A mass m constrained to move on a frictionless horizontal surface is attached to a frictionless peg by an ideal, massless spring with spring constant k. The unstretched length of the spring is l1, as shown in Figure 1. When the mass moves in a circle about the peg with constant angular velocity ω0, the length of the spring is l2 as shown in Figure 2.
Express your answers to parts a - d in terms of some or all of the quantities m, k, ω0 and l1, and any necessary constants.
(a) Determine the length l_2.
(b) Assume the total energy of the system in Figure 1 is zero. Determine the total energy of the rotating system in Figure 2.
(c) Determine the magnitude of the angular momentum of the system .
While the mass is rotating about the peg with angular velocity ω0, it is struck by a hammer that provides a small impulse directed inward toward the peg.
(d) Determine the torque exerted on the mass by this hammer strike.
(e) On the axes below, sketch graphs to indicate qualitatively the manner in which the length of the spring l and the angular velocity ω will vary with time in the subsequent motion.
You may either sketch the graphs on the axes provided below , or reproduce the axes with your work.
