A spool with thread wound on it, of mass m, rests on a rough horizontal surface. Its moment of inertia relative to its own axis is equal to `I=gammamR^2`, where `gamma` is a numerical factor, and R is the outside radius of the spool. The radius of the wound thread layer is equal to r. The spool is pulled without sliding by the thread with a constant force F directed at an angle `alpha` to the horizontal (figure). Find:
(a) the projection of the acceleration vector of the spool axis on the x-axis,
(b) the work performed by the force F during the first t seconds after the beginning of motion.

Answer

`[(F(costheta-(r)/(R)))/(m(1+gamma)),(F^(2)t^(2)(costheta-(r)/(R)))/(2m(1+gamma))]`