Sin(alpha)?What are the Simplified Forces at Point O?

[mm391]

Homework Statement

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.

Homework 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

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?

 

[PhanthomJay]

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.

 

[mm391]

So

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

|R|=((16F)^2+(8F))^(1/2)