One of your remarks is very perceptive: "Since there is nothing special physically about 1 kg, the equation shouldn't switch its scaling at that point, should it?" That's exactly right.
Honestly, I can't follow the previous questions. So let's just illustrate how this works.
Say that something is accelerating at 5 m/s2
. If this object has a mass of 3 kg, then the force, given by F=ma, is 15 kg m/s2
or 15 Newtons. What if the mass is instead 0.3 kg? Then you'd get F=1.5 N, by exactly the same method.
So I'm not sure what the mystery is. But your point that there's nothing special about the particular mass we chose to call 1 kg is exactly right, and also true for our other familiar units.
(published on 03/20/09)