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I have found it helpful to discuss an imaginary society that evolved
on a giant spaceship coasting at constant velocity far from any
planet. The question is: could their physicists have discovered
Newton's laws. It takes some convincing and some thought
experiments, but eventually we agree that an object (say a liter
bottle of water) would have inertia, would accelerate when pushed and
could be shown to accelerate faster than a two-liter bottle
experiencing the same push.
Then we have them land on a planet -- first encounter with this thing
called gravity. Suddenly, everything that is not impeded has a
preferred direction of acceleration. That all objects "fall" with
that same acceleration is an empirical observation (because we are
chapters away from NLG). But we can infer that there must be a force
causing this. And it must be that the force is bigger when it acts
on objects with more mass.
So my point is, I don't see anything pedagogically problematic with
defining W=mg where g is the locally observed acceleration in m/s2.
If a student complains "But it isn't accelerating," I reply that it
would if there were no other force besides this mysterious force
whose presence we infer.
Using this sequence, I find less confusion about "masslessness" and
"weightlessness". We had mass before we ever encountered "gravity".
We have weight when we are in a neighborhood where things that you
drop accelerate.