# Simple Vector Problem - Cable Tensions

1. Aug 16, 2011

### IOwnAndPwnU

1. The problem statement, all variables and given/known data

A 125 N traffic light is hanging from two flexible cables. The magnitude of the force that each cable applies to the 'eye ring' holding the lights is called the cable tension. Find the cable tensions if the light is in equilibrium.

I have attached a scan from the textbook which contains a diagram.

2. Relevant equations

Not sure exactly what equations are there, except pythagoras theorem for magnitude, SOH-CAH-TOA.

3. The attempt at a solution

I assigned the first tension cable (left one) as vector a, the second one (right one) as b and the traffic light as g.

a = (x1cos150, y1[/SUB/sin150)
b = (x2cos45, y2[/SUB/sin45)
g = (0, -125)

And I think: a + b + g = 0

Answer is: T1 = 125($\sqrt{3}$-1) N; T2 = 87.5(3$\sqrt{2}$-$\sqrt{6}$) N.

Thank you!

#### Attached Files:

• ###### vectorproblem.jpg
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Last edited: Aug 16, 2011
2. Aug 16, 2011

### Quinzio

There's nothing attached to the message.

3. Aug 16, 2011

### IOwnAndPwnU

That's weird, I remember the image showing up during the preview. I re-attached it though.

4. Aug 16, 2011

### Quinzio

You have to first balance the horizontal forces (left-right) to make them zero, then you calculate the vertical ones.

5. Aug 16, 2011

### IOwnAndPwnU

Umm...how do you do that?
This is actually from a math course.

6. Aug 16, 2011

### Quinzio

Well, decompose the force of each cable into an horizontal and a vertical component.