A 2-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle is 3...

A 2-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle is 30^o, the angular velocity of the arm about a horizontal axis through O is 50 deg/s clockwise and its angular acceleration is 200 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 500 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^o position.