If coefficient of kinetic friction between the block A and the inclined surface is 0.2. determine the acceleration of block A and block B.

$T_A a_A=T_B a_B \\ T.a_A=T.a_B \\ a_A=a_B=a$

From FBD of block A,

$∑f_y =o \\ R_1=6 ×9.81 ×\cos⁡75 \\ =15.234 N \\ ∑f_x=0 \\ T-6a=6 ×9.8 \sin75+0.2 ×15.234 \\ T-6a=59.9 ---------- (1) $

From FBD of block B,

$∑f_y =0 \\ T+12 ×a=12 ×9.81 \\ T+12 a=117.72---------- (2) $

From (1) and (2)

$T=79.173 N $ And $a=3.212 m/s^2 $

Acceleration of block A and B,

$a_A=a_B=3.212 m/s^2 $