Three forces, one graph, one crazy problem

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SUMMARY

The discussion centers on solving a physics problem involving three forces acting on an object, specifically Force 1 (33.0 N at 30.0° to the left of the +y axis) and Force 2 (21.0 N along the +x axis). The objective is to determine the magnitude and direction of Force 3 such that the vector sum of all three forces equals 0 N. The user, Phoenix, has calculated the components of the forces but is confused about the correct application of vector sums. The solution involves using the equations F1y = F3y and F1x + F3x = F2 to find the unknown Force 3 and its angle.

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Homework Statement


Three forces are applied to an object, as indicated in the drawing. Force 1 has a magnitude of 33.0 Newtons (33.0 N) and is directed 30.0° to the left of the +y axis. Force 2 has a magnitude of 21.0 N and points along the +x axis. What must be the magnitude and direction (specified by the angle in the drawing) of the third force 3 such that the vector sum of the three forces is 0 N?
(Image attached)
magnitude N
theta °



Homework Equations



F=ma



The Attempt at a Solution



I have made the entire table involving the magnitudes, directions, Fx, and Fy of the three forces plus the totals overall. Earlier in class we worked a little bit on vector sums, but now I realize that I don't know whether or not the vector sum involves the Fx or Fy. I've attempted to add the bits together (I figured out the Fx and Fy's by using cosine and sine) for instance, for F1 the Fy force is 28.6 and the F2 Fy force is 0. However, the answer is not 28.6. What am I doing incorrectly?

Thanks,
Phoenix
 

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For equilibrium F1y = F3y and F1x + F3x = F2
From these two equations you can find F3 and the angle.
 

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