What is the tension in the rope?

[matthayzon89]

Can someone help me understand tension?

Can someone please help me understand how to find tension? PHYSICS?
I am trying to prepare for a upcoming test and I am having trouble understanding how to find tension. I have copied a problem from my sample test and provided the answer as well.

Can someone explain how they got this answer for tension in detail so I understand it once and for all?

Homework Statement

A tightrope walker with a mass of 60.00 kg stands at the center of a rope which was initially strung horizontally between two poles. His weight causes the rope to sag symmetrically, making an angle of 4.80 degrees with the horizontal. What is the tension in the rope?





Thank You,
Dr. Zan

Homework Equations

This is what I need help with. I know there is some sort of equilibrium in this problem:/

The Attempt at a Solution

I know the correct answer: 3520 N But would like to understand how this answer is achieved

 

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if you examine the force diagram of the human, the force of gravity pulls down. Unless there is an acceleration, something this motionless setup has none of, the sum of forces on the human must equal zero. Treating the force of tension as a force vector, which component cancels out the force of gravity? Which component of the leftmost tension is canceled by the same component of the rightmost tension?

Once you answer these two questions, you see how to find one component of the tension. Using right triangle trigonometry, the hypotenuse then can be found (the total tension).