Pulling on a weakened rope - where will it tear? Let's say I have a rope of 10m length and it is weakened in 3 spots:
at 2.5m, at 5m and at 7.5m. Weakened means that if enough tension is applied it will tear at these points (all points are equally weakened).
This rope is connected to an immovable wall. There is a person on the other side pulling it.
My question is where will the rope tear?
Follow up question: If two people are fighting over a piece of weakened rope, what is the optimal strategy in applying the pulling force, assuming that the rope is weakened at several points and the winner is the one who has the largest piece of rope at the end?
 A: I suspect the result depends on how fast you increase the pulling force. If you pull abruptly, I would expect the rope will tear at the weakened point that is the farthest from you, as the tension wave from the wall will first arrive at that point, whereas, if the pulling force is increased very slowly, I would guess the point of tear can be determined by some random factors. 
A: I would say that not in the middle, either one of the other points. This is my argument:
The string when pulled from both extremes (the same in both cases you ask) it will vibrate in its eigen-frequencies, shown in the picture below taken from Wikipedia. This oscillation will add strain to the points of rope.
But as can be seen, while the point in the middle receives strain contribution from half of the eigen-frequencies (i.e. is displaced and therefore stretched), the points in $1/4$ and $3/4$ will receive contributions from 3 out of every 4 eigen-frequency. Therefore the center point should resist a bit more than the others. Due to symmetry, it is hard to predict which one of the other would break easier.

