A Pendulum, consisting of a bob of mass M on a cord of lengthL, is interrupted i

Question

A Pendulum, consisting of a bob of mass M on a cord of lengthL, is interrupted in its swing by a peg a distance d below itspoint of suspension. a) If the bob is to travel in a full circle of radius (L-d)around the peg, what is the minimum possible speed it can have atthe lowest point in its motion, just before it starts to go around?Ignore any decrease in the length of the string due to the peg'scircumference. b) From what minimum angle must the pendulum bereleased so that the bob attains the speed calculated in a)?

Explanation / Answer

a) speed of the bob at the top point of the circle of radius (L-d)= u mu2/(L - d) = mg mu2/2 + mg*2*(L - d) = mv2/2 v = [u2 + 4g(L - d)] = [5g(L -d)] b) mv2/2 = mgL(1 - cos) = arccos[1 - v2/(2gL)] = arccos[(5d -3L)/(2L)]

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