Serway & Jewett — Rotation of a Rigid Object about a Fixed Axis: Problem 34

A smooth cube of mass \(m\) and edge length \(r\) slides with speed \(v\) on a horizontal surface with negligible friction. The cube then moves up a smooth incline that makes an angle \(\theta\) with the horizontal. A cylinder of mass \(m\) and radius \(r\) rolls without slipping with its center of mass moving with speed \(v\) and encounters an incline of the same angle of inclination but with sufficient friction that the cylinder continues to roll without slipping. (a) Which object will go the greater distance up the incline? (b) Find the difference between the maximum distances the objects travel up the incline. (c) Explain what accounts for this difference in distances traveled.