Prove the statement - When two equal masses undergo one dimensional nbsp-elastic collision- they interchange their velocities-

Dear student Suppose that one body is moving along +X. speed before collison= nbsp;u and after collision it moves with speed v Let second particle is initiall ...

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Standard XII

Physics

2D Collision Example

prove the sta...

Question

prove the statement " When two equal masses undergo one dimensional elastic collision, they interchange their velocities."

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Solution

Dear student
Suppose that one body is moving along +X.
speed before collison= u
and after collision it moves with speed v
Let second particle is initially at rest and after collision its speed is v₁
$u \sin g c o n s e r v a t i o n o f m o m e n t u m m u + 0 = m v + m v_{1} u = v + v_{1} . . . . . 1) n o w u \sin g c o n s e r v a t i o n o f k i n e c t i c e n e r g y o f s y s t e m \sin c e c o l l i s i o n i s e l a s t i c \frac{1}{2} m u^{2} + 0 = \frac{1}{2} m v^{2} + \frac{1}{2} m {v_{1}}^{2} u^{2} = v^{2} + {v_{1}}^{2} . . . . . . . 2) p u t t i n g t h e v a l u e o f e q 1 i n e q 2 w e g e t {(v + v_{1})}^{2} = v^{2} + {v_{1}}^{2} 2 v v_{1} = 0 h e n c e e i t h e r v = 0 o r v_{1} = 0 N o w p u t t i n g v = 0 i n e q 1 w e g e t v_{1} = u a n d i f v_{1} = 0 w e g e t v = 0 h e n c e i t p r o v e s t h a t a f t e r c o l l i s i o n v e l o c i t y g e t i n t e r c h a n g e$
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