The math help thread

The top problem above still confuses me. I understand your assumptions with the fact that F and T both have a net of zero. However, with all that said can I assume that Fpy is zero? And your last equation is puzzling. I just don't really understand why the 98*1 is there. I dunno, that last past just instilled mass confusion. I think my values are right though going from Noah's values above. 98.1N for the Pin Joint and 137.7N for the Tension in the Rope.

No you may not assume Fpy is zero because it is a pin that holds the mass on an axis (going through the paper). Fpy is zero only if the element at that point can move, such as a rolling wheel. And the last equation is a torque equation centered around the pin. 98*1 is simply the force of the mass multiplied by the distance from the pin.

With problems as simple as this one, there are two things that should be true:
1.) There should be a complete force triangle. If you took all the force vectors and laid them head to tail with each other, you should get a complete triangle. If not, the system is in motion. Failure to satisfy this condition is a pretty big indicator that you interpreted the system wrong.
2.) The forces involved (when not parallel) all should intersect at a single point when you extend their vectors (line of action). I have no idea how true this is when you have four or more forces...

EDIT: Looks like I screwed up the last equation. It should really be 0 = 98*1 - Fr*sin(45)*2 xD