Pulley + ramp problem

Block A is suspended from a vertical string. The string passes over a pulley and is attached to block B. The mass of block B is 1.8 kg. The mass of block C is 0.75 kg. If the coefficient of kinetic friction is 0.100 between block B and the ramp and the coefficient of static friction between block B and C is 0.900, determine the maximum mass of block A, such that block C does not slip off.

2. Relevant equations
f = ma

3. The attempt at a solution

I drew a FBD for block C and was able to calculate its force of friction which is: 5.61 N (μmgcosθ)

I also found out that the force of gravity for Block B is (M)(G)(COSθ). But I don’t know what the force of Block C on B would be. If I could find that, I will be able to find the Force of Normal for Block B and solve for the force of friction for block B as well.

After that, I am not too sure what I must do next. I am thinking of solving for acceleration but not too sure if that will help.

Any help or any push in the right direction would be very helpful.



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