Calculating Resultant Force: Comparing Methods and Identifying Errors

AI Thread Summary
The discussion focuses on calculating the resultant force using two different methods: the law of cosines and vector component breakdown. The initial calculation using the law of cosines yields a resultant force of 49N, while the component method results in 55N. Participants suggest that breaking down each force vector into x and y components and then applying the Pythagorean theorem is the most effective approach. The discrepancy between the two methods raises questions about the accuracy of the initial calculation. Ultimately, the consensus leans towards the vector component method as the more reliable technique for determining the resultant force.
vipertongn
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Ok so I have something like this...not drawn to scale

http://i53.tinypic.com/303l5k6.gif

I can see that with the law of cos I can get 49N

However...with this other method where you set Sum of F=0

With sqrt(Fx^2+Fy^2)=R

sqrt((40*cos(20)+20*cos(30))^2+(40*sin(20)-20*sin(30))^2)

I get 55N

Is there soemthing wrong? I'm pretty sure the first answer is correct...but I don't know why this one isnt...
 
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The second one looks right, so I'm guessing the first is wrong... what do you mean using the law of cos?

I think the best way is to just break down each force vector into its x and y components; add those to find the resultant, then use the Pythagorean theorem to find the magnitude of the resultant (that's effectively what you did with your second method).
 

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