# Strings holding a cube from above and below

I was watching a Walter Lewin lecture on Newton's laws (which was great, by the way), and at the end, he presented this problem;
There's a string hanging from the ceiling (actually not the ceiling, it was just a surface), and a cube is hanging from that string. There is another string, attached below the cube. Both strings are massless, and the cube's mass is 2 kg. If the bottom string is pulled until one of the two strings break, which string will break, the bottom or the top one?
The students in the lecture all guess that the top string will break, but when Professor Lewin pulls the bottom string, that's the one that breaks. He does it again, but this time the top string breaks! The third time, the bottom one breaks. He tells his students to think about what's going on, and the lecture ends there.
I'm not really sure, but the best I can figure is this;
For the top string, the tension is equal to the weight of the cube plus the tension of the bottom string.
For the bottom string, the tension is equal to the applied force (because of Newton's 3rd Law: the string pulls the cube down, which pulls the string up) plus (maybe, I'm not really sure about this one) the tension of the top string.
Since the forces on both strings are equal, they should snap at the same time (maybe, I'm not sure that's possible), but since there are small imperfections, one string will snap a little bit earlier.
If this is right, please let me know so I can sleep tonight.
If not, please tell me what's actually going on so I can sleep tonight.
Either way, thanks for helping me solve this.

Ah, fine, they had negligible mass.

WannabeNewton
It's ok Gphysics, massless is a term used all the time for these types of strings. Anyways, I watched the lecture you referred to. Notice there is a very important difference in the way he pulls it and the bottom one breaks (1st time) and the way he pulls it and the top one breaks (2nd time) and again pulls it and the bottom one breaks (3rd time). Did you see the nature in which he pulled it? The 1st and 3rd times he pulls it incredibly fast whereas the 2nd time he pulls it very slowly.

For reference: go to 44 minutes.

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WannabeNewton
In case you haven't studied impulsive forces yet, here is one way to think about it. In the second scenario, he pulls it extremely slowly so as to keep the lower string pulled at essentially constant speed in which case we know that the tension in the bottom string that is acting on the mass is just the applied pulling force (call it F) so the tension in the top string (if the block is to not accelerate) will be F + mg so the top string, feeling a larger force, will break first. In the 1st and 3rd cases however he applies enough force F to break the bottom string almost instantaneously (an impulse response) and it happens over such a short time period that the top string doesn't really feel it.

EDIT: BTW I have NO idea what pheonix is saying. Not sure if he's trolling or inebriated but relativity is not relevant here.

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Oh, WOW. Now I feel really stupid...
I HAVE studied impulses, and this would have been a fairly simple problem. I just happened to be looking at my book while he was pulling the string :S. I like to look over my Kleppner book while I watch mechanics lectures sometimes, just to get more details (like to get how to derive an equation that the teacher would just put on the board, like a=v^2/r). I only HEARD what he was saying :(...

Thank you phoenix, and thanks WannabeNewton, you're always really helpful!

rcgldr
Homework Helper
In addtion to the impulse, the other factor involved is the tension in the strings is related to the stretch of the strings (and vice versa). If the bottom string is pulled quickly, then the momentum of the hanging mass prevents the top string from stretching much before the bottom string breaks due to excessive stretch and tension.

Yeah, that's a very important factor.