Two crates of mass 5.0 kg and 9.0 kg are connected by a rope that runs over a pulley of...

Two crates of mass 5.0 kg and 9.0 kg are connected by a rope that runs over a pulley of mass 4.0 kg as shown in Figure P8.57. (a) Make a sketch showing all the forces on both crates and the pulley. (b) Express Newton’s second law for the crates (translational motion) and for the pulley (rotational motion). The linear acceleration a of the crates, the angular acceleration of the pulley, and the tensions in the right and left portions of the rope are unknowns. (c) What is the relation between a and (d) Find the acceleration of the crates. (e) Find the tensions in the right and left portions of the rope.