Varignons theorem fail question

[sukibelle]

hi guys
In my lecture we were told to just sum the components of a force ( * respective x y distances) to obtain moment. I've been trying to do practice questions in hibbeler but my answers are always wrong and I've found that it;s because of the way they're summed/ subtracted.
Here's the question http://i53.tinypic.com/1267h4i.jpg for anyone that has the textbook it's 419 in the SI textbook.

Homework Statement

So I need to find the moment created about A by F = 80N

Homework Equations

M= Fd
= -Fx* y - Fy* x

The Attempt at a Solution

=-80cos20*0.15sin60 - 80sin20*0.15cos60
=11.82 clockwise...

answer is 7.71 anti clockwise which is obtained via Fx y - Fy x...

what is it about varignons theorem that has clearly gone over my head? :(

 

[PhanthomJay]

The force is applied at the pink circle. Your components should be applied at that point. The x comp produces a ccw moment and the y comp produces a cw moment. Check your work by using M = r X F.

 

[sukibelle]

thank you for replying so fast. i see that now. my concern is that i seem to answer the questions a bit backwards to my lecturer and i'll show you what i mean- i use r x F because it's like that in hibbeler but if i use her method it doesn't align. i don't know if there actually is a difference, most of the time when the direction is different there isn't much of a concern because it's uniform across the question if you know what I'm saying?
http://i54.tinypic.com/mah53k.jpg

 

[PhanthomJay]

Whether you use r X F or Varignon's theorem, the results are always the same. The method you choose to use depends on which is simpler for the problem at hand. In the last example you posted, it is much simpler to use Varignon's theorem, as shown in the figure. Using r X F in this example would be more difficult, because you would have to first determine the magnitude and direction of the position vector from B to the point of application of the force, then determine the interior angle between the force and position vector at the point of application of the load (which is about 179 degrees with a quick calc). In either case, the direction of the moment is cw or ccw using the right hand rule (you can choose cw as positive or ccw as positive, just be sure to be consistent).

Using Varignon, the moment of a force is equal to the sum of the moments of the force components, where the moment of a force component is equal to the perpendicular distance from the line of action of the force to the pivot point. A lot easier in this example, as it often is.