Understanding tension?

Question

I'm trying to understand tension. So here it goes: I'll start from the beginning. Let's assume I'm in space and can move around and apply forces. Let's say a rope is attached to a body(which is in space). 1) Let's say the body is immovable. Then the force with which the rope is pulled will be the tension in the rope. Right? 2) Okay, now let's say the body has a mass M and I apply a force F. The body will accelerate towards me with a acceleration F/M. Obviously, the rope will slacken, so to keep the tension in the rope constant, I will have to accelerate away from the body, maintaining my distance to still apply the force. (I just mentioned that because no one really talks about how one can apply a constant force without having to 'keep up' with the body to keep applying the force. I just wanted to make sure that that truly is the case.) Now let's say, I pull the rope and then let it slacken i.e. not try to maintain a constant force, then if I was able to measure the acceleration of the body and if I know it's mass, I will be able to find the force I applied and hence, the tension (=force applied) for that period of time on the rope. Is that correct? 3) Okay. Now, let's say I pull the *rope* with X newtons of force and another person holds the *body* and pulls it in the opposite direction with Y newtons of force, shouldn't be the tension in the rope now be (X+Y) newtons, even if the body accelerates in one direction? If the person instead *pushes* the body with Y newtons then shouldn't be the tension (X-Y) newtons in the rope now? 4) Let's say the ends of the rope are attached to two bodies and the rope is currently slackened. I then give both the bodies some initial velocity in the opposite direction to each other. Hence, the rope at some point will become taut. Is it possible to tell the force, the two bodies will experience when the rope becomes taut and hence find the tension the string will experience? Please correct me if I'm wrong in any of these. I would really appreciate the help. Thank you.

Answer 1

In any problem like this, you have to define the context---AKA the "frame of reference". If you are in empty space, and there is exactly one other object, then you will be pulled together by the gravitational force.

Ignoring that basic reality, if you connect a rope to the other object and pull, you and the object will both be accelerated towards each other. Unless you continue to reel in the rope, it will of course go slack as the objects move together.

Keep all your reasoning grounded in the basic principles.