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I have a text book which gives two diagrams of beads suspended from strings with different angles, and worked examples to calculate the tension in the strings.

The first bead is suspended by $2$ strings attached to a rod, both strings at angles to the vertical (the bead is at the bottom, the rod is across the top). The text book tells me to label the tensions $T_1$ and $T_2$.

In the next diagram, one of the threads is now vertical, while the other is at an angle. This time the text book tells me the tensions are equal.

Why are they different in one layout, but equal in another?



Agh, sorry - missed some vital info!

In the second diagram, there is a horizontal force applied to the bead to keep it in equilibrium!

(I still don't understand why the tensions in the strings would be equal though!)

And some more vital info. I think I'm almost there now. In the second example, the bead is suspended not by two pieces of string, but by $1$! The bead is somewhere in the middle of the string. The diagrams are so similar, I thought there were two strings in each diagram! (That'll teach me to read the question!)

I suspect the tensions in the two parts of the string have to be equal because otherwise the string wouldn't be in equilibrium. Or something. Can anyone confirm that for me?

(For the interested, the text book is the Edexcel AS and A Level Modular Mathematics. The page is 98.)

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Could you provide some more information? For instance, what text and page number? Or, are there other strings or something else in these diagrams? In particular, I don't see how the bead in the second diagram could be at rest unless the horizontal components of the tensions in the two strings add to zero. Yet there would be no horizontal tension in a strictly vertical string while there would be horizontal tension in an angled string. – Mike Spivey Oct 19 '10 at 23:17
It seemed like you ended up figuring this out all by yourself. The rest of us could have been of more help if you had heeded Mike Spivey's comment and posted all the details of the problem in the first place, rather than revealing bits of information as and when you realized that they may be significant. – Rahul Oct 22 '10 at 7:02
Anyway, yes, as long as all external forces on the string are normal to the string (presumably it is a frictionless string, in which case this would be true), the tension on the string is constant. If it weren't, a segment of the string with different tensions at the two ends would experience a net force. – Rahul Oct 22 '10 at 7:05

Simply put, the tensions are equal because that's the way the problem is set up--it's a given, and you're supposed to use this information to solve for something.

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Hi Tristan - thanks for the answer. The question doesn't directly tell you the tensions are equal - it's only stated during the "worked example" part. Which suggests its something that you are supposed to infer from the question. – Tim Gradwell Oct 22 '10 at 6:34

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