Question

"A solid cylinder and a thin-walled hollow cylinder have the same mass and radius. They are rolling horizontally along the ground toward the bottom of an incline. They center of mass of each cylinder has the same translational speed. The cylinders roll up the incline and reach their highest points. Calculate the ratio of the distances (solid/hollow) along the incline through which each center of mass moves."

I already know the answer is 3/4. I just need some help in finding out how to get this solution.

Answer 1

Conside the ratios of kinetic energies of the two cylinders. Each rolls up the incline a distance that is proprtional K.E.

The differences are due to differing amounts of rotational kinetic energy, which depends upon the moment of inertia. They are not the same for the two cylinders. The hollow cylinder has a higher rotational KE, but the same translational KE, as the solid cylinder. It is the total KE that matters.

Answer 2

The kinetic energy at a given V is independent of R. It is not necessary to have the two cylinders have the same mass or radius, in order to get the 4:3 ratio of distances.