Show that the forces form a couple (algebraic)

AI Thread Summary
The discussion revolves around proving that the forces acting on triangle ABC form a couple and determining the moment of that couple in relation to the triangle's area. The forces are defined as ka, kb, and kc, acting along the sides BC, CA, and AB, respectively. The user attempts to resolve the forces into horizontal and vertical components, leading to two equations that should equal zero. Guidance is sought on confirming the correctness of this approach and understanding the significance of the triangle's legs in relation to the forces. The conversation emphasizes the importance of visualizing the triangle and the forces to clarify their interactions.
Kinhew93
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Homework Statement



A Triangle ABC has sides of length a, b and c labelled according to the usual convention. Forces of magnitude ka, kb and kc act along BC, CA and AB respectively, with the direction given by the order of the letters. By considering the vector sum of the forces, or otherwise, show that these forces form a couple, and find the moment of the couple in terms of the area of the triangle.

The Attempt at a Solution



Let the angles at B and C be theta and alpha respectively.

Resolving horizontally: [ka - kb.cos(alpha) - kc.cos(theta)]N
Resolving vertically: [kb.sin(alpha) -kc.sin(theta)]N

So I assume that the first step is to show that the above expressions are both equal to 0, but I'm not sure how to do that. Any tips? Is my approach correct?

Thanks :)
 
Physics news on Phys.org
Sketch and label the triangle. What does each leg of the triangle represent in terms of a force. Is it obvious what they add up to?
 
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