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Question Number 90923 by ajfour last updated on 26/Apr/20

Commented by ajfour last updated on 26/Apr/20

$A b a l l o f m a s s m h i t s h o r i z o n t a l l y$ $a n d e l a s t i c a l l y t h e c e n t r e o f a$ $h i n g e d s q u a r e p l a t e o f s i d e s a n d$ $m a s s M . F i n d v e l o c i t y v o f b a l l$ $j u z t a f t e r i m p a c t .$
	Answered by mr W last updated on 26/Apr/20

	$I = \frac{{M s}^{2}}{3}$ $b e f o r e t h e h i t :$ $E = \frac{1}{2} {m u}^{2}$ $a f t e r t h e h i t :$ $E = \frac{1}{2} {m v}^{2} + \frac{1}{2} I ω^{2} = \frac{1}{2} {m u}^{2}$ $\Rightarrow v^{2} + \frac{{M s}^{2}}{3 m} ω^{2} = u^{2}$ $I ω - \frac{s}{2} m v = \frac{s}{2} m u$ $\Rightarrow ω = (u + v) \frac{3 m}{2 M s}$ $v^{2} + {(u + v)}^{2} \frac{3 m}{4 M} = u^{2}$ $3 m (u + v) = 4 M (u - v)$ $\Rightarrow v = \frac{4 M - 3 m}{4 M + 3 m} u (b a c k w a r d s +)$
	Commented by ajfour last updated on 27/Apr/20

	$V e r y N i c e a n d c o r r e c t, S i r!$
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