First slide

Two block problem

Question

A block is placed over a plank which in turn is placed on a smooth level horizontal surface. The coefficient of friction between the block and plank is $0.2$ . Initially both are at rest, suddenly the plank starts moving with accelerations $a = 4 m s^{- 2}$ . The displacement of the block in 1sec is ( $g = 10 m / s^{2}$ ).

Moderate

A

2m relative to ground
B

2m relative to plank
C

1m relative to plank
D

3m relative to ground

Solution

$p s e u d o f o r c e a c t i n g o n t h e b l o c k m a a n d f r i c t i o n a l f o r c e i s μ m g n e t f o r c e b a c k w a r d d i r e c t i o n w . r . t p l a n k i s m (a - μ g) = m a^{'} a^{'} = 4 - 0.2 x 10 = 2 m s^{- 2} d i s p l a c e m e n t w . r . t t o p l a n k i s \frac{1}{2} 2 (1^{2}) = 1 m$

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