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Unformatted text preview: PHY6938 Proficiency Exam Spring 2002 April 5 , 2002 Mechanics 1. As shown in the diagram, two blocks with masses M 1 and M 2 are attached by an unstretchable rope around a frictionless pulley with radius r and moment of inertia I . There is no slipping between the rope and the pulley. The coefficient of kinetic friction between the blocks is the same as between block 1 and the surface, . A horizontal force F is applied to M 1 . Find the acceleration of M 1 . M1 M2 F I First draw a free-body diagram for M 1 , M 2 , and the pulley, being careful to label all the forces and find the line along which they act. Firstly lets examine M 2 . It has a tension due to the string, gravity, a frictional force due its motion relative to M 1 , which we can assume is to the left, and the normal force which M 1 exerts on it to stop it from moving vertically. m 2 N m 2 2 T 2 f 2 g Note that the tension T 2 in the top half of the string does not have to equal that in the bottom half if we cannot ignore the pulleys moment of inertia and it is accelerating. Now do the same for M 2 . Note that the two forces on M 1 due to M 2 are prescribed by m 1 m 1 f 1 F N N g 1 2 f 2 T 1 Newtons third law to be equal and opposite to those on M 2 due to M 1 . Finally, we have the free-body diagram for the pulley We can now write down the equations of T T 2 1 I motion for these three objects. In the past we have written independent coordinates and written down constraint equations which we have formally added to our system...
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