Figure 1
Figure 2
1979M3. A mass m constrained to move on a frictionless horizontal surface is attached to a frictionlpeg by a massless spring having force 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 , b , and c in terms of m,k,ωo and l1.
a. Determine the length l2
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.
d. 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. 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.
