Question

Two spaceships float at rest near a stationary observer standing on an asteroid. The ships are connected by a taut cable, which is strong but will eventually break if stretched to some arbitrary degree. The asteroid observer sees the spaceships begin to accelerate at precisely the same instant in time and at precisely the same rate, in a direction parallel to the rope connecting the two. What happens to the cable?

Answer 1

as the spaceships are connectged by a taught rop, so when the spaceships begin to accelerate in direction parallel to the connecting rop, there can be three things

1. both accelerate in same direction, in that case the rope begins to move along with the space ships.

2. both accelerate in antiparallel direcitons towards each other where the rope becomes loose

3. both accelerate in antiparallel directions away from each other in which case the rope will break if it has to at the same instant