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## 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

[tex]\sum[/tex]M=0

[tex]\sum[/tex]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:

[tex]\sum[/tex]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!

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