# Equilibrium in a tractive apparatus - tension and pulleys

1. Jan 31, 2010

### sethro_gt

1. The problem statement, all variables and given/known data
Determine the magnitude and direction (theta) of F in the diagram of

2. Relevant equations
ΣFx = 0
ΣFy = 0
F = ma

3. 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.

2. Jan 31, 2010

### sethro_gt

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....