5. A hollow cylinder of mass m, radius Rc, and moment of inertia I = mRc2 is pushed against a spring (with spring constant k) compressing it by a distance d. It is then released and rolls without slipping on a track, and through a vertical loop of radius RL. Assume RC << RL (a) When the cylinder reaches the top of the vertical loop, what is the minimum (linear) speed it must have to avoid falling off? Draw a free-body diagram to support your answer.
(b) What is the minimum compression of the spring necessary to prevent the cylinder falling off?
(c) Perform two “Cross-checks” on you solutions to check the validity of your solution, and/or examine the behavior of the system.