Please solve the questions and show the calculations clearly. The final answers are written next to the questions but please show the calculations. We have a quiz?

87. A block, A of mass, M is suspended from a light string that passes over a pulley and is connected to block B of mass 2M. Block B sits on the surface of a smooth table. Block C, of mass 3M, sits on the top of block B. The surface between block C and block B is not frictionless. When the system of three blocks is released from rest, block A accelerates downward with a constant acceleration, a, and the two blocks on the table move relative to each other. The moment of inertia of the pulley is | = 1.5 MR, Present all results in terms of M, g, and a. a. Find the tension force in the vertical section of the string. AL Cga) b. Find the tension force in the horizontal section of the string. Mp - 2.5 Mal The acceleration of block A was determined from a series of experiments: a =2 m/s. c. Find the coefficient of kinetic friction between the two blocks on the table. -EL;' d. Find the acceleration of block C. 9-9 3 2 93. A uniform rod of mass, M; and length, L is fixed on one end, and the other is free to rotate with respect to point C on a frictionless horizontal table. The angular velocity of the rod is w and initially stays unchanged. The rod strikes a stationary sphere of mass, M; with the free end. After the collision, the rod stops and the sphere moves to the right with a velocity, v. The moment of inertia of the rod with respect to point Cis | = g ML?. Present all answers in terms of: My, My, L, and w. Views From Above Before Collision After Collision a. Determine the velocity of the sphere, v after the collision by using the conservation of angular momentum, e o M Determine thesl'lnar momentum of the rod just before the collision. ','HW Determine the linear momentum of the sphere after the collision. N;W Is the linear momentum of the system of two objects conserved during the collision? Explain. Is the angular momentum of the system of two objects conserved? Explain. mnooo 86. A billiard ball of mass M and radius R is struck by a cue stick along a horizontal line though the center of mass of the ball. The ball initially slides with a velocity vo. As the ball moves across the rough billiard table its motion gradually changes from pure translational through rolling with slipping to rolling without slipping. The moment of inertia of the ball is | = 2; MR? and the coefficient of kinetic friction is p. M o >' [ . a. Expressthe linear velocity, v of the center of mass of the ball as a function of time t while it is rolling with slipping. V= Vo~ Pot b. Express the angular velocity, w of the ball as a function of time while it is rolling with slipping. - Spat i i : ] ) e 2Vo 28 Find the time at which the ball begins to roll without slipping. 5 d. When the ball is struck it acquires an angular momentum about te fixed point A on the surface of the table. During the motion the angular momentum about point A remains constant despite the friction force. Explain why this occurs. 0