10.69.Model:This is a two-part problem. In the first part, we will find the critical velocity for the ball to go over the top of the peg without the string going slack. Using the energy conservation equation, we will then obtain the gravitational potential energy that gets transformed into the critical kinetic energy of the ball, thus determining the angle .θVisualize:We place the origin of our coordinate system on the peg. This choice will provide a reference to measure gravitational potential energy. For to be minimum, the ball will just go over the top of the peg. Solve:The two forces in the free-body force diagram provide the centripetal acceleration at the top of the circle. Newton’s second law at this point is 2GmvFTr+=where T is the tension in the string. The critical speed cvat which the string goes slack is found when
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