Originally Posted By: paul

I never said that the mass would be stopping , that was your

A u-bend does stop the mass in 1 dimension, which is all we're considering, and all we need to consider. In order to turn it around. You have to decellerate it down to 0 then back up to full speed. This consumes _NO_ energy because it's an elastic 'collision'. Of course in the real 3D system the _speed_ remains constant throughout the turn, but the component of velocity in the only direction we're considering with must drop to zero and change sign.


there is (((( ALWAYS )))) 1 mass in 1 turnaround and

That means we have to change the force it applies when going through:

In 7.8s 20 masses enter the turnaround.
Each mass spends 7.8/20 = 0.39s turning around.
Reversing the direction changes its momentum by 3900*2=7800 Ns
If the turning is done by applying a constant force between the mass and the tube, then that force is:
F = 7800Ns / 0.39s = 20,000N
So this force of magnitude 20,000N is applied continuously at the 1st turnaround.

Just as before, this is double, but opposite the constant 10,000N force applied by the accelerator.

And of course just as before I still havn't mentioned the 2nd turnaround which will help. But I don't know how you want it to work yet. See below..


you always seem to forget the other turnaround so your
+156200Ns plus -156200Ns = ZERO
they cancel each other out.

I purposely omitted it because I didn't know what the setup should be. If there are masses going through the 2nd turn at the same speed as all the masses in the 1st turn (39m/s), then they're entering the accelerator already doing 39m/s and will overtake some of the masses starting at 0. But we calculated the forces at the 1st turn assuming all masses were accelerated from 0 to 39, not 39 to 39+39. So the force in the 1st turn now depends on which mass is going through it, and will always be equal or higher in magnitude than at the 2nd turn which takes some stragglers from the previous acceleration boost.


there is (((( ALWAYS )))) 20 masses being accelerated
there is (((( ALWAYS )))) 20 masses free floating

I'm not sure this is physically possible. Could you produce an animation?