A wedge has two equally rough faces each inclined at 30° to the horizontal.Masses of 5kg and 2kg ,one on each face,are connected by a light string passing over a smooth pulley at the top of the wedge.The coefficient of friction μ, between each masses and the surface of the wedge is 0.2.Find the acceleration of the masses when they are released.


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Question Number 22893 by NECx last updated on 23/Oct/17

$A w e d g e h a s t w o e q u a l l y r o u g h$ $f a c e s e a c h i n c l i n e d a t 30 ° t o t h e$ $h o r i z o n t a l . M a s s e s o f 5 k g a n d 2 k g$ $, o n e o n e a c h f a c e, a r e c o n n e c t e d$ $b y a l i g h t s t r i n g p a s s i n g o v e r a$ $s m o o t h p u l l e y a t t h e t o p o f t h e$ $w e d g e . T h e c o e f f i c i e n t o f f r i c t i o n$ $μ, b e t w e e n e a c h m a s s e s a n d t h e$ $s u r f a c e o f t h e w e d g e i s 0.2 . F i n d$ $t h e a c c e l e r a t i o n o f t h e m a s s e s$ $w h e n t h e y a r e r e l e a s e d .$
	Answered by ajfour last updated on 23/Oct/17

	$a = \frac{(M - m) g \sin 30 ° - μ g \cos 30 ° (M + m)}{M + m}$ $= \frac{15 - 7 \sqrt{3}}{7} m / s^{2}$ $\Rightarrow a \approx (2.143 - 1.732) m / s^{2}$ $\approx 0.4 m / s^{2}$
	Commented by NECx last updated on 23/Oct/17

	$t h a n k z s i r . . . . . p l e a s e c a n i t b e$ $e x p l a i n e d w i t h a d i a g r a m . I^{'} l l$ $a p p r e c i a t e t h a t . T h a n k s i n a d v a n c e .$
	Commented by NECx last updated on 23/Oct/17

	$t h a n k s s i r$
	Commented by ajfour last updated on 23/Oct/17

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