Start with a free-body diagram:
http://img297.imageshack.us/img297/3702/1254156394brittany.jpg
The tension in the cord is the sum of the weight of the bucket (m2) and the sand (m3), i.e.
T=(m2+m3)g
To start motion, T >= μs*N ....(1)
where
μs = the coeff. of static friction
N = normal reaction from the table
=m1*g
m1=mass of the block
Using equation (1), m3 can be isolated and calculated (<10 kg).
Check my thinking and calculations.
A 28.0kg block is connected to an empty 1.80kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.41 and the coefficient of kinetic friction between the table and the block is 0.35. Sand is gradually added to the bucket until the system just begins to move .
Calculate the mass of sand added to the bucket.
Calculate the acceleration of the system.
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