Tension in Suspended Traffic Light Problem

[Lori]

Homework Statement

Homework Equations

Weight = Tension in y direction??

The Attempt at a Solution

I thought that W = the tension in the y direction of the two cables so that T2y and T1y are both 20 N each. Thus, i calculated that the tension in AC is 33 N ( cos(53.1) = 20/T1 --> T1 = 20/ cos(53.1) = 33N

But the answer is 24? What is wrong with my answer?[/B]

 

[DoItForYourself]

Hello,

T1_y is not equal to T2_y.

Hint : The problem becomes easier if you analyse W in two directions (1 on the AC line and 1 on the AB line).

 

[Lori]

Hello,

T1_y is not equal to T2_y.

Hint : The problem becomes easier if you analyse W in two directions (1 on the AC line and 1 on the AB line).

Wouldn't it make sense if they are equal though? I'm just surprised since I would've immediately assumed that they were the same... in what cases would they be the same? But, i do understand that T1y + T2y = W right?

Nevermind, i think i understand that they both wouldn't be T=20 because they are at different angles

 

[DoItForYourself]

But the angles with the y-axis are different for each cable. If the angles were 45 degrees, the cables would have the same length and then T1_y=T2_y=20 N.

Of course, their sum is equal to 40 (because ΣF_y=0).

 

[haruspex]

Wouldn't it make sense if they are equal though?

It often helps to consider a more extreme example. What if one cable were vertical, or very nearly?