Will Object Move When Rockets Synchronously Fire & Shutoff?

[nemesiswes]

Hi, A while ago I posted a question that had to do with whether a hypothetical box that contained the Earth and the sun would move when the gravity, the sun was switched off.
It was locked for being too out there, not bound to real physics which is not allowed on this forum or at least needs to be in the General Discussion I would think. I agree that it was and so that is why I came up with a different idea along the lines of it that this time, I believe is grounded in REAL physics.

Here is the link to the old one if your curious what is was about.
https://www.physicsforums.com/showthread.php?t=618658
Ok, so on to the new theoretical situation.

I included a picture to show what I mean.

You have a 300,000 Km long thin carbon fiber beam. (I say carbon fiber so it is lite but strong. Also I am not sure what it would weigh) (could be any material I guess)
The beam is in space away from in any gravitational sources.
The time taken at minimum to traverse the beam is 1 second obviously.
On each end of the beam, there is a rocket attached to the beam.
The rockets are oriented so they face push toward each other. (they have exactly the same thrust)
The two rockets are synchronized so that when A shuts off, B shuts off exactly 1 second later.
The rockets can shut off very quickly, faster then 1 second.
T-0 = both rockets firing
T-1 = Rocket A shuts off, Rocket B still firing
T-2 = Rocket B shuts off, Rocket A is offSo here is what happens, we start at a point where both rockets are firing with equal thrust.
The beam and the rockets move nowhere because there is no net force acting on them since both rockets cancel out. At T-1, Rocket A shuts off, then at t-2 which is exactly 1 second later Rocket B shuts off. So the question is that if Rocket A shut off and there was a 1 second period where only Rocket B was producing thrust since after T-2 Rocket B shut off, does Rocket B's side start to move and then 1 second later , the other side (rocket A). This is what I think, I assume at T-1 Rocket A starts to move backwards away from Rocket B because the Beam starts to uncompress. Both rockets were firing and the beam would have been under compression, so without Rocket A countering the force generated by Rocket B, Rocket A starts to move backwards in the direction Rocket B is pushing. At this same moment, Rocket B does not move at all because as far as it knows, Rocket A is still on. Between T-1 and T-2, two things happen, a wave of UN-compression move's back through the beam toward Rocket B causing the beam to move toward Rocket A. At this same moment, Rocket B is pushing the beam toward Rocket A, A compressive wave moves through the beam toward Rocket A. I am not sure what happens when these waves meet? I have mixed ideas of what happens, I think they cancel since Rocket B is still firing, it has waves behind which continue on toward Rocket A. At T-2 Rocket B shuts off and the beam continues to move in the direction rocket B was pushing the beam toward.

So I have tried to ground this in reality as much as I can. So what happens, does the beam continue to move in the direction rocket B was pushing toward since no counter acting force was generated between T-1 and T-2 even though there is a 1 second delay before Rocket B starts to move and Rocket B shuts off at the exact time any information of Rocket A shutting off Reaches it. Does the beam move at all?

 

[voko]

The total impulse given to the system is 1 second of rocket B's thrust. So the system as a whole will be moving in that direction. In addition to that, the system will oscillate longitudinally. The amplitude of the oscillations will be very significant because the oscillatory motion will have double the energy of the linear motion.