College Physics question help! Best answer

A 25.5 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 is 0.485 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.
Calculate the mass of sand added to the bucket.
kg

(b) Calculate the acceleration of the system.
m/s2 (downward)

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in order to start the system moving, the tension in the cord must equal the force of static friction on the block

this force is us m g = 0.485*25.5kg*9.8m/s/s = 121.2N

as long as the system is in equilibrium, the tension in the rope satisfies

T - m bucket g =0

as long as the system is in equilibrium, the tension in the rope = the weight of the bucket

for this to weight 121.2N, the total mass must be 12.4kg, so you have to add 11.4 kg of sand

once the bucket begins to move down, the block moves and the frictional force acting on it depends on the kinetic coeff of friction

writing newton's second law for both bucket and block

block: T - uk M g = M a
bucket: T - m g = - ma

m=mass bucket, M=mass block (and the minus sign in -Ma indicates the accel is down)

subtract equations:

mg - uk M g = (M+m)a

a= (m - uk M)g/(M+m) = (12.4kg - 0.32*25.5kg)*9.8m/s/s/(37.9kg
a=1.10m/s/s

What table???