I didn't quite realize what you meant by force balances, I'm really sorry about that. For some reason I saw "components of F2" and assumed it to be the components in the vector.
It would end up as:
|F2| = mg/sin(theta)
And lead to:
F1 = mgcos(theta)/sin(theta)
I think I see what I wasn't...
F2 = <|F2|cos(theta), |F2|sin(theta), 0>
And its magnitude is equal,
|F2| = sqrt((|F2|cos(theta))^2 + (|F2|sin(theta))^2)
= sqrt(|F2|^2 * (cos^2 (theta) + sin^2 (theta)))
= sqrt(|F2|^2)
= |F2|
For some reason |F2| came out equal to F2y/cos(theta) on my homework, but that's saying that |F2| is...
Oh. For this problem, doing that made my homework site count it wrong for some reason, so I ruled it out.
F2x would equal |F2|cos(theta) based on that.
F2 would be the weight plus any force being exerted that moves it, but it's not moving so it's just the weight?
Would it be this?
|F2y| = Fgrav + Ftension
I'm not quite sure what else it could be than that. It seems to be what would be the actual equation for it though. There's just no acceleration in the problem, which would cause it to be canceled out.
I named the ropes inversely, but F1 would be 0 because it's the flat line. Sorry about the mixup, I'll fix that.
F2 is the opposite of gravity because it cancels out gravity's force, so -mg.
Homework Statement
A box of mass X kg hangs motionless from two ropes, as shown in the diagram. The angle of rope 1 is specified amount of degrees. Choose the box as the system. The x-axis runs to the right, the y-axis runs up, and the z-axis is out of the page.
What is the magnitude of |F2|...