Why Is the Calculation of the Moment Sign Confusing in Force-Couple Systems?

[blue996]

Homework Statement

http://img827.imageshack.us/img827/371/diagramv.th.jpg

I'm supposed to determine the equivalent force-couple system at point A, but that's not actually what I'm posting about. I got the problem right except for the sign calculating the moment.

The Attempt at a Solution

R<sub>x= -200 N - (3/5) (150 N) = -290 N
Ry= (4/5) (-150 N) + 150 N = 30 N
R = Sqrt( (-290 N)² + (30N)² = 291.5 N

Theta= arctan (30/-290 N) = 185.9

Here, calculating the moment, the answer should be:
=(-200 N*.13 m)-(150N)(.3 m) +(4/5)(150N)(0.15m)-(50 N*m)=-103 N*m

Now I know that 50 n*m is negative, but why is (-200N)(.13m) positive? I'm trying to think about how to apply the RHR, but I'm getting confused... I know you're supposed to rotate the position vector towards the force vector when they're placed tail to tail.
if the Force vector is <--- and the position vector (from A to the force vector is how I imagined it, I think this is where I'm going wrong) is ^ then I get my thumb pointing outward, which is CCW and thus negative. :(

So that's where I am, I'm not sure when calculating the moment if a force is either positive or negative signed.</sub>

 

[PhanthomJay]

But the moment from the 200 N force about A is negative (ccw=negative), so why are you saying it is positive? Don't look at the sign of the force when determining moments...just use clockwise or counterclockwise, using right hand rule.

 

[blue996]

The problem took the clockwise from the horizontal as the positive direction for moments, but the answer to the moment for that particular component (-200 N)(0.13m). I guess because they put the negative sign within the parenthesis instead of outside I thought it was part of the sign of the force, not related to the sign of the moment.

Ack, thanks. I guess I was just overthinking it and getting myself confused...

 

[PhanthomJay]

yes, you are right, the negative should have been outside thw parentheses, to avoid confusion. Always take the force as a positive number..as you would if the force was at an angle say perpendicular to the point about which you were summing moments. Most conventions use ccw as plus, but I always use cw as plus. In the end, it doesn't matter, as long as you are consistent.