Calculating Resultant Force: Comparing Methods and Identifying Errors

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SUMMARY

The discussion centers on calculating the resultant force using two different methods: the law of cosines and vector component analysis. The first method yields a resultant force of 49N, while the second method, which involves summing the x and y components of the forces, results in 55N. The discrepancy arises from the application of the law of cosines versus the vector breakdown approach. The consensus is that breaking down each force vector into its components and applying the Pythagorean theorem is the most reliable method for determining the resultant force.

PREREQUISITES
  • Understanding of vector components in physics
  • Familiarity with the law of cosines
  • Knowledge of the Pythagorean theorem
  • Basic trigonometry skills
NEXT STEPS
  • Study vector decomposition techniques in physics
  • Learn about the law of cosines and its applications in force calculations
  • Explore the Pythagorean theorem in the context of resultant forces
  • Practice problems involving resultant force calculations using both methods
USEFUL FOR

Physics students, engineers, and anyone involved in mechanics or force analysis will benefit from this discussion, particularly those seeking to understand the nuances of calculating resultant forces accurately.

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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