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The conceptual problem seems to result from the term "zeroing
out." When we say that g in a given location, is 9.8 m/s^2,
we refer to what is measured in an elevator at rest with
respect to the center of our planet (or outside of that
elevator). It is the g calculated from the universal
gravitational force, either in Spain or in N.Z.
What might be measured in a falling elevator is called
apparent acceleration. And we know how it is connected to 9.8
m/s^2. I do not remember students being confused, especially
when the rotation of the earth is neglected.
What else am I missing?