I can't get my forces to balance in a trivial moments problem.
There is uniform rod of weight W, leaning at an angle a from the vertical. It is fixed at the top and at the bottom.
Resolving W perpendicularly (p) and parallel (||) to the rod,
Wp = Wsin(a), W|| = Wcos(a)
Take moments about the bottom, then I get a force at the top acting perpendicularly to the rod of W/2 . sin(a).
Similary taking moments about the top, I get a force acting perpendicularly at the bottom, of W/2 . sin(a).
The || components at top and bottom at W/2 . cos(a).
Resolving vertically at the top & bottom, I get
Ftopv = W/2 . sin(a). sin(a) + W/2 . cos(a) .cos (a) = W/2
And the same for the bottom, which both add up neatly to W, as expected.
When I look at the horizontal components, I don't get a neat answer.
What should I get?
Please.