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Collision Examples I

two bodies of...

Question

two bodies of masses M1 and M2 (M1 not equal to M2) moving with initial velocity u1 and u2 (u1>u2) along a straight line in the same direction, suffer perfect head on collision. Find their velocities after the collision

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Solution

$D e a r s t u d e n t l e t v_{1} t h e s p e e d o f m_{1} a n d v_{2} b e t h e s p e e d o f m_{2} a f t e r c o l l i s i o n l e t a l l v e l o c i t i e s, i n i t i a l a n d f i n a l b e r i g h t w a r d s . b y c o n s e r v a t i o n o f m o m e n t u m m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2 . . . . . . . . . . . . . . . . . (1)} \sin c e t h i e r i s a p e r f e c t l y e l a s t i c c o l l i s i o n c o e f f i c i e n t o f r e s t i t u t i o n e = 1 = \frac{v e l o c i t y o f s e p a r a t i o n}{v e l o c i t y o f a p p r o a c h} 1 = \frac{v_{2} - v_{1}}{u_{1} - u_{2}} . . . . . . . . . . . . . . . . . . . . . . . . . (2) o n s o l v i n g (1) a n d (2) v_{1} = \frac{u_{1} (m_{1} - m_{2}) + 2 m_{2} u_{2}}{(m_{1} + m_{2})} v_{1} = \frac{u_{2} (m_{2} - m_{1}) + 2 m_{1} u_{1}}{(m_{1} + m_{2})} R e g a r d s$

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