Work done by sliding friction on an incline

Abstract When a ball slides down an incline, the friction force acts to dissipate kinetic energy. The total mechanical work done by the friction force is equal to the decrease in kinetic energy, and is determined by the displacement of the point of application of the friction force. The friction force does work to increase the rotational kinetic energy and to decrease the translational kinetic energy of the ball. The change in the translational kinetic energy is determined by the displacement of the centre of mass. Two different work-energy theorems are therefore needed to describe the work done by the friction force.