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Question Number 39776 by ajfour last updated on 10/Jul/18

Commented by ajfour last updated on 11/Jul/18

$F i n d t h e a c c e l e r a t i o n o f w e d g e,$ $i f g r o u n d i s s m o o t h w h i l e t h e$ $d i s c s p u r e l y r o l l s o n t h e w e d g e .$ $m a s s o f w e d g e i s M^{'} = M + m .$ $T h e c o n n e c t i n g r o d i s l i g h t a n d$ $o f l e n g t h l .$
Commented by ajfour last updated on 11/Jul/18

Commented by ajfour last updated on 11/Jul/18

$M g R \sin α + M A R \cos α - F R \cos δ = \frac{3}{2} {M R}^{2} (\frac{a}{R})$ $m g r \sin α + m A r \cos α + F r \cos δ = \frac{3}{2} {m r}^{2} (\frac{a}{r})$ $\Rightarrow (M + m) r R (g \sin α + A \cos α) = \frac{3 a}{2} (M + m) r R$ $\Rightarrow a = \frac{2 (g \sin α + A \cos α)}{3}$ $2 (M + m) A = (M + m) a \cos α$ $\Rightarrow a = 2 A / \cos α$ $\Rightarrow 6 A = 2 g \sin α \cos α + 2 A \cos^{2} α$ $o r A = \frac{g \sin α \cos α}{3 - 2 \cos^{2} α} .$
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