Pulley problem: sand being poured into a bucket tied to a block

[N_L_]

I am having trouble setting up the following problem. I can work it out if there is no acceleration, however with acceleration it seems like there are too many variables.

http://img160.imageshack.us/img160/9126/untitled4bd.jpg

What I have so far:



mass of block = 28 kg = Mblock
mass of sand = total mass of filled bucket - 1.35 kg = Msand
acceleration = a
Force tension = Ft
Force friction = Ffr

The two objects will have the same Ft and the same acceleration.

The sum of the forces in the X direction = Ft - Ffr = Mblock * a
The sum of the forces in the Y direction = Msand*g - Ft = Msand*a

Am I correct in thinking that since just enough sand is being added to make the block move, that the friction being used is static friction...to determine the amount of sand that needs to be added?

 

[phucnv87]

Consider
$\mu=0.45$, $k=0.32$, $M=28kg$, $m_0=1.35kg$, $m=m_{Sand}$
a) $(m_0+m)g=\mu Mg$
b) $(m_0+m)g-kMg=(M+m_0+m)a$[/color]