If the ball is to swing completely around the peg, what value must distance d exceed?

Question

The string is L= 80 cm long, has a ball attached to one end, and is fixed at its other end. A fixed peg is at point P. Released from rest, the ball swings down until the string catches on the peg; then the ball swings up, around the peg. if the ball is to swing completely around the peg, what value must distance d (point P) exceed? ( hint: The ball must still be moving at the top of its swing. Do yo see why?)

Answer 1

From the rather incomplete description of the setup, I'd suppose the action occurs in a vertical plane, the ball is initially extended a distance L = 0.8 m horizontally from the attach point of the string, and the peg is oriented horizontally, perpendicular to the vert. plane and directly below the attach point. In that case I'd say it's a conservation of energy problem. After falling and being wrapped around the peg, the ball can only rise to its original height. It must have velocity at this point or it drops onto the peg or falls to the wrong side of it. So the peg must be infinitesimally more than L/2 below the attach point. I don't know what d represents but if it's distance below the attach point, d > L/2. This assumes the peg's diameter is negligible.