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2D Moment Equilibrium Question

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    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 .

    [​IMG]

    2. Relevant equations
    [tex]\sum[/tex]M=0
    [tex]\sum[/tex]F=0


    3. 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=Mcdue to A+Mcdue to G=0
    Mcdue 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:
    MD=+(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!
     
    Last edited: Oct 16, 2008
  2. jcsd
  3. Oct 16, 2008 #2

    PhanthomJay

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    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.
     
  4. Oct 16, 2008 #3
    Great! Thank you, I see what you mean... Next time I'll be sure to use the shorter version :)
     
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