Cable Y-Hangs and Pulleys

You can imagine a person hanging from a cable that forms a Y in shape between to cliffs.  What are the forces in the cables?   Well we can build this by adding a wight in the middle of a system, and measuring the cable tension by hanging other weights off pulleys like so...

The more weight you add to each end, the more shallow the cable gets.   In other words, the more horizontal the rope, the more tension it contains.  Can the rope be perfectly flat with a point load in the middle?   The answer is no, you would need infinite cable tension!   If cables are horizontal you have infinite tension, if cables are perfectly vertical, you have half the load carried.

What about uneven loading, or changes in cable angle like so?

The more vertical rope in this case takes more tension than the less steep rope, but why is that?   For discussion (sum forces in X and Y).


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