Given 2 magnets of equal weight (w0) and each with a magnetic strength (t0) placed inside a straight hollow cylindrical tube. One of the magnets is attached to one end of the tube and the other magnet is free to move inside the tube. The other end of the tube is open to space/vacuum.
The tube is travelling in space with a velocity (v0) such that it is oriented vertically towards direction of motion. The end with the magnet attached is the leading end (towards direction of motion).
Consider 2 cases:
Case 1: The free flowing magnet and the tube both are travelling at the same velocity (v0) and the free flowing magnet is at the initial distance (d0) such that both magnets exert can pull on each other.
Case 2: The tube and free magnet are moving at velocity v0. Their distance of initial separation is (d1) such that the magnets exert no pull at each other (so d1 remains same unless an external force is applied). Assume, at some time (t0) an external push to the free magnet (in direction of motion) such that it is now moving with a velocity (v0+v1) and the tube at the same velocity (v0).
What does the conservation of momentum predict when both magnets finally come in contact.
The Attempt at a Solution
My understanding is as follows:
Case 1: Both magnets when they physically come in contact and stick together, the tube would continue travelling in the direction of motion with the same initial velocity (v0).
Case 2: When both magnets come in contact and stick together, due to conservation of momentum the new velocity of tube would increase and would be exactly (v0+v1/2).
P.S. The tube has negligible weight so we assume it as 0.
Is my interpretation correct? Or does the resultant velocity depend on other factors like the magnetic strength too?