t to the pipe during it's travels.
pp = 0-F*t+2(p1+F*t)-2*p1-F*t

There's could also be a slight error because I did everything in the frame of the pipe's initial rest state, but assumed no pipe movement.

This assumption would be valid if the pipe hardly moved at all, say if it had a really huge mass. That's fine, even a huge mass will keep drifting through space given a little momentum.

Edited by kallog (06/15/10 03:12 AM)