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

1. Jan 13, 2012

### mm391

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?

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Last edited: Jan 13, 2012
2. Jan 13, 2012

### PhanthomJay

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.

3. Jan 15, 2012

### mm391

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)