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

Question:

A 2-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle θ is 30°, 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° position.