The 3 blocks each of mass 10 kg,have the coefficients of static and kinetic friction at the surfaces of contact as m s = 0.3 and mk = 0.2,respectively.Determine the acceleration of each plate when the forces as shown in the figure are applied.
a) aB = 5.114 m/s2,aC = 0
m/s2,aD = 3m/s2,.
b) aB = 0
m/s2,aC = 5.224m/s2,aD = 0.962m/s2.
c) ab = 1m/s2,a,C = 2.4m/s2,aD = 0.65m/s2.
d) aB = 2.5m/s2,aC = 0.12m/s2,aD = 1.1m/s2.

Free body diagram-
The frictional and normal forces acting on the blocks are as shown in the figure.
Equations of motion-
1.Block C-
-
Fmax = 110-0.2(20)(9.81)-0.3(10)!9.81) = 10a;
a = 4.133m/s2.

2.Block D-
As Fmax acting on D = 0.3(10)(9.81) = 29.43>10.
Motion does not occur to the left.
a.Consider the block does not slip on block C-
For this case

1.943< 2.171 for F max.Thus the block slips on block C.
b.Consider the block moving towards right-

This proves that the block infact moves towards right with a = 0.962m/s2.
3.Block B-
As 5 < frictional force,the block does not move towards left.
Consider C does not slip on B-
For this case,Fmax = 110-0.2(10)9.81-0.3(20)(9.81)
= 10a
a = 3.152 m/s2.Acceleration of C.
Acceleration of B for this case,a = -0.5 m/s2<3.152.
Thus the block C slips on B.
a.Consider the block to be moving towards right

This contradicts with the basic assumption.
It can be safely concluded that the block does not move from its position.