The coefficient of friction between the blocks is `0.5`. Find the acceleration of each block if `F is (a) 21 N ,(b) `35 N` and (c ) `40 N`.

Explanation

Let the blocks move together with acceleration `a`.
`a = (F)/(( 2 + 5)) = (F)/(7)`
`a' = mu g = 0.5 xx 10 = 5 m//s^(2)`
(a) `a = (F)/(7) = (21)/(7) = 3 m//s^(2)`
`a lt mu g (=5)` , the blocks move together with acceleration `3 m//s^(2)`
(b) `a = (F)/(7) = (35)/(7) = 5 m//s^(2)`
`a = mu g (=5)` , the blocks move together with acceleration `5 m//s^(2)`
( c) `a = (40)/(7) = 5.7 m//s^(2)`
Upper block : `a gt mu g (= 5)` , blocks move with different acceleration
`uarr : N_(0) = 20 N`
`f_(max) = mu n_(0) = 0.5 xx 20 = 10 N`
`f_(max) = 10 = 2 a_(1) rArr a_(1) = 5 m//s^(2)`
Lower block :
`40 - 10 = 5 rArr a_(2) = 6 m//s^(2)`
The upper block will move towards backward direction w.r.t. the lower block with acceleration ` = a_(2) - a_(1) = 6 - 5 = 1 m//s^(2)`.