A 26.0 kg block is connected to an empty 1.00 kg bucket by a cord running over a

Question

A 26.0 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 is0.430 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.

(a) Calculate the mass of sand added to the bucket (Hint: Use the coefficient of static friction.) _______kg

(b) Calculate the acceleration of the system. (Hint: Use the coefficient of kinetic friction.) ________m/s^2 (downward)

Explanation / Answer

balancing force on block in x and y direction is N - mg = 0---> N = mg

F = uN = us m1g

also T-Ff = ma

as a = 0 , T = Ff

Balancing force on bucket in Y direction m2g -T = ma

m2g = T   

solving above two,

m2 g = us m1 g

m2 = 0.43 * 26 = 11.18 kgs

mass of sand added = 11.18 - 1 = 10.18 kg

b. whne system begin to move, accleration of bucket = accleration of block

M1 g - umqg = (m1 +m2) a

a = (26*9.8) -(11.18 * 9.8 * 0.32)/(26 +11.18)

a = 5.9 m/s^2

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