Reactions with crate and pulley

[stinlin]

So I had an exam yesterday and ran into a problem like this. The crate was suspended in such a way that it's CG didn't seem to line up with the given measurements. Also, the tension in the cables around the pulleys are equal (nothing is said about the tension in the blue cable). There's a pin joint at the bottom area and a roller on that incline. How would you go about analyzing this system? Mainly my question is - if you sum moments about a, what do you do about the 150 lb crate and those pulleys? Thanks!

http://img507.imageshack.us/img507/9034/lamelh0.png

^^ Image

 

[radou]

Try looking at the crate separately. Which forces are acting on it? You should be able to find the force in the green string. Now, look at the system without the crate with the force in the green string acting on it. Write out the equations of equilibrium.

P.S. There is a neat graphical way to solve this. The force in the roller must be perpendicular to the direction of rolling. Further on, the force in the green string has a known direction, and the point of coincidence of the lines of these two forces is thereby known. Now, by drawing a line through that point and the point of the pin joint, you'll find the direction fo the force in the pin joint. Since you now have three forces, all of which directions are well known, and since you know the magnitude of one of them (the force in the green string), you can calculate your reactions graphically by simple vector addition and proper length and force scale selection.