Assignment On Couples and moments

[darklide]

[Urgent]Assignment On Couples and moments

Homework Statement

Two coplanar couples equal and opposite moments balance each other
Hint:
Case1: lines of action constituting the couple intersect

Case2: lines of action constituting the couple do not intersect

Above is what the lecturer gave us. I have really no clue what to do. I have to submit this assignment on monday :S

Homework Equations

Equations on moments and couples i guess

The Attempt at a Solution

Have tried to draw vector diagrams but didnt go too far :(

 

[learningphysics]

What is the question?

 

[darklide]

Good question!
lol kidding
In fact I am not sure, the lecturer only gave what I've written above
so i guess i have to show two cases where

"Two coplanar couples equal and opposite moments balance each other"

Thats my problem its supposed to be kinda basic but am not sure on how to show it :S

 

[learningphysics]

When a force couple has the line of action of the two forces intersect... then the moment is 0. The forces act along the same line... eg: two people pulling at a rope.

first case: So he's asking for a case with two force couples where the two couples each have equal and opposite forces acting along the same line? How about two pairs of people... each pair pulling on a rope in opposite directions? seems a strange case... I'm wondering if I'm understanding the question.

The second case is more significant. when the lines of force constituting a couple aren't intersecting, that means the moment is nonzero. Can you think of a real life case with two opposite couples balancing each other?

 

[darklide]

I'm wondering if I'm understanding the question.

Im same here. I got this question since monday and I've tried to think about it but if ever i get an answer I am not even sure that its good. Or else just as u said before, the case appears to be strange...

Im going to ask the lecturer for more details about the question and I am going to post whatever she told me this afternoon.

 

[andrevdh]

What I've investigated so far is to see what happens to the resultant moment on a system in the first case.

If you draw a diagram with two sets of parallel lines (each set separated by a different distance, say $$a$$ and $$b$$) intersecting each other at some arbitrary angle, say $$\theta$$, and the sets of forces for the couples , $$F_a$$ and $$F_b$$, you can get an equation for the resultant if you slide the force pairs along the lines of action till they meet at the intersection points. The resultants, $$R_a$$ and $$R_b$$ (same magnitude), form another couple. I have not solved for the distance between the resultants in terms of $$a$$ and $$b$$ yet though.

 

[darklide]

thx a lot :D
But concerning couples, isn't it that the moment=Fd (where d is the distance between the two forces) whatever the distance is and whatever the angle is?

Im asking that coz i must start the assignment by defining what moment is and then what a couple is...