Problem 1: The sketch below is a side view of a water well's bucket, light rope and cylindrical windlass. The windlass handle is removed to allow the bucket to descend from rest at the top of the well to the water at the bottom. The mass of the bucket is m. The radius, mass and moment of inertia of the cylindrical windlass are R, M and I. (Recall that the moment of inertia of a uniform disk is (1/2)MR.) Part 1: Apply a fundamental principle to write an expression for determining the bucket's acceleration and the pulley's angular acceleration as it descends into the well. Part2: Apply a fundamental principle to the same system and write an expression for determining the bucket's speed just before it touches the water surface which is a distance h below the location of the bucket's bottom when the bucket was released. Part 3: Apply a fundamental principle to the system consisting of just the bucket to determine the tension in the rope while the bucket is moving into the well. (Hint: You many need to apply your results from Part 1.) For each part of the problem, what is/are the key principle(s) will you need to help solve? What assumption(s)/approximation(s) do you need to help you solve the problem? Draw a diagram representing the physical situation. Identify and label all relevant forces. Identify what is your system and what is the surrounding for Parts 1 & 2. (Separate answer to each Part)