A bucket for collecting water from a well is suspended by a rope which is wound around a pulley. The empty bucket has a mass of 2.0 kg, and the pulley is essentially a uniform cylinder of mass 3.0 kg on a frictionless axle. Suppose a person drops the bucket into the well.
Part A
What is the bucket's acceleration as it falls?
Solution: We will consider two different methods to obtain the solution.
Method 1
Systems: The pulley and the bucket are treated as separate objects. The bucket can be treated as a point particle, but the pulley must be treated as a rigid body. The pulley and the bucket are each subject to external influences from the rope and from gravity. The pulley is also subject to a normal force from the axle.
Model: Fixed-Axis Rotation
Approach: Begin with free body diagrams for the two objects.
PICTURE
We then write Newton's second law a