Rolling friction example

In this example we will derivate equations of statics equilibrium for roller on slope. Slope is inclined to the ground. Between slope's surface and ground level is angle α. Between slope's surface and roll exists rolling friction and sliding friction. Sliding friction is described by factor μ. Rolling friction is described by factor ƒ. Force is placed parallel to the slope's surface and accurate in roll's center. Subject of exercise is to designate equilibrium equations and value of force F which will provide balance in system.