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.

 

[kyle8921]

I would approach this problem by first identifying the key variables involved and setting up a free body diagram to visualize the forces acting on the system. In this case, the key variables are the mass of the stick, length of the stick, diameter of the bowling ball, angle of the stick, and the friction between the objects and the floor.

Next, I would use Newton's laws of motion to analyze the forces acting on the stick. Since the stick is in contact with the bowling ball and the floor, there are three forces acting on it: the weight of the stick, the normal force from the floor, and the force from the bowling ball. The weight of the stick can be calculated using the formula W = mg, where m is the mass of the stick and g is the acceleration due to gravity. The normal force from the floor can be calculated using the formula N = mgcosθ, where θ is the angle the stick makes with the horizontal. The force from the bowling ball can be calculated using the formula F = mgcosθ/tanθ, where θ is the angle the stick makes with the horizontal.

To find the horizontal and vertical components of the force exerted by the floor on the stick, I would use trigonometry to break down the normal force into its horizontal and vertical components. The horizontal component would be equal to Nsinθ, and the vertical component would be equal to Ncosθ. These components can then be used to calculate the net force acting on the stick in the horizontal and vertical directions.

Additionally, I would take into consideration the friction between the objects and the floor. This friction force would act in the opposite direction of the motion of the stick and can be calculated using the formula Ff = μN, where μ is the coefficient of friction between the objects and the floor.

By using these calculations and considering all the forces acting on the stick, I would be able to determine the horizontal and vertical components of the force exerted by the floor on the stick. This would provide a better understanding of the dynamics of the system and help in finding a solution to the problem.