Stefan Jeglinski said, "Would you say that my example of visualizing the
independent accelerations on the inclined plane is invalid?"
Resolving the acceleration into its x and y components is not invalid,
it just doesn't speak to this issue. For a frictionless incline, the
two forces are the gravitational force and the normal force. According
to JD, we should say there exists the equation F(g) + F(N) = m[a(g) +
a(N)]. The acceleration a(g) is down and a(N) is pointed normal to the
surface. Your accelerations a(x) and a(y) are not the same as, and do
not correspond to, a(g) and a(y). Indeed, your a(x) is not a(g) even
though they are both down, because a(g) would be about 9.8 m/s^2, and
your a(x) is nowhere near 9.8 m/s^2 unless the incline is nearly
vertical.
If we view the incline with friction, the equation is F(g) + F(N) + F(f)
= m[a(g) + a(N) +a(f)], and obviously a(x) and a(y) cannot the three
accelerations JD is talking about.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu