In the figure below,a particle A of mass 2kg is lying on a rough wooden block.The particle A is connected by a light inextensible horizontal string passing over a smooth light fixed pulley at the edge of the block,to a particle B of mass 3kg which hangs freely. The coefficent of friction between the particle A and the surface of the block is μ. Given that the string is taut and the system is released from rest such that the particle move with an acceleration of 4ms^(−1) . Find a) the tension b) the value of μ.


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Question Number 38420 by Rio Mike last updated on 25/Jun/18

$I n t h e f i g u r e b e l o w, a p a r t i c l e A o f$ $m a s s 2 k g i s l y i n g o n a r o u g h w o o d e n$ $b l o c k . T h e p a r t i c l e A i s c o n n e c t e d b y$ $a l i g h t i n e x t e n s i b l e h o r i z o n t a l s t r i n g$ $p a s s i n g o v e r a s m o o t h l i g h t f i x e d$ $p u l l e y a t t h e e d g e o f t h e b l o c k, t o a$ $p a r t i c l e B o f m a s s 3 k g w h i c h h a n g s$ $f r e e l y . T h e c o e f f i c e n t o f f r i c t i o n$ $b e t w e e n t h e p a r t i c l e A a n d t h e s u r f a c e$ $o f t h e b l o c k i s μ .$ $G i v e n t h a t t h e s t r i n g i s t a u t a n d t h e s y s t e m i s r e l e a s e d f r o m r e s t s u c h t h a t t h e p a r t i c l e m o v e w i t h a n$ $a c c e l e r a t i o n o f 4 {m s}^{- 1} . F i n d$ $a) t h e t e n s i o n$ $b) t h e v a l u e o f μ .$
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