How to Determine Tensions in Cables for a Suspended Speaker System?

[Melawrghk]

Homework Statement

A speaker system is suspended by the cables attached at and . The mass of the speaker system is 92.5kg, and its weight acts at G. Determine the tensions in the cables hanging from (a)D and (b)E .

Homework Equations

$$\sum$$M=0
$$\sum$$F=0

The Attempt at a Solution

First, I decided to find reactions at C. I drew the arrows on the diagram, where the horizontal one going to C is Cx and vertical one is Cy. Vertical arrow pointing to A will be further referred to as Ay.
So I got:
Mc=Mc_{due to A}+Mc_{due to G}=0
Mc_{due to A}=92.5*9.81*1.5
Ay * 1 = 1361.14N
Since the moment is positive, Ay has to be pointing downwards
Thus Ay (vector)=-1361.14N. From this, we can find Cy:
$$\sum$$Fy = -1361.14N+Cy-907.425N=0
so Cy=2269
There are no x-direction forces, so Cx=0

Now that we know reactions at C, we can "cut" the cables (E&D) and find E using moment around D:
M_D=+(1.5)*(1361.14)-2269*(.5)-(1)(0) - E*1.5=0
From which E (vector)=-604.81

Then we can use E, to find D:
Sum of Fy = -1361.14+2269-604.81+D=0
D=-303.05

Is that right? Or have I made some wrong assumptions?
Also, I got negative numbers for E and D because they're forces that are acting down. But how would I put in the answer? Tension should be positive 'cause it's just a magnitude, right?
Thanks!

 

[PhanthomJay]

Your results look good, however, if you are just looking for the cable tensions, you could have saved yourself some time by just isolating the speaker by cutting the cables E and D, and solved for the tensions without looking at the frame at all. Your negative sign means that the cable forces (tensions) act down , pulling away from the beam, as they must. If you did the FBD of the speaker, the tension values would be positive, i.e., acting up, pulling away from the speaker, as they must.

 

[Melawrghk]

Great! Thank you, I see what you mean... Next time I'll be sure to use the shorter version :)