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## Homework Statement

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?

## Homework Equations

F=ma

FFriction = μmg

## The Attempt at a Solution

I made equations for all 3 masses:

box C:

m

_{C}a=m

_{c}g-T. box B:

m

_{B}a=F

_{S}box A:

m

_{A}a=T-F

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

m

_{C}g = a(m

_{A}+m

_{B}+m

_{C})

However I still have 2 unknowns ([itex]a[/itex] and m

_{c})

I attempted to figure out acceleration using the equation for box B:

m

_{B}a=F

_{S}

m

_{B}a=μm

_{B}g

a = μg

a = (0.750)(9.8)

a = 7.35 m/s^2

but that seems to be a sketchy way to do it?