Trying to recall rope-tension problem

[FallenShadow]

Homework Statement

I'm trying to recall this problem my ap physics teacher told us about a while ago in order to tell a friend, but I can't really remember the details.

The basic idea is that you attach a rope to a fixed point (say, on a ceiling). The rope has a certain maximum tension past which it will break at some point. I think what we did is we simplified the system; we said that the rope has some mass that we can pretend is concentrated at one point. As it turns out, even if you applied the exact same force, if you pulled really hard on the rope, it would break on one side of that point; if you pulled slowly, it would break on the other side. (Actually, it may have been vice versa, I can't remember) The question then basically asked, why is this?

Homework Equations

F=ma

The Attempt at a Solution

I'm just trying to recall the details of the problem; under which circumstances does it break on the upper side of the rope or the lower? Perhaps somebody familiar with the problem could restate it more articulately. If you recall the reason why it breaks at different points, I'd appreciate that too; I think it had something to do with the fact that our basic model of forces made an untrue assumption as it applied to this problem.

Thanks.

 

[PhanthomJay]

The problem runs something like this:

A lead cylinder hangs on a string. By another string, another cylinder is hung on the previous cylinder. If you pull fast enough, the lower string tears, if you pull slowly, the upper one tears. How does one explain this?

The solution requires some thought; the strings are extensible, and you need to consider impulse to explain why the lower string breaks first when you pull quickly. Give it some thought. There should be no untrue assumptions, but there might be some incorrect ones.

 

[FallenShadow]

Thank you; that phrasing is much more concise and clear than what I had. You're pulling on the cylinder you just hung, correct?

If I were to draw a picture...

(Fixed end)
(String) <- this breaks if you pull slowly
(Cylinder)
(String) <- this breaks if you pull quickly
(Cylinder) <- you pull on this

correct?

 

[PhanthomJay]

Yes, that's correct. Now, go for it! Everytime I see this problem, I have to think it out again. It's a little tricky, and your apt to find as many reasons for its solution as there are responders. Note: both strings are made of the same material, and have the same breaking strength.

 

[Saladsamurai]

Wow! I have never seem this one. Interesting and now I will be thinking about it for awhile!

 

[FallenShadow]

Thank you!