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.)