A pulley system with two objects stacked on each other

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

Block B, with mass 5.00kg, rests on block A, with mass 8.00kg , which in turn is on a horizontal tabletop. There is no friction between block A and the tabletop, but the coefficient of static friction between block A and block B is 0.750. A light string attached to block A passes over a frictionless, massless pulley, and block C is suspended from the other end of the string. What is mass of block C?

2. Relevant equations
F=ma
FFriction = μmg

3. The attempt at a solution
I made equations for all 3 masses:

box C:
mCa=mcg-T.

box B:
mBa=FS

box A:
mAa=T-FS

added all three equations, the internal forces (tension and friction) cancel and I get:

mCg = a(mA+mB+mC)

However I still have 2 unknowns ([itex]a[/itex] and mc)
I attempted to figure out acceleration using the equation for box B:

mBa=FS
mBa=μmBg
a = μg
a = (0.750)(9.8)
a = 7.35 m/s^2
but that seems to be a sketchy way to do it?

Attached Images
File Type: jpg blocks.JPG (9.3 KB)

http://ift.tt/1eX9Jj4

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