Mechanics dynamics - example 7

Roller is rolling to the slope's top with start velocity v0. Roller executes flat motion because it is rotating around its axis of symmetry and moves progressive motion. Between roller contact surface with slope surface exists rolling friction. Rolling friction is described by rolling friction factor ƒ[m]. Roller has mass m[kg] and radius r[m]. Slope's inclination angle α is known. Subject of example is to find road s which roller has traveled until it had stopped. The principle of conservation of total mechanical energy will be applied.