Force Vector Problem: Find Magnitude & Direction of F3

[dwagz]

Homework Statement

Three forces are applied to an object, as shown in the figure. Force F1 has a magnitude of 26.8 Newtons (N) and is directed 30.0° to the left of the +y axis. Force F2 has a magnitude of 15.2 N and points along the +x axis. A third force F3 is applied such that the vector sum of the three forces is 0 N. What are (a) the magnitude and (b) direction of this third force? Specify the direction as a positive angle relative to the negative x axis, as shown in the figure.

Picture: http://s236.photobucket.com/albums/ff132/airpenny123/?action=view&current=ch01p_46.gif

Homework Equations

F3X = F1X + F2X
F3Y = F1Y + F2Y

F3= √F3X^2 + F3Y^2

The Attempt at a Solution

F1X = (-26.8N)(.8660)
F1X = -23.21N

F2X = 15.2N

F3X = -23.21N + 15.2N = -8.01N

F1Y = (26.8N)(0.5)
F1Y = 13.4N

F2Y = 0

F3Y = 13.4N + 0 = 13.4N

I found the components of F3X = -8.01 and F3Y = 13.4. When I plug the components into: F3= √F3X^2 + F3Y^2, I get 15.6115 N, which apparently is wrong. I've been on this problem forever and I don't know what I'm doing wrong.

As for this part of the question: "Specify the direction as a positive angle relative to the negative x axis, as shown in the figure." I am completely lost...

Thanks for any help.

 

[Redbelly98]

Welcome to PF

I see two problems.

Since the vector sum is zero, the equations should read

F1x + F2x + F3x = 0​

and similarly for the y-components.

Also, calculating the x-component of F1 does not involve cos(30).

As for this part of the question: "Specify the direction as a positive angle relative to the negative x axis, as shown in the figure." I am completely lost...

They just mean the angle from the -x direction.

 

[dgiordan]

why is that my prof taught us to get first the force sumation in X and in Y and use phytagorean theorem and then get the direction ..

 

[Redbelly98]

Welcome to Physics Forums.

why is that my prof taught us to get first the force sumation in X and in Y and use phytagorean theorem and then get the direction ..

That is pretty much how you do this sort of problem, or anything that involves adding vectors. I'm not sure what specifically is confusing you about it?