The acceleration of the block and ramp may be found rather easily by applying the 2nd Law to the two-object system. The center of mass cannot accelerate up or down if the block does not move up or down the ramp, which is a given. Therefore, the net external force in the vertical direction is zero. The acceleration of the center of mass in the horizontal direction is simply the net external horizontal force F divided by the total mass of the system. It is concluded that the acceleration of the two-object system is directly to the left and given by:
This is the acceleration of the center of mass, but because there is no relative motion of the block on the ramp it is also the acceleration of each individual object.
Now consider the forces acting on the block. Lacking information about the...