Three forces, one graph, one crazy problem

[Phoenixtears]

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

 

[rl.bhat]

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

 

[baba89]

Hi Phoenix,

First of all, great job on setting up the table and using the correct equations to solve for the forces. It seems like you have a good understanding of the concepts involved in this problem.

To answer your question about the vector sum, it is important to understand that the vector sum includes both the Fx and Fy components. This is because forces are vectors and have both magnitude and direction. So when we add forces, we are adding both the magnitude and direction of each force.

In this problem, you will need to use trigonometry to find the Fx and Fy components of the third force (F3). Then, you can use the Pythagorean theorem to find the magnitude of F3, and inverse trigonometric functions to find the direction (angle) of F3.

I hope this helps clarify things for you. Keep up the good work!