Question

A 8 kg block is connected to an empty 1.00 kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.5, Sand is gradually added to the bucket until the system just begins to move.Find the mass of sand added.

Answer 1

for 8kg block
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body moves forward after m kg sand put in 1 kg block .
so, friction act on it backward ,

at equilibrium condition,
fr = T
uN = T ---(1)

for 1 kg block ,
at equilibrium condition,
when body start to move downward
T = ( m + 1) g
put eqn in here
uN = (m +1)g
uMg = ( m +1)g
uM = m +1

m = uM -1 = 0.5× 8 -1 = 4 -1 = 3 kg