Equilibrium in a tractive apparatus - tension and pulleys

AI Thread Summary
The discussion focuses on solving a physics problem involving tension and pulleys in a tractive apparatus. The user initially struggles with determining the magnitude and direction of force F, expressing confusion over the relationship between multiple variables and equations. They eventually deduce that the tension in the rope is consistent at 98N and proceed to calculate the x and y components of the known angles. By ensuring that these components combine with force F to equal zero, they find the angle theta. The conversation emphasizes the importance of understanding tension in pulley systems for solving equilibrium problems.
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Homework Statement


Determine the magnitude and direction (theta) of F in the diagram of

3-32.jpg


Homework Equations


ΣFx = 0
ΣFy = 0
F = ma

The Attempt at a Solution



I tried using the sum of components but I end up with three variables and two equations. I've always had issues with figuring out tension through a pulley system. I'm hoping for some insight as to what parts of the diagram are relevant to finding F.

So far I've figured F(ab) = cos45(98N) = 138.6N but I can't figure out how to relate that to F and Fac and Fcd.

is Fcd equal to ΣFy?

This is from my statics book and my physics text isn't helping either.
Any clues are appreciated, thanks.
 
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Ok I think I got it. Someone else posted a similar problem that I didn't find before.

So tension is the same through the entire rope = 98N

Knowing that I found the x & y components of the two known angles, 45 and 75. These components have to combine with those of F to equal 0. Then I found they theta with these values.

I hope it is this simple...
 
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