A small ball swings in a horizontal circle at the end of a

Chapter 12, Problem 12.93

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A small ball swings in a horizontal circle at the end of a cord of length \(l_{1}\), which forms an angle \(u_{1}\) with the vertical. The cord is then slowly drawn through the support at O until the length of the free end is \(l_{2}\). (a) Derive a relation among \(l_{1}, \ l_{2}, \ u_{1}, \ and \ u_{2}\). (b) If the ball is set in motion so that initially \(l_{1} = 0.8 m\) and \(u_{1} = 35^{\circ}\), determine the angle \(u_{2}\) when \(l_{2} = 0.6 m\).

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