Two blocks of different masses are hanging on two ends of a string passing over a frictionless pulley. The heavier block has mass twice that of the lighter one. The tension in the string is 60 N. Find the decrease in P.E. during the first second after the system is released?

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Solution

$F o r p u l l e y m a s s s y s t e m, e q u a t i o n o f m o t i o n i s g i v e n b y : f_{1} = m_{1} g - T f_{2} = T - m_{2} g w h e r e T i s t h e t e n s i o n i n t h e s t r i n g m_{2} i s t h e l i g h t e r m a s s = m m_{1} i s t h e h e a v i e r m a s s = 2 m s o e q u a t i o n s o f m o t i o n a r e g i v e n b y : 2 m a = 2 m g - T a n d m a = T - m g o n s o l v i n g w e g e a = \frac{g}{3} m / s^{2} i n i t i a l v e l o c i t y i s z e r o . v e l o c i t y a f t e r o n e s e c o n d i s v = u + a t v = 0 + \frac{g}{3} v = \frac{g}{3} W e k n o w t o t a l e n e r g y o f t h e s y s t e m r e m a i n s c o n s e r v e d s o g a i n i n k i n e t i c e n e r g y i s o n e s e c o n d w i l l b e e q u a l t o t h e d e c r e a s e i n p o t e n t i a l e n e r g y . = \frac{1}{2} m_{1} v^{2} = \frac{m g^{2}}{9}$

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