(Solved): 2. A block of mass, m=6kg, lies on a rough horizontal table. It is connected to a bucket of Mass, ...

2. A block of mass, $m=6\mathrm{kg}$, lies on a rough horizontal table. It is connected to a bucket of $Mass,M=1\mathrm{kg}$, by a string going over a massless and frictionless pulley. The coefficient of static and kinetic friction are ${?}_3=0.26$ and ${?}_k=0.18$ respectively. The bucket, initially empty, remains at rest when the block is released. a. Define the coordinate system(s) of your choice and determine the tension acting at each end of the string. b. Determine the minimum mass $M_{\text{min }}$ of the bucket that allows the system to be in motion. c. The bucket is now fllled with water so that the bucket mass $M=4\mathrm{kg}$ (which is larger than $M$ min). What is the magnitude of the acceleration of the block and that of the bucket? d. Determine the tension acting at each end of the string for the case of the weighted bucket. e. Assuming that the block is released from rest when the bottom of the weighted bucket is initially a height of $\mathrm{H}=2.00\mathrm{m}$ above the floor, how much time passes before the bucket reaches the floor?