the pipe is 152.4 meters long

152 / 20 = 7.6 meters

so the masses begin acceleration seperated by 7.6 meters each.

so we can have a turnaround radius of 4.83 meters.

this means we will need to add 9.66 meters to the lenght of the pipe because of the two turnarounds , however we still accelerate the masses a distance of 152.4 meters.

this way there is 1 mass in the middle of each turnaround when the acceleration begins.

so the turnarounds will need to be used to slightly accelerate the masses in the turnarounds bringing them up to a slight velocity before accelerating them at 5 m/s/s.

if we have to the pipe can always be lenghtened to avoid collisions between the masses.

Im only trying to show the concept not provide you with plans to build anything , so if you are considering collisions forget it.

the 20 masses in the free floating side are held in place by a opposing rail gun accelerator.

the opposing accelerator is removed after the masses are accelerated slightly as I mentioned earlier.

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.

No , you dont decelerate the mass .... the mass is only changing direction.

what you are talking about above is simple direction.

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

No , we do not apply any force while the mass moves through the U turn.

the mass itself applies a force to the U turn and that force is its mass * velocity

100kg * 39.0385 m/s/s = 3903.85 N

which is exactly opposed at the other U turn..........
because its in zero g.

Reversing the direction changes its momentum by 3900*2=7800 Ns

changes the momentum of the mass but not the momentum that is
either applied or subtracted from the pipes momentum.

knowing that the masses passing through the turnarounds cancel
each other out , why do you insist on discussing them?

where are you going with this , there is no gain or loss to pipe momentum because the masses pass through the turnarounds.

because we are not including any friction between the masses and the turnarounds.

its like you are arguing about two 5 lb weights tied to a string then flung over a clothesline.

they just sit there because they both present the same force to each other.

3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.