In the following problems, string is light, pulleys are smooth and massless.
(a) find the acceleration of each block and tension in the string.
(b) If tension in the string is `15 N` and acceleration of each block is `1 m//s^(2)`, find the value of friction coefficients `mu_(1)` and `mu_(2).

Explanation

(a) `100 - T = 10 a` (i)
Block B :
`_|_^(ar)` to the plane : `N_(0) - 50 cos 37^(@) = 0`
`N_(0) - 50 xx 4//5 = 0 rArr N_(0) = 40 N`
`f = mu N_(0) = (1)/(2) xx 40 = 20 N`
Along the plane :
` T - 50 sin 37^(@) - f = 5a`
`T - 50 xx (3)/(5) - 20 = 5a`
`T - 50 = 5a` (ii)
Adding (i) and (ii) , we get
`50 = 15 a rArr a = (10)/(3) m//s^(2)`
`T = (200)/(3) N`
(b) Block on the horizontal surface :
`uarr N_(0) - 50 = 0`
`f_(1) = mu_(1) N_(0) = 50 mu_(1)`
`larr : T - f_(1) = 5a`
`15 - 50 mu_(1) = 5 xx 1 rArr mu_(1) = (1)/(5)`
Block on he inclined plane :
`_|_^(ar)` to the plane : `N' - 50 cos 37^(@) = 0`
`N' - 50 xx (4)/(5) = 0 rArr N' = 40 N`
`f = mu_(2) N' = 40 mu_(2)`
Along the plane : `50 sin 37^(@) - T - f = 5a`
`50 xx (3)/(5) - 15 - 40 mu_(2) = 5 xx 1`
`40 mu_(2) = 10 rArr mu_(2) = (1)/(4)`