A uniform solid cylinder of mass 2.0 kg and radius 0.20 m is projected across a…
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A uniform solid cylinder of mass 2.0 kg and radius 0.20 m is projected across a horizontal rough surface with an initial center-of-mass speed of 6.0 m/s and no initial rotation. The coefficient of kinetic friction between the cylinder and the surface is 0.25.
Answer the following.
(a) Derive an expression for the cylinder’s angular speed ωf when pure rolling first occurs, in terms of its initial speed v0 and radius R.
(b) Derive an expression for its center-of-mass speed vf at that same instant.
(c) Calculate vf numerically for the given values.
(d) Determine the fraction of the cylinder’s initial translational kinetic energy that has been converted to thermal energy by the time pure rolling is reached.
(e) Describe qualitatively how the magnitude of the kinetic-friction force acting on the cylinder changes, if at all, during the slipping interval before pure rolling is achieved.