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Couple of a Triangle Question

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data

    In the figure F1= 27.9KN, F2= 39.8KN, F3= 61.8KN
    What distance d is required for the net couple moment on the triangle to be 1140 counterclockwise?
    Express your answer to three significant figures and include the appropriate units.
    link to image http://imgur.com/cBnLJ

    2. Relevant equations

    I'm thinking the only really relevant equation is Mc=rXf or Mc=|r||F|sin(theta)

    3. The attempt at a solution

    So I wrote each moment in terms of d using trig. I got:
    Mf1= 27900d Nm
    Mf2= 19900d Nm
    Mf3= 61800cos(30)d Nm
    Then I set the sum of the three moments (with direction taken into respect) equal to 1140 Nm.
    1140 = 11900d + 61800cos(30)d - 27900d
    d~= 0.03038 m or 3.04*10^-2 m.

    Unfortunately this was wrong and I have no clue where I went wrong. Any help would be greatly appreciated.
     
  2. jcsd
  3. Oct 25, 2012 #2

    CWatters

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    Where did 11900 come from? I know F2-F1=11900 but can't see how you got F2*D-F1*D from the drawing if indeed that's how you got to 11900.

    Can you tell us which point you choose as origin, which direction you assumed as +ve and write the equation in terms of F1, F2 and F3 rather than substituting the values.

    for example your equation above appears to be...

    Total = (F2 - F1)d + F3Cos(30)d - F1d

    Is that right?
     
  4. Oct 25, 2012 #3
    I didn't choose any point as an origin. The question asked about the couple on the entire triangle. And sorry here's my work for the equations:

    It says that the total moment couple has to be 1140 counterclockwise, so I assumed counterclockwise as the positive direction for all the moments.
    Then this is the part I wasn't too sure of. I figured that F2 and F3 would cause counter clockwise rotation while F1 would cause clockwise rotation.
    Therefore 1140=MF2+MF3-MF1
    subbing in: 1140=19900d+61800cos(30)d-27900d
    1140=45520d
    d=0.025m
    WOW. I think I made an arithmetic error. just got it with 0.025m. I feel like an idiot. Thanks for the help though man
     
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