Statics- Resultant couple moment

[rico22]

Homework Statement

If F_1 = 100N , F_2 = 120N and F_3 = 80N , determine the magnitude and coordinate direction angles of the resultant couple moment.

Homework Equations

M=Fd
M=r x F
M_R=Ʃ(r x F)

The Attempt at a Solution

I found the couple moment for each force:
M₁=F₁d=100(0.2) or (-20j using right hand rule)
M₂=F₂d=120(0.2) or +24i
M₃=F₃d=80(0.2) or -16k
M₄=this is what I am having problems with...not sure how to get the moment for F4... if do 150(.3)(cos30)=38.97 i get the wrong resultant.

The correct answer should be (M_C)_R=71.9 Nm...
Any help would be greatly appreciated.

 

[tiny-tim]

hi rico22!

The correct answer should be (M_C)_R=71.9 Nm...

i don't get 71.9 unless i use .33 instead of .3

 

[TSny]

Note that the F4 couple is not in the x-direction. It is parallel to the xy plane but it has both x and y components which you will need to work out.

 

[tiny-tim]

Note that the F4 couple is not in the x-direction.

ooh, i didn't notice that!

i read the axis of that pipe, and the short line above the positive x-axis, as one continuous straight line!

yes, now i get 71.9 … thanks, Tsny ​

 

[rico22]

thanks for the replies guys...