Two crates of mass m1 = 15 kg and m2 = 25 kg are connected by a cable that is strung over a pulley of mass mpulley = 20 kg as shown in Figure P8.58. There is no friction between crate 1 and the table. (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 a(alpha) 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 a(alpha)? (d) Find the acceleration of the crates. (e) Find the tensions in the right and left por- tions of the rope.

Two crates of mass m1 = 15 kg and m2 = 25 kg are connected by a cable that is strung over a pulley of mass mpulley = 20 kg as shown in Figure P8.58. There is no friction between crate 1 and the table. (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 a(alpha) 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 a(alpha)? (d) Find the acceleration of the crates. (e) Find the tensions in the right and left por- tions of the rope.