Question

7) (8 pts.) A solid cylinder of mass M and radius R is mounted to an axle through its center. The axle is attached to a horizontal spring of constant k, as shown in the figure. Initially the cylinder is at rest and the spring is un-stretched. The cylinder is pulled a distance A and then released. The cylinder then rolls back and forth without slipping. (a) What is the total mechanical energy of the system just before the cylinder is released? Express your answer in known quantities. (b) What is the total mechanical energy of the system when the disk passes through the equilibrium position? Express your answer in terms of M, speed of the center of mass v, moment of inertia I, and the angular speed ??rolling. (c) What is the linear speed of the center of mass v of the cylinder when it passes through the equilibrium position? Express your answer in terms of k, M, and A. (d) What is the angular frequency ?? and period T of the simple harmonic motion of this spring-rolling mass system? Express your answer in terms of k and M. (e) Assume that we have the same spring and mass, only now the cylinder is released from rest on a frictionless surface at a distance A from the equilibrium position. What is the period of the simple harmonic motion of the system? Express your answer in terms of k and M. Fig. 3: Figure for problem 7.

          7) (8 pts.) A solid cylinder of mass M and radius R is mounted to an axle through its center. The axle is attached to a horizontal spring of constant k, as shown in the figure. Initially the cylinder is at rest and the spring is un-stretched. The cylinder is pulled a distance A and then released. The cylinder then rolls back and forth without slipping.
(a) What is the total mechanical energy of the system just before the cylinder is released? Express your answer in known quantities.
(b) What is the total mechanical energy of the system when the disk passes through the equilibrium position? Express your answer in terms of M, speed of the center of mass v, moment of inertia I, and the angular speed ??rolling.
(c) What is the linear speed of the center of mass v of the cylinder when it passes through the equilibrium position? Express your answer in terms of k, M, and A.
(d) What is the angular frequency ?? and period T of the simple harmonic motion of this spring-rolling mass system? Express your answer in terms of k and M.
(e) Assume that we have the same spring and mass, only now the cylinder is released from rest on a frictionless surface at a distance A from the equilibrium position. What is the period of the simple harmonic motion of the system? Express your answer in terms of k and M.
Fig. 3: Figure for problem 7.

7) (8 pts.) A solid cylinder of mass M and radius R is mounted to an axle through its center. The axle is attached to a horizontal spring of constant k, as shown in the figure. Initially the cylinder is at rest and the spring is un-stretched. The cylinder is pulled a distance A and then released. The cylinder then rolls back and forth without slipping.
(a) What is the total mechanical energy of the system just before the cylinder is released? Express your answer in known quantities.
(b) What is the total mechanical energy of the system when the disk passes through the equilibrium position? Express your answer in terms of M, speed of the center of mass v, moment of inertia I, and the angular speed ??rolling.
(c) What is the linear speed of the center of mass v of the cylinder when it passes through the equilibrium position? Express your answer in terms of k, M, and A.
(d) What is the angular frequency ?? and period T of the simple harmonic motion of this spring-rolling mass system? Express your answer in terms of k and M.
(e) Assume that we have the same spring and mass, only now the cylinder is released from rest on a frictionless surface at a distance A from the equilibrium position. What is the period of the simple harmonic motion of the system? Express your answer in terms of k and M.
Fig. 3: Figure for problem 7.

Added by Alfonso C.

Question

Please give Ace some feedback