Forces and Vectors adding to zero

[sdoi]

Homework Statement

Given F1= 36N[25degrees N of E] and F2= 42N [15 degrees E of S], determine the force F3 that must be added to the sum of F1+F2 to produce a net force of zero.

Homework Equations

Sine law, a/sina= b/sinb
Cosine law: c^2= a^2 + b^2- 2(a)(b) Cos(theta)

The Attempt at a Solution

I first went about the question by drawing a vector diagram of all the two know forces, and then I broke down each force into horizontal and vertical components.

For F1:
F1y= 36N sin25
F1y= 15.2N

F1x= 36NCos25
F1x= 32.6N

For F2:
F2y= 42NCos15
F2y= 40.5N

F2x= 42NSin15
F2x= 10.8N

Then I added all of the x and y values:
ƩFx= 32.6N +10.8N
ƩFx= 43.4N

ƩFy= 40.5N +15.2N
ƩFy=55.7N

I then went on to find the resultant vector:
F=√43.4N^2 + 55.7N^2
F=70.6N

From this point on I have no idea where to go.

 

[gneill]

Pay attention to the reference axes for the angle specifications. The angles for the two forces have been specified with respect to different axes, so you'll need to be careful about extracting their components.

Once you've calculated the magnitude of the resultant be sure to also locate it on the Cartesian plane -- you want its angle with respect to some reference axis.

Suppose you were to take the components of that resultant force. What values would you add to each of them in order to leave them at zero? Make those values the components of your "new" vector.

 

[sdoi]

Within my calculations I have used the appropriate angles, right? I've kept each axes in mind.

Did I calculate the resultant correctly? I'm not entirely sure how to find the angle. I do however know from my diagram that it will be some degree N of W.

Without the appropriate angle I cannot begin to draw a proper diagram to find the x and y components

 

[SammyS]

sdoi,

Please delete your other similar thread.

 

[sdoi]

I'm working on it, I can't seem to find it in my PF.

 

[SammyS]

Try it at this link.

https://www.physicsforums.com/showthread.php?t=536096"

 

[gneill]

Within my calculations I have used the appropriate angles, right? I've kept each axes in mind.

Did I calculate the resultant correctly? I'm not entirely sure how to find the angle. I do however know from my diagram that it will be some degree N of W.

Without the appropriate angle I cannot begin to draw a proper diagram to find the x and y components

Well, F2 is specified as lying "15 degrees E of S". That would place it in the 4th quadrant with a negative y component...

As for your resultant vector, you can sketch the vector using the components and determine the trig to find an appropriate angle from some axis.

 

[sdoi]

And that simple mistake complicated everything. That pretty much fixes all of the problems I was having. Thank you very much!