A 28.0-kg block is connected to an empty 2.72-kg bucket by a cord running over a

Question

A 28.0-kg block is connected to an empty 2.72-kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.47 and the coefficient of kinetic friction between the table and the block is 0.27. Sand is gradually added to the bucket until the system just begins to move. Ignore mass of cord.

A.Calculate the mass of sand added to the bucket.

Express your answer to two significant figures and include the appropriate units.

B.Calculate the acceleration of the system.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Here ,

a)

let the mass of sand in bucket is m

for moving the block

us * M * g = ( 2.72 + m ) * g

0.47 * 28 = (2.72 + m )

m = 10.44 Kg

the mass of sand added to the bucket is 10.44 Kg

b)

Now , let the acceleration of system is a

(28 + 10.44 + 2.72) * a = (10.44 + 2.72) * 9.8 - 0.27 * 28 * 9.8

a = 1.33 m/s^2

the acceleration of the system is 1.33 m/s^2

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