A 28.0 kg block is connected to an empty 2.00 kg bucket by a cord running over a

Question

A 28.0 kg block is connected to an empty 2.00 kg bucket by a cord running over a frictionless pulley (as shown below). The coefficient of static friction between the table and the block is 0.45 and the coefficient of kinetic friction between the table and the block is 0.32. Sand is gradually added to the bucket until the system just begins to move. (a) Calculate mass of the sand added to the bucket. (b) Calculate the acceleration of the system

A 28.0 kg block is connected to an empty 2.00 kg bucket by a cord running over a frictionless pulley (as shown below). The coefficient of static friction between the table and the block is 0.45 and the coefficient of kinetic friction between the table and the block is 0.32. Sand is gradually added to the bucket until the system just begins to move. Calculate mass of the sand added to the bucket. Calculate the acceleration of the system

Explanation / Answer

Fnet = F(tension) - F(friction) = 0 (moments before movement)

F(tension) = F(friction)

mg(bucket) = mu*mg

(2 + m)(9.8) = (0.45)(28)(9.8)

(2+m) = (0.45)(28)

m = 0.45*28 - 2 = 10.6kg

F(net) = F(tension) - F(friction)

= mg - mu*Fn

= (10.6 + 2)(9.8) - (0.32)(28)(9.8) = 35.672N

35.672 = ma = (28 + 10.6 + 2)*a

a = 0.879 m/s^2

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