A 1.5-lb ball that can slide on a horizontal frictionless

Chapter 13, Problem 13.96

(choose chapter or problem)

A 1.5-lb ball that can slide on a horizontal frictionless surface is attached to a fixed point O by means of an elastic cord of constant k = 1 lb/in. and undeformed length 2 ft. The ball is placed at point A, 3 ft from O, and given an initial velocity \(v_{0}\) perpendicular to OA. Determine (a) the smallest allowable value of the initial speed \(v_{0}\) if the cord is not to become slack, (b) the closest distance d that the ball will come to point O if it is given half the initial speed found in part a.