One end of a string of length L is attached to a nail driven into a wall. A small ball is attached to the other end of the string. Another nail is driven into the wall a distance l directly underneath the first nail. A student holds the ball so that the string is horizontal and parallel to the wall. The student then releases the ball. Subsequently, the string wraps around the “bottom” nail. What is the minimum distance l that allows for that to happen?


First let’s round up the usual assumptions: neglect the air drag and other mechanical energy losses, neglect the mass of the string relative to the ball, and neglect the circumference of each nail relative to the smaller length l such that the radius of the circular arc followed by the ball...

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