AP Physics Free Response: Friction between two blocks

1. The problem statement, all variables and given/known data

Block A of mass 2M hangs from a cord that passes over a pulley and is connected to block B of mass 3M that is free to move on a frictionless horizontal surface. The pulley is a disk with frictionless bearings, having a radius R and moment of inertia 3MR^2. Block C if mass 4M is on top of block B. The surface between blocks B and C is NOT frictionless. Shortly after the system is released from rest, block A moves with a downward acceleration a and the two blocks on the table move relative t each other

vertical tension in rope on right of pulley = 2Mg-2Ma

horizontal tension on rope on left of pulley = 2Mg-5Ma

Q: if a (linear accel) = 2m/s^2 determine the coefficient of kinetic friction between blocks B and C



2. Relevant equations

static friction is less than or equal to coefficient of static multiplied by Fnormal

kinetic F = kinetic coefficient multiplied by Fnormal





3. The attempt at a solution

i played around with a number of things but really have no clue what im doing.
i wrote down the idea that the horizontal tension which was found to be 2mg-5ma must be more than the maximum static friction. then I isolated blockc (4M) and found the normal force to be 4MG ( i think) but i cannot figure out where the kinetic frictional force is acting since the both blocks are moving. AP exam on monday. its killing me that i can't get this. PLEASE HELP!!!

 

ok. so i must be missing something fundamental. yesterday i finally found an answer of .1 for the coefficient of kinetic f. but now, isolating block b with friction pulling to the left and horizontal tension as a force on the right i am getting some odd answers that cannot fit a coefficient. ie 4, -2/3

what i did yesterday was i used nsl on block b
T.hor-frict.kin= 3Ma
T.hor = 2Mg-5Ma (from nsl for rotation)
so...
2Mg-5Ma-mk4Mg= 3Ma
cross out Ms
2g-5a-3a=mk4g
sub in g=10 and a=2
20-10-6=mk40
divide by 40
mk=0.1

this seems to be a reasonable answer but i dont understand (if it is right) why it worked with the normal force from block c.
is this even correct?