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|?
The equation for finding the magnitude of the force is Force/cos(theta).
The equation for finding the force on the x-axis is |F2|sin(theta).
The Attempt at a Solution
I understand that the formula for |F2| is F2y/cos(theta), but I was wondering what the concept behind it would be? My book describes it as using "directional" cosines? It
Also, for F2x, I'm extremely confused as to why the F2 needs to be multiplied by sin(theta), rather than cosine theta, other than it just giving you F2y. My book doesn't say anything about finding F2x, but is it related to taking the derivative of cosine?
It seems counter-intuitive to use cosine for the y-axis and sine for the x axis, but that's the process to get the same value as the correct answer?
Here's the free body diagram: