Need physics help for calculating the acceleration

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30.5 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 0.430 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. Calculate the acceleration of the system

Nov 23rd, 2015

Thank you for the opportunity to help you with your question!

at the moment that the system is about to move, the tension in the cord equals to 30.5*0.43 *9.8 = 128.53 N

which equals to the weight of the sand and the bucket. So the mass of the sand is 

(128.53-1.00*9.8)/9.8 =  12.12 kg, 

after it move, the friction is kinetic friction, let the acceleration be a and the tension be T 


30.5 *a = T-30.5*.320*9.8

13.12 a  =128.53-T

add the two equation, we have 

43.62 a = 128.53 - 95.65 = 32,88

a= 0.754 m/s^2

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 24th, 2015

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