Block B, with mass 5.00 kg, rests on block A, with mass 8.00 kg, 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 the largest mass that block C can have so that blocks A and B still slide together when the system is released from rest?
coefficient of static friction = Fmax/normal force
The Attempt at a Solution
At first I took found the weights of blocks A and B.
[w Block A = 8.00kg(9.8m/s^2)] = 78.4 N
[w Block B = 5.00(9.8m/s^2)] = 49 N
w of A+B = 78.4+49= 127.4 N
I calculated that the normal force of Blocks A+B = 127.4 N. Then since the weight of block C which is unknown would equal the tension in the rope, I figured I would use this information using the coefficient of friction to find the mass of block C.
So then I set 0.750 which was the coefficient of friction = to fmax/normal force.
0.750 = Fmax/127.4
I found the Fmax=36.75 N
Then I divided 36.75 N by g to get the mass of block C. I got the mass of block C to be 3.75 kg. Apparently this is incorrect and the correct answer is 9.75 kg.
Can anyone pease help me? Thank you very much.