Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_63

3/63 A 2-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle \(\theta\) is \(30^\circ\), the angular velocity of the arm about a horizontal axis through O is \(50 \text{ deg/s}\) clockwise and its angular acceleration is \(200 \text{ deg/s}^2\) counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of \(500 \text{ mm/s}\). Determine the necessary minimum gripping force \(P\) if the coefficient of static friction between the sphere and the gripping surfaces is \(0.50\). Compare \(P\) with the minimum gripping force \(P_s\) required to hold the sphere in static equilibrium in the \(30^\circ\) position.