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The feel of weightlessness (and, consequently, weight) is more
than the reaction force exerted by the floor. As I pointed out,
it's not the same as floating neutrally bouyant. If you don't
understand that, next time you go to the swimming pool, jump
feet first off the ten meter tower. You'll feel your testicles
as weightless - dramatically! It is quite a deterrent to going
off feet first; I much prefer to go head first.
Many of my students fly experiments on the "vomit comet"
(Canada is committed to pay for more flights than it can fill).
I am told that half of them get sick. Fortunately this does not
happen in our swimming pool at SFU when people float.