Friction and Newton?

Question

A 27.0 kg block is connected to an empty 1.00 kg bucket by a cord running over a frictionless pulley (Fig. 4-57). The coefficient of static friction between the table and the block is 0.415 and the coefficient of kinetic friction between the table and the block is 0.320. Sand is gradually added to the bucket until the system just begins to move.

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Answer 1

You omitted asking a question.
I will give you the amount of sand required to start movement and the acceleration of the block once moving

the Normal force of the block is 27.0*9.81
and the max static friction is
27.0*9.81*0.415
or
110 N
when the bucket weighs 110 N, it will begin to move.

The amount of sand is
110/9.81-1
10.2 kg of sand

Once the system moves, the frictional force becomes

27.0*9.81*0.320
or
84.76 N
the net force is therefore
110-84.76
or
25.14 N
this is equal to (27+11.2)*a
a=0.658 m/s

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