A small object with a mass of 0.250 kg has been attached to a massless string, and is moving in a circle on a perfectly level frictionless tabletop. The string passes through a hole in the center of the table, and is held by a person. Suppose that initially the mass is rotating with an angular speed of 15.0 rad/s around a circle of radius 0.400 m. The person then pulls the string in such a way as to reduce the radius of the circle at a constant rate. The person stops reducing the radius when the object is making a circle of radius 0.200 m. How much work did the person do in the course of reducing the radius of the circle?
Solution: We will approach the problem in two ways. First, we will use the work-energy theorem to obtain the answer in a straightforward manner. We will then compare our answer to that obtained using the (considerably more complicated) method of computing the integral of the force times displacement along the path.
Method 1
System: The object as a point particle undergoing pure rotation, acted upon by external forces from the string (tension), the earth (gravity) and the table (normal force).
Model: Work-Energy Theorem.