You say the mass's momentum changes by +2 units and the pipe's momentum changes by -1 units. Why the discrepancy?
well if you are speaking about a mass that is moving in one direction , then it changes its direction to the opposite direction then yes it does change by 2 units but not by +2 units.
while the mass travels through the 1st turn its momentum
changes from -1 to 0 through the 1st half of the 1st turn.
then as the mass travels from half way through the 1st turn until it finishes passing through the 1st turn the mass
changes its momentum from 0 to +1
its momentum has changed 2 units but it never did achieve
a +2 momentum change in either the (-) or the (+) direction.
Whatever momentum the mass transfers to the pipe, the pipe has to receive from the mass. If the mass gains 2, the pipe has to lose 2.
TRUE
If the mass gains 2, the pipe has to lose 2.you mean if the accelerator causes the mass to gain 2 in one direction the pipe has to gain 2 in the opposite direction.
To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.http://www.youtube.com/watch?v=L2mdAvdPhT4 when the ball that is attached to the string in the pendulum example in the above MIT video is dropped the ball transfers its momentum to the table and the ball would not just stop when it is half way through the pendulum.
No it wouldnt . the ball does not stop it keeps going and the only reasons the ball does not go as high as the position it was dropped from is gravity and a small amount of air resistance.
so the ball on the string pulls on the string.
the pole that the string is attached to pushes downward on the table and this push is a force caused by the ball swinging on the string.
just like the mass passing through the 1st turn.
except the pipe is moving, so as the mass passes through the 1st turn the mass applies a force to the pipe, and this force stops the pipe.
if the pipe were not moving , and the mass passed through the 1st turn , then the pipe would move in the (-) direction and the mass would stop.
because the pipe would not have momentum and the mass would have momentum , the mass would transfer its momentum to the pipe.
just like a pool ball transfers all of its momentum to another pool ball if struck at just the correct angle.
Another way to look at it:
Imagine the pipe and mass both have the same mass.
In step 2 it's effectively two identical objects travelling towards each other at the same speed.
No the mass and the pipe have different speeds.
wasnt the mass 100kg and the pipe 1000kg before I changed the pipe length to 1000 meters vs 500 ft.
so the force that is applied to accelerate the 100kg mass could not accelerate the 1000kg pipe and the 100kg mass to the same speed.
You say that when they hit and bounce off, _one_ of them stops
yes the one that has +1 momentum stops , its the pipe , it stops.
it stops because of the -1 momentum of the mass.
the mass continues moving because the pipe is also transfering momentum to the mass while the mass is transfering momentum to the pipe.
no other energy is expended durring the collision such as bending the pipe or the mass or in general deforming the mass or the pipe.
now remember this is in space , so just like the spacecraft that exhaust its thrust the mass would keep going forever if it didnt encounter the 1st turn.
but its a little different because the acceleration of the mass gave the pipe the exact same amount of momentum that the mass recieved , so before they collide the two had 2 units of momentum between them.
so we started with 2 units , -1 mass and +1 pipe.
durring the collision we used up 1 unit stopping the pipe
and after the 1st turn we end up with 1 unit , which is the +1 momentum of the mass.
so the 2nd turn should stop the mass as it passes through the 2nd turn.
this means that the accelerator may have to extend into the 2nd turn just a little so that the mass will enter the accelerator.
we still have the following after the completion of the first 3 stage event.
1) acceleration +1 pipe , -1 mass
2) 1st turn 0 pipe , +1 mass
3) 2nd turn +1 pipe , 0 mass
the pipe moves durring the acceleration , then stops
then the pipe moves durring the 2nd turn.
the pipe is moving and the mass is not.
theres really nothing odd about that.
if your worried about the free energy part of it just think about this.
if all you have is a straight rail gun in space.
you shoot a 100kg mass from a 100kg rail gun
what do you have?
you have 2 masses with the same exact momentum.
one mass goes in one direction the other mass goes in the opposite direction.
now if that rail gun were inside a long pipe and the mass and rail gun strike the ends of that pipe at the same time you would have 2 impacts that would total to twice the amount of energy you supplied to fire the rail gun.
you could capture that energy and that would be free energy
because you got back the energy you expended and you also got back an equal amount of energy to boot.
To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.but thats not how that works.
when the rail gun pushes against the mass 1/2 the energy is expended to push the mass and 1/2 the energy is expended to push the rail gun.
so in reality you could only capture the same amount of energy that you expended.
but both masses moved a distance and it cost you nothing.
that is still free energy because you moved things a distance and it cost you nothing.
