Max Mass of Block C to Slide Block A & B Together

[superdave]

Block B, of mass m_B, rests on block A, of mass m_A, which in turn is on a horizontal table top View Figure . The coefficient of kinetic friction between block A and the table top is mu_k and the coefficient of static friction between block A and block B is mu_s. 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.

http://session.masteringphysics.com/problemAsset/1007012/5/yf_Figure_5_66.jpg

What is the largest mass m_C that block C can have so that blocks A and B still slide together when the system is released from rest?

Okay, I get:

a = [m_c *g - (m_a + m_b)*g * mu_k]/(m_a + m_b)

and the max a is m_b * g * mu_s.

I set them equal, and end up with
m_c = (m_a + m_b)(mu_k + mu_s * m_b)

but that isn't correct. help?

 

[Saketh]

the max a is m_b * g * mu_s.

m_b * g * mu_s is a force, not an acceleration.

 

[MadScientist1085]

I'm stuck on the same problem. I get the same acceleration that you get, but for the Max Acceleration I get (mu_s * m_b * g) / m_b, and then i set them equal to each other, but I still get it wrong. There must be something I am overlooking.