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Friction and Vertical Circular Motion Problems

A simple pend...

Question

A simple pendulum consists of a bob of mass m and a string of length R suspended from a peg $P_{1}$ on the wall. A second peg $P_{2}$ is fixed vertically below the first one at a distance 3R/7 from it.The pendulum is drawn aside such that the string is horizontal and released. Calculate the maximum height (with respect to the lowest point) to which it rises

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Solution

$W h e n b o b w i l l r e a c h t o l o w e s t p o i n t i t s p o t e n t i a l e n e r g y = m g R n o w i t w i l l g o u p t o R h e i g h t f r o m i t s l o w e s t p o i n t b u t n o w e f f e c t i v e l e n g t h o f s t r i n g w i l l b e (R - \frac{3}{7} R) = \frac{4}{7} R S o m a x i m u m h e i g h t u p t o w h i c h i t r i s e s = R - \frac{4}{7} R = \frac{3}{7} R F r o m P_{2}$

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