Will Accelerating Spaceships Break Their Connecting String?

[jstefans]

Homework Statement

1) Two spaceships are at rest with a distance x between them and tied together with
a string. An observer standing in between the two spaceship sends them both a signal.
As soon as the signal reaches each spaceship (same time in the observer frame)
both spaceships start accelerating at a constant and equal acceleration. Will the string tear?

2)Now the two spaceships are flying at v with respect to the observer. They are again
at a distance x apart in the observer's fram and tied together with a string. The observer
sends a signal in such a way that the signal reaches the spaceships at the same time in the observer's fram.
As soon as each spaceship receives a signal they again start accelerating at a constant
and equal acceleration. Will the string tear apart?

Homework Equations

Note: my professor claims he does not know the exact answer.

The Attempt at a Solution

It seems like the answer to A) is no because the string will shrink but so will the distance between the two spaceships.

I'm completely lost as it comes to B. I assume the string does break just based on a purpose for the questions.

Thank you so much!

 

[Jhero]

Thank you for your interesting question. I would like to provide some insights and possible solutions to your scenario.

Firstly, in scenario A), the string will not tear. This is because as the spaceships accelerate, the string will experience a tension force that keeps it taut. The acceleration of the spaceships will also cause the distance between them to shrink, but the string will also shrink accordingly and maintain its tension. Therefore, the string will not tear unless the tension force exceeds the breaking strength of the string.

In scenario B), the situation is a bit more complicated. The string may or may not tear, depending on the specific values of the parameters involved. If the acceleration of the spaceships is small enough and the velocity is high enough, the tension force on the string may be enough to break it. This is because the tension force is affected by both the acceleration and the velocity of the spaceships. However, if the acceleration is large enough, it may counteract the tension force and prevent the string from tearing.

In conclusion, whether the string will tear or not in scenario B) depends on the specific values of the acceleration and velocity of the spaceships. Without knowing these values, it is difficult to determine the exact answer. I suggest discussing this further with your professor and conducting some calculations or simulations to gain a better understanding.

I hope this helps and good luck with your studies!