A block ( M = 8 kg) is connected to an empty bucket ( m = 1.00 kg) by a cord running over an ideal pulley. The coefficients of static and kinetic friction between the tabletop and the block are 0.5 an

Question

A block ( M = 8 kg) is connected to an empty bucket ( m = 1.00 kg) by a cord running over an ideal pulley. The coefficients of static and kinetic friction between the tabletop and the block are 0.5 and 0.4 respectively. Sand is gradually added to the bucket until the block just begins to slide. The mass of sand added to the bucket (in kg) is [ g = 10 m/s 2 ]

TestHub · Accepted Answer

The bucket hangs from a movable pulley, so the bucket weight is shared by two cord segments:

$2 T = (1 + x) g$

Block just slides:

$T = μ_{s} M g = 0.5 (8) (10) = 40 N$

$(1 + x) (10) = 80 \Rightarrow 1 + x = 8 \Rightarrow x = 7 kg$

Answer: 7.

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