A solid cylinder of radius d=0.5m and mass M=4kg is released from rest at the top of an incline making an angle of 45 degrees with the horizontal. The cylinder elevation to the center of mass is h = 12m. You can assume that the cylinder is rolling without slipping. a) Find the total kinetic energy of the cylinder at the top of the loop of R=3m b) Determine the minimum height h that allows the cylinder to make it through the loop (it never loses contact with the track) c) If you replace the cylinder with a spherical thin shell of the same radius d=0.5m and the same mass M=4kg , explain in detail how the answer to the minimum h of part b) would change. M R

A solid cylinder of radius d=0.5m and mass M=4kg is released from rest at the top of an incline making an angle of 45 degrees with the horizontal. The cylinder elevation to the center of mass is h = 12m. You can assume that the cylinder is rolling without slipping. a) Find the total kinetic energy of the cylinder at the top of the loop of R=3m b) Determine the minimum height h that allows the cylinder to make it through the loop (it never loses contact with the track) c) If you replace the cylinder with a spherical thin shell of the same radius d=0.5m and the same mass M=4kg , explain in detail how the answer to the minimum h of part b) would change. M R