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Hi there,

I found a thread from 2004 that perfectly answered my homework question here, but I don't understand how the person who responded came up with the answer. I would have just replied to the thread and resurrected it, but it says the thread is no longer open for replies. I'll paraphrase it here:

Original question: Arlene is to walk across a high wire strung horizontally between two buildings 10 m apart. The sag in the rope when she is at the mid-point should not exceed 10 degrees. If her mass is 50 kg what must be the tension in the rope?

Original answer: The sum of forces in the vertical direction would look like this: 0 = 2Tsin(10) - 490.5, T = 1412.3384 N

I actually had the exact same problem with the exact same numbers, but I have no idea why 1412.33 N is the right answer.

I know the equation where ΣF

_{y}= F

_{N}- mg

I also get that the ΣF

_{y}is 0 if there is no movement in the y direction.

0 = F

_{N}- mg.

mg = 50kg X 9.8m/s

^{2}= 490 N

0 = FN - 490 N...

How do you know that F

_{N}= 2Tsin(θ)? I can't find that equation anywhere in the dynamics chapter in my book, my notes, or my teacher's powerpoint. This is supposed to be homework from the dynamics chapter, and I would have been totally unable to solve this problem if I hadn't found this website. I also tried googling the formula and didn't find anything helpful.

Do I just need to take this for granted or is there somewhere I can see how the 2Tsin(θ) was derived?

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