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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 xaxis runs to the right, the yaxis runs up, and the zaxis is out of the page.
What is the magnitude of F2?
Homework Equations
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The equation for finding the magnitude of the force is Force/cos(theta).
The equation for finding the force on the x axis is F_{2}sin(theta).
The Attempt at a Solution
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I understand that the formula for F_{2} is F_{2y}/cos(theta), but I was wondering what the concept behind it would be? My book describes it as using "directional" cosines? It
Also, for F_{2x}, I'm extremely confused as to why the F_{2} needs to be multiplied by sin(theta), rather than cosine theta, other than it just giving you F_{2y}. My book doesn't say anything about finding F_{2x}, but is it related to taking the derivative of cosine?
It seems counterintuitive 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:
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