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Resolving Vecotrs and Forces and Finding the moment of the resultants about a point?

  1. Jan 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Reduce the system of forces in the diagram at point O. We know that F1 =F2 = 2F^(1/2), F =2F,and alpha =Pi/4. OA=AB=BD=a.

    2. Relevant equations

    Pythagoras
    Trig Functions
    F = Fxi + Fyj + Fzk
    The magnitude of force F is:
    F= (F2+F2+F2)^(1/2)
    R=(ƩF)i+(ƩF)j+(ƩF)k
    |MO| =|r|×|F|sinα
    3. The attempt at a solution

    Fx1 = 2F^(1/2).Cos(alpha)?
    FX2 = 2F^(1/2).Cos(alpha)?
    Fx3 = 2F?

    Fy1 = 2F^(1/2).Sin(alpha)?
    Fy2 = 2F^(1/2).Sin(alpha)?
    Fy3 = 0?

    R = (Fx1+Fx2+Fx3)i + (Fy1+Fy2+Fy3)j?
     

    Attached Files:

    Last edited: Jan 13, 2012
  2. jcsd
  3. Jan 13, 2012 #2

    PhanthomJay

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    Re: Resolving Vecotrs and Forces and Finding the moment of the resultants about a poi

    yes, now sum moments of the initial given x comp of forces about O. That value divided by the resultant sum of the x comp forces will give you the y distance of the x resultant from O. Do a similar calc for moments of the y comps about O to get the x distance of the y resultant from O. The resultant passes thru that calculated point.
     
  4. Jan 15, 2012 #3
    Re: Resolving Vecotrs and Forces and Finding the moment of the resultants about a poi

    So

    R=-2Fi+(2*2^(1/2)*F^(1/2)

    |R|=((16F)^2+(8F))^(1/2)
     
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