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Homework5_2010 - ME 562 Advanced Dynamics Summer 2010...

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ME 562 Advanced Dynamics Summer 2010 HOMEWORK # 5 Due: July 16, 2010 Q1. ( see Problem 6-1 in the text for the figure). A fixed smooth rod makes an angle of 30 with the floor. A small (negligible radius) ring (say P 1 ) of mass m can slide on the rod and supports a string which has one end connected to a point on the floor; the other end is attached to a particle (say P 2 ) of mass 2 m . Assume that the string and the rod lie in the same vertical plane . Since there are two objects with mass, one can use their Cartesian coordinates with respect to a (x,y) system with origin at the lower left corner. Let l be the length of the string. Since the ring is constrained to move along the rod, and l is constant, the four coordinates (x 1 ,y 1 ) and (x 2 ,y 2 ) are constrained. Also, let a be the coordinate of the point on the floor where the string is attached, and b be the height of the point where the rod is attached to the vertical wall. Then,
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