Calculating Tension in Vines: A 5.0kg Monkey at Rest on Vines A and B

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To calculate the tension in the vines supporting a 5.0 kg monkey at rest, it's essential to recognize that the sum of forces must equal zero. The angles of the vines allow for the decomposition of tension into horizontal and vertical components, leading to two equations: one for horizontal forces and one for vertical forces. Each equation must be set to zero, resulting in a system of two equations with two unknowns, the tensions in vines A and B. By isolating one tension in terms of the other, you can solve for both tensions. Understanding this approach is crucial for successfully completing the assignment.
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Okay, I got an assignment from my teacher that I'm having trouble starting.

A 5.0-kilogram monkey hangs initially at rest from two vines, A and B. Each of the vines has a length of 10 meters and negligible mass. Vine A is 30 degrees above the horizon in quadrant II, and Vine B is 60 degrees above the horizon in quadrant 1.

I know that the two tensions keep the monkey at rest, so the sum of the forces = 0. But how do I calculate the tension in the vines?
 
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Since you have the angles, you can find the horizontal and vertical force components. Each must add to zero, giving you two equations and two unknowns (the two tensions).
 
This is essentially the same type of question i asked. You have to isolate tension one from T2 and substitute. I am lost from then on lol
 
when you say each, do you mean the two horizontal equal zero, and the two vertical equal zero? or each by themselves?
 
I meant that you'll get two equations:
(1) The sum of the horizontal force components = 0
(2) The sum of the vertical force components = 0
 
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