Solve 3-Force Member: Weight W=50N on Disk

[dontdisturbmycircles]

Homework Statement

http://img210.imageshack.us/img210/5118/probrb4.jpg
The weight W=50N acts at the center of the disk. Use the fact that the disk is a three force member to solve for the tension in the cable and the reactions at the pin support.

Homework Equations

The Attempt at a Solution

Okay, I realize that the forces must converge at a point directly above the center of mass of the disk, but I don't immediately see the geometrical solution. I could solve it trivially by summing the forces in the x and y and taking a moment but that's not really using the fact that the disk is a three force member. I know the direction of T (tension in rope) obviously, and this kind of gives me an indication as to the direction of the reaction at the pin support but I again, I don't think there is enough there geometrically...

 

[Astronuc]

Well, the sum of the forces in the x and y directions must equal zero, since this is a statics problem, AND the sum of the moments acting on the disc must also equal zero.

It would appear that the pivot on the left is at the same elevation as the CM of the disc? And it's moment arm is R.

The cable seems to be attached at the top vertically above the center of the disc, and there is a moment there (in the -x direction) and its moment arm is also R.