A stick with a mass of 0.214 kg and a length of 0.427 m rests in contact with a

Question

A stick with a mass of 0.214 kg and a length of 0.427 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 22.17 cm, and the angle θ the stick makes with the horizontal is 39 °. You may assume there is no friction between the stick and the bowling ball, though friction with the floor must be taken into account?

Explanation / Answer

let the normal reaction by the ball on the stick be N, which makes an angle of 39 degrees with the vertical. normal reaction by the floor on the stick be N' and the horizontal force by the stick on the ball is F. considering torque equilibrium about the base of the stick; mg *(0.427/2) *cos39 = N*0.427 => N = 0.815 N considering vertical equilibrium of the stick; N' +N* cos 39 = mg => N' + 0.78 N = 2.097 => N' = 1.46 N considering horizontal equilibrium of stick; F = N sin39 => F = 0.513 N a). 0.815 N b). 1.46 N c). 0.513 N

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