Explanation Consider the pendulum assuming the datum line is coinciding with point A and it is parallel to the string connecting the pendulum. Calculate the minimum velocity of the pendulum for which the pendulum completes a circle. Determine the minimum velocity of pendulum at which the pendulum has zero tension in the string. Here take the newton’s second law of motion in the vertical direction. ∑ F y = m a n m g = m a n a n = g M=mass of the pendulum G=acceleration due to gravity Here substitute a n = v 2 ( l − a ) we get: v 2 ( l − a ) = g v = g ( l − a ) This velocity is known as minimum velocity for which the pendulum will describe a circle So, the condition is v ≥ g ( l − a ) − − − − − ( 1 ) . Find the gravitational potential energy of the pendulum at the position D. So V e D = − m g ( l − 2 ( l − a ) ) = − m g ( 2 a − l ) Find the kinetic energy of pendulum at point D. T D = 1 2 m v 2 Pendulum possess elastic potential energy when is at position D

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ISBN: 9781260265521

Author: BEER

Publisher: MCG

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Chapter 13.2, Problem 13.78P

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The smallest v_o for which pendulum bob will describe a circle about the peg.

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