Calculating Moment, kind of confused

[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.

 

[rwisz]

First of all, it's great that you're asking questions and trying to understand the concept of calculating moments. Let's break down the problem and go through the steps together.

1. The first step is to determine the equivalent force-couple system at point A. This means finding the resultant force and moment at point A.

2. To find the resultant force, you correctly used the formula R = sqrt(Rx^2 + Ry^2). This gives you the magnitude of the resultant force, which is 291.5 N.

3. Next, we need to find the direction of the resultant force. This is where the theta value comes in. You correctly calculated the angle using the formula theta = arctan(Ry/Rx). However, the value you got for theta is not correct. The correct value is theta = arctan(30/290) = 5.9 degrees.

4. Now, let's move on to calculating the moment. The formula for moment is M = Fd, where F is the force and d is the perpendicular distance from the force to the point of rotation (in this case, point A).

5. The force that is causing a moment at point A is the 150 N force. To find the perpendicular distance, we need to draw a line from point A to the line of action of the force. This line should be perpendicular to the force vector.

6. Once you have drawn this line, you can see that the perpendicular distance is 0.15 m.

7. Now, let's apply the formula M = Fd. The force is 150 N and the perpendicular distance is 0.15 m. So the moment caused by this force is (150 N)(0.15 m) = 22.5 Nm.

8. We also need to consider the moment caused by the 200 N force. This force is acting at a distance of 0.13 m from point A. So the moment caused by this force is (200 N)(0.13 m) = 26 Nm.

9. Finally, we need to consider the moment caused by the 4/5(150 N) force. This force is acting at a distance of 0.3 m from point A. So the moment caused by this force is (4/5)(150 N)(0.3 m) = 36 Nm.