1. An Atwood's machine has two objects of mass 4 kg and 6 kg connected by a massless string that passes over a pulley consisting of a uniform disk of mass 2 kg and radius .1 m. The string does not slip on the pulley. a. Find the magnitude of the acceleration of the objects. b. What is the tension in the string supporting the 4 kg mass? c. What is the tension in the string supporting the 6 kg mass? 2. A loop of radius .5 m and mass of .8 kg rolls without slipping at a speed of 10 m/s toward an incline of slope 30*. What distance up the incline will the hoop roll (assuming it rolls without slipping)? 3. A solid disk of mass 2 kg and radius 2 m is given a horizontal push of 20N at a point .3 m above its center. a. What is the minimum u between the disk and the floor to allow rolling without slipping? b. If the disk rolls without slipping, what is, i. the acceleration of the center of mass ii. the linear speed of the center of mass after 5 seconds iii. the total kinetic energy after 5 seconds C. If u, = .2 and p = .1, what is, 1. the acceleration of the center of mass? ii. the linear speed of the center of mass after 5 seconds iii. the total kinetic energy after 5 seconds 4. A bowling ball of mass M and radius R is thrown such that at the instant it touches the floor it is moving horizontally with a speed vo and is not rotating. It slides for a time t, a distance s, before it rolls without slipping and moves with a speed of V 1. a. If u, is the coefficient of sliding friction between the ball and floor, find ty, 51, and v1 b. Let u = .06 and v. = 8 m/s. Now find find t, 5,, and v. c. Find the ratio of the final kinetic energy to the initial kinetic energy for the ball. 5. A 100 W motor provides power to a round tube filled with water that is free to turn about a frictionless axle. a. Starting from rest, after 5 seconds, the tube is rotating at a rate of 4 revolutions per second. What is its moment of inertia, I? b. How much torque is supplied by the motor at t = 5 seconds? c. Nome imagine the motor is shut off after 5 seconds, and water begins leaking from the center of the tube. 1/3 of its mass is lost, but the remaining mass maintains the same distribution. What is the new rotational rate in terms of revolutions per second? 6. A uniform rod of length L = 2m and mass M = .2kg hangs vertically from a pivot on one end and is initially at rest. It is then struck by a ball of putty of mass m = .1kg at a distance of d = .8L = 1.6m below the pivot. If the putty sticks to the rod, what must be the speed, v, of the putty such that the maximum angle the rod rotates is 90"
