Question

a 28kg block is connected to an empty 1.35kg bucket by a cord running over a frictionless pulley. the coefficient of static friction between the table and the block is .450 and the coefficient of kinetic friction between the block and the table is .320. sand is gradually added to the bucket until the system just begins to move. calculate the mass of the sand added to the bucket

Answer 1

11.25 kg of sand. The coefficient of static friction tells you what fraction of the normal force is needed to start the object moving. Since the block is on a horizontal surface, the normal force is the same as the mass of the block. Therefore M = 28 * 0.450 = 12.60 So once the mass hanging off the cord reaches 12.60 kg, the block will start to move. And since the bucket masses 1.35 kg, you need to subtract the mass of the bucket from the total mass needed, giving M = 12.60 - 1.35 = 11.25