maybe it's because your a is already a component of g? so discounting normal force, there is only one force -Fg- acting on the object on an incline. in your other problem, a is a different force than g.
if I'm wrong, please do correct me
i assumed the question to be asking for a solution that only requires energy arguments. as you can see, i go into Newtonian mechanics in the latter part of the solution. Is there a way to solve this question using energy/power alone?
Q: An inclined plane at 30 degrees is 6.4m long. A book, which has a kinetic coefficient of friction with the incline of 0.2, is placed at the top and immediately begins to slide. Using energy considerations, how long will it take for the book to reach the bottom of the incline?
my solution...