A crate of books is to be put on a truck by rolling it up an incline of angle θ using a dolly. The total mass of the crate and the dolly is m. Assume that rolling the dolly up the incline is the same as sliding it up a frictionless surface.
(a) What is the magnitude of the horizontal force that must be applied just to hold the crate in place on the incline?
(b) What horizontal force must be applied to roll the crate up at constant speed?
(c) In order to start the dolly moving, it must be accelerated from rest. What horizontal force must be applied to give the crate an acceleration up the incline of magnitude a?