Zero Torque and static equilibrium

[map7s]

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.

 

[dicerandom]

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.

 

[kyle8921]

I would approach this problem by first understanding the concepts of torque and static equilibrium. Torque is the rotational force applied to an object, while static equilibrium refers to the state in which an object at rest has no net force or torque acting on it.

In this scenario, the stick is in contact with the bowling ball and the floor, and is at rest. This means that the stick is in static equilibrium, and the net force and net torque acting on it must be zero.

To find the magnitude of the force exerted on the stick by the bowling ball, we can use the equation for torque: τ = rFsinθ, where τ is the torque, r is the distance from the pivot point (in this case, the point where the stick touches the bowling ball), F is the force, and θ is the angle between the force and the lever arm.

In this case, the force exerted by the bowling ball is perpendicular to the stick, so θ = 90°. The lever arm is the distance from the pivot point to the center of the bowling ball, which is half of its diameter, or 10.55 cm. Plugging in these values, we get:

τ = (0.1055 m)(F)(sin 90°) = 0

Since the stick is in static equilibrium, the torque must be zero, which means that the force exerted by the bowling ball must also be zero.

Next, we can find the horizontal and upward components of the force exerted on the stick by the floor. Since there is no friction between the stick and the bowling ball, the stick is only in contact with the floor. This means that the force exerted by the floor must be equal and opposite to the force exerted on the stick by the bowling ball, in order to keep the stick in static equilibrium.

To find the horizontal component of the force, we can use the equation Fx = Fcosθ, where Fx is the horizontal component of the force, F is the total force exerted by the floor, and θ is the angle between the force and the horizontal.

In this case, θ = 30°, so:

Fx = Fcos 30° = (F)(√3/2)

To find the upward component of the force, we can use the equation Fy = Fsinθ, where Fy is the upward component of the force and