A smooth cube of mass m and edge length r slides having speed v on a horizontal surface having negligible friction. The cube then moves up a smooth incline which makes an angle with the horizontal. A cylinder having mass m and radius r rolls without slipping with its center of mass moving with speed v and encounters an incline of the similar angle of inclination however with sufficient friction which the cylinder continues to roll without slipping.
(i) Which object will go the bigger distance up the incline?
(ii) Determine the difference between the maximum distances the objects travel up the incline. (Employ any variable or symbol stated above all along with the given as necessary: g for the acceleration of gravity.)
(iii) Describe what accounts for this difference in distances traveled.