Kinematics of Machines

Problem 6. A puck of mass m is attached to a cord passing through a small hole in a frictionless table (see figure on next page). The cord is pulled downward with a tension T. The puck is initially orbiting with speed v, in a circle of radius r;. The tension is then slowly increased so that the radius of the circle starts decreasing. It is increased sufficiently slowly so that you may assume that the mass on the table is in perfect circular motion at all times. This decreases the radius of the circle to r. (a) The process just described conserves angular momentum. Explain why. (b) Use angular momentum conservation to determine the speed of the puck when the radius is r . v0 find the tension tension in the cord as a function of r. (d) How much work is done in moving m from r; to r? Note:The tension changes with r.(c



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