How Do You Calculate Tension in Different Cord Configurations?

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To calculate tension in different cord configurations, it's crucial to understand the forces acting on the object, which typically include the weight of the object and the tension in the cords. The tension equations can vary based on the orientation of the cords, leading to both positive and negative values in calculations. For equilibrium, the sum of forces in both the x and y directions must equal zero, which is represented by the equations EFx = 0 and EFy = 0. Drawing a free-body diagram helps visualize these forces and clarify the relationships between them. Understanding these principles is essential for solving tension problems effectively.
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Homework Statement


An 80 N traffic light is supported at the midpoint of a line between two poles that are 30 m apart. If the light sags a vertical distance of 1 m at the midpoint, what is the tension in the supporting line?

A 20 lb picture is hung from a nail so that the supporting cords make an angle of 60. what is the tension of each cord segment?

Here is the actual homework problem i have to solve: An 80 N picture is hung from a nail as indicated. Assume the zeros in the 80 N weight are significant. The angle between the cords in 78 degrees. What is the tension in the each cord?

Homework Equations


I am lost here.


The Attempt at a Solution


And lost here.

There are 2 examples in my instructor's lecture notes that he sends to us by mail that has a street light and another picture hanging from 2 cords. in the street light problem, the tensions are all positive:

Tax = TaCosdegree
Tay = TaSindegree
Tbx = TbCosdegree
Tby = TbSindegree

and so on. But in the picture problem, some of the equations have a negative out front. such as:

Tbx = TbCos60
Tby = TbSin60
Tax = -TaCos60
Tay = TaSin60.

why is that? why would some problems be all positive and some get negatives in others? I have realized that i am suppose to set EFx = 0. where the E is the sigma symbol which i believe stands for equilibrium or net. and i am suppose to set EFy = 0.

can someone please help me understand this? my instructor has been out sick since last monday with swine flu and he has not returned to work yet.
 
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Welcome to PF.

It's best to start by drawing a free-body diagram. For these problems, there should be 3 forces acting on the object.
 

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