Zero Torque and static equilibrium

AI Thread Summary
To solve the problem of static equilibrium for a stick resting against a bowling ball and a rough floor, it's essential to analyze the forces and torques acting on the system. The stick's weight and the forces from the bowling ball and floor must balance, leading to zero net force and zero net torque. A free body diagram can help visualize these forces, including the vertical and horizontal components exerted by the floor. The calculations will involve determining the force from the bowling ball and the horizontal and upward forces from the floor. Understanding these principles is crucial for accurately solving the problem.
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A stick with a mass of 0.206 kg and a length of 0.450 m rests in contact with a bowling ball and a rough floor, as shown in the figure below. The bowling ball has a diameter of 21.1 cm, and the angle the stick makes with the horizontal is 30°. You may assume there is no friction between the stick and the bowling ball, though friction with the floor must be taken into account.
(a) Find the magnitude of the force exerted on the stick by the bowling ball.
(b) Find the horizontal component of the force exerted on the stick by the floor.
(c) Repeat part (b) for the upward component of the force.

I had absolutely no idea how to get started on this problem.
 
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Draw a force body diagram. The stick is just sitting there so the sum of the forces in each direction must be zero and the sum of the torques must be zero.
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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