A 28.0-kg block is connected to an empty 2.18-kg bucket by a cord running over a

Question

A 28.0-kg block is connected to an empty 2.18-kg 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 0.28. Sand is gradually added to the bucket until the system just begins to move. Ignore mass of cord. (Figure 1) Calculate the mass of sand added to the bucket. Express your answer to two significant figures and include the appropriate units. Calculate the acceleration of the system. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Letting M1 = block and M2 = bucket+sand,

M1 = 28 kg

M2 = 11.48 kg

A free body diagram will show that after motion starts,

The cord tension T = [M1*M2*g*(1 + µk)] / (M1+M2) = (28*11.48*9.8*(1+0.28)) / (28+11.48) = 102.24 N

acceleration a = (M2*g - T)/M2

a = 0.9040 m/s²

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