How Does Friction Influence Motion on an Incline?

[pumpernickel]

The figure below shows a block of mass m resting on a 20° slope. The block has coefficients of friction µs = 0.74 and µk = 0.52 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg.


(a) What is the minimum mass m that will stick and not slip?
(b) If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have?


fs= μs*N
F=M*A

I got part A correct.
m = 19.6 ÷ (9.8 * sin 20 + 0.74 * 9.8 * cos 20) = 1.93

but part B is not, I tried to use the same equation but change the static friction to kinetic

and got 2.4 as the mass

then F= MA
F = 2.4 (A)

I made a FBD and came up with

WME-fk - wsin$\theta$=a(M1+M2)

Is this on the right track?

thanks

 

[NascentOxygen]

but part B is not, I tried to use the same equation but change the static friction to kinetic

and got 2.4 as the mass

But the question states that the mass remains at the value 1.93