Find tension /tensions in the string/strings in the following cases:

Explanation

Block `A : N_(1) - 20 = 0 rArr N_(1) = 20 N`
`f_(1) = muN_(1) = (1)/(2) xx 20 = 10 N`
Block `B : N_(2) - 40 =0 rArr N_(2) = 40 N`
`f_(2) muN_(2) = (1)/(2) xx 40 = 20 N`
`rarr : 60 - (f_(1) + f_(2)) = ( 2 + 4)a`
`60 - (10 + 20) = 6a rArr a = 5 m//s^(2)`
`rarr : T - f_(1) = 2a`
`T - 10 = 2 xx 5 rArr T = 20 N`
Tension in string ` = 20 N`
(b) For the block on the table
`uarr : N_(0) - 40 = 0 rArr N_(0) = 40 N`
`f = muN_(0) = (1)/(4) xx 40 = 10 N`
Pulling force ` = 40 - f - 20 = 40 - 10 - 20 = 10 N`
Total mass to be pulled` = 4 + 4 + 2 = 10 kg`
Common acceleration `a = (10)/(10) = 1 m//s^(2)`
`40 - T_(1) = 4a = 4 xx 1 rArr T_(1) = 36 N`
`T_(2) - 20 = 2a = 2 xx1 rArr T_(2) = 22 N`
(c ) For the block on the table
`uarr : N_(0) - 40 = 0 rArr N_(0) = 40 N`
`f = muN_(0) = (1)/(4) xx 40 = 10`
Pulling force `= 40 + 20 - f = 60 - 10 = 50 N`
Total mass to be pulled ` = 4 + 2 + 4`
` = 10 kg`
Common acceleration `a = (50)/(10) = 5 m//s^(2)`
`40 - T_(1) = 4a = 4 xx 5 = 20 rArr T_(1) = 20 n`
`T_(2) - f = 4a`
`T_(2) - 10 = 4 xx5 rArr T_(2) = 30 N`