A block of mass in = 30.0 kg is connected to an empty bucket by a massless cord

Question

A block of mass in = 30.0 kg is connected to an empty bucket by a massless cord naming over a frictionless pulley. The mass of the empty bucket is 1.00 kg and the bottom of the bucket is 0.600 m above the floor. The coefficient of static friction between the table and the block is 0.475 and the coefficient of kinetic friction between the table and the block is 0.350. Sand is gradually added to the bucket until the system just begins to move. (a) What is the mass of the sand added? (b) What is the tension in the cord just before the system starts moving? (c) What is the tension in the cord after the system starts moving? (d) How long after it starts moving does the bucket reach the floor?

Explanation / Answer

just begins moving when friction = ustatic N and a = 0

(1 + M)*9.81 - friction = (1 + M+30)a

(1 + M)*9.81 - 0.475*30*9.81 = 0

M=13.25 kg

b) T = friction = 0.475*30*9.81= 139.8 N

c)

now a is not zero and friction = ukinetic N

(1 + 13.25)*9.81 - 0.355*30*9.81 = (1+30+13.25)*a

a=0.7981 m/s^2

(1 + M)g - T = (1+ M)a

(1+13.25)*9.81 - T = (1+13.25)*0.7981

T=128.42 N

d) y = y0 + v0y t + 1/2 a t^2

0 = 0.6 - 0.5*0.7981*t^2

t=1.23 s

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