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Question Number 53325 by mr W last updated on 20/Jan/19

Commented by mr W last updated on 20/Jan/19

$T w o b a l l s h a v e e q u a l s i z e . B a l l A h a s$ $m a s s m a n d r e s t s . B a l l B h a s m a s s$ $n m (n i s i n t e g e r g r e a t e r t h a n 1) . B a l l$ $B m o v e s w i t h v e l o c i t y v t o w a r d s b a l l$ $A a n d b e h i n d b a l l A t h e r e i s a w a l l .$ $A s s u m e t h e r e i s n o f r i c t i o n a n d a l l$ $c o l l i s i o n s a r e e l a s t i c a n d t h e w a l l i s$ $f a r a w a y e n o u g h .$ $H o w m a n y t i m e s w i l l b o t h b a l l s$ $c o l l i d e w i t h e a c h o t h e r ?$
Commented by ajfour last updated on 20/Jan/19

$t o o g o o d a q u e s t i o n S i r, l e t m e t w o$ $d a y s a t l e a s t .$
Commented by mr W last updated on 20/Jan/19

$t h a n k s s i r! w a i t i n g f o r y o u r r e s u l t . . .$
Commented by tanmay.chaudhury50@gmail.com last updated on 20/Jan/19

$i h a v e s e e n s i m i l a r q u e s t i o n i n y o u t u b e . . . s h a r i n g$ $t h e l i n k . . .$
Commented by tanmay.chaudhury50@gmail.com last updated on 20/Jan/19

Commented by tanmay.chaudhury50@gmail.com last updated on 20/Jan/19

Commented by mr W last updated on 20/Jan/19

$t h a n k s f o r t h i s r e s u l t b u t w h i c h i c a n n o t$ $f o l l o w y e t . i^{'} l l g o t o w a t c h t h e v i d e o,$ $b u t a t f i r s t i^{'} l l t r y t o s o l v e i n m y$ $o w n w a y . m y u n d e r s t a n d i n g i s :$ $d u r i n g t h e f i r s t x c o l l i s i o n s t h e$ $e n e r g y w i l l b e t r a n s f e r e d f r o m b a l l B$ $t o b a l l A . d u r i n g t h e n e x t y c o l l i s i o n s$ $t h e e n e r g y w i l l b e t r a n f e r e d b a c k t o$ $b a l l B a n d b a l l B w i l l b e f i n a l l y f a s t e r$ $t h a n b a l l A a n d n o f u r t h e r c o l l i s i o n$ $i s p o s s i b l e .$
Commented by tanmay.chaudhury50@gmail.com last updated on 20/Jan/19

$t a n θ = \sqrt{\frac{m_{L}}{m_{H}}}$ $N_{c} θ = π$ $N_{c} = \frac{π}{θ} = \frac{π}{{t a n}^{- 1} \sqrt{\frac{m_{L}}{m_{H}}}} [N_{c} = n u m b e r o f c o l l i s s i i n]$ $1) e x a m p l e . . \frac{m_{L}}{m_{H}} = \frac{1}{100}$ ${t a n}^{- 1} (\sqrt{\frac{1}{100}})$ ${t a n}^{- 1} (\frac{1}{10}) \approx \frac{1}{10}$ $N_{c} = \frac{π}{\frac{1}{10}} = 10 π \approx 31 n u m b e r o f c o l l i s i o n$ $2) e x a m p l e t w o \frac{m_{L}}{m_{H}} = \frac{1}{10000}$ ${t a n}^{- 1} (\sqrt{\frac{m_{L}}{m_{H}}})$ ${t a n}^{- 1} (\frac{1}{100})$ $N_{c} = \frac{π}{\frac{1}{100}} = 100 π = 314 n u m b e r o f c o l l i s s i o n$ $3) \frac{m_{L}}{m_{H}} = \frac{1}{n}$ ${t a n}^{- 1} (\sqrt{\frac{1}{n}}) \approx \frac{1}{\sqrt{n}}$ $N_{c} = \frac{π}{\frac{1}{\sqrt{n}}} = π \sqrt{n} n u m b e r o f c o l l i s s i o n . .$ $s i r p l s c h e c k t h e v i d e o i n y o u t u b e . . . a l s o$ $c h e c k m y a n s w e r . .$ $n u m b e r o f c o l l i s s i o n N_{c} = π \sqrt{n}$
Commented by tanmay.chaudhury50@gmail.com last updated on 20/Jan/19

$t h a n k y o u s i r . . . i h a v e j u s t t r i e d t o u n d e r s t a n d$ $t h e v i d e o . . . y o u p l s g o t h r o u g h i t . . . a m i r e a l l y$ $u n d e r s t o o d i t y e t . . . y o u p l s c r o s s c h e c k . . .$ $h i w e v e r y o u r l o g i c r e g a r d i n g c o l l i s s i n a n d$ $e n e r g y t r a n s f e r r e a l l y e x c e l l e n t . . .$ $t h a n k y o u s i r . . .$
Commented by mr W last updated on 22/Jan/19

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