How Do You Calculate the Forces Acting on a Stick Leaning on a Bowling Ball?

[physgirl]

So there's a stick with a mass M and a length of L. It's resting in contact with a bowling ball and a rough floor (no friction b/w the ball and the stick, but there is friction b/w the objects and the floor). The balling ball has a diameter of D and the angle the stick makes with the horizontal is theta. So how would you find the horizontal and vertical components of the force exerted by the floor on the stick?

I don't know how to even approach this problem :(
It probably has something to do with torque and the overall torque equalling 0. But I don't know what the different torques that have to add up to 0 are... [I was able to find the distance b/w the floor and the contact point b/w the ball and stick though (the height)]

 

[Doc Al]

Identify the forces that act on the stick. (Draw yourself a diagram, showing the point of application of each force and its direction.) Hint: If you count the force exerted by the floor as two forces (Fx & Fy) then there are 4 forces acting on the stick. Hint 2: What is the direction of the force that the ball exerts on the stick?

Then apply the conditions for equilibrium:
(1) Forces must add to zero (both horizontal and vertical components)
(2) Torques about any point must add to zero

I recommend that you calculate torques about the contact point between stick and floor. Solving those equations (3 of them) will give you the force components that you want.

Hint 3: The angle that the stick makes plus the size of the ball give you enough information to determine the distance between the points where the stick touches the ball and the floor. This will prove useful.