I am unsure about this thought experiment: I stand on a scale with some weight in my hands. When I move the weight upwards, the scale shows a higher number for some time. This is clear to me as I accelerated the weight away from the scale and thus received acceleration into the scale. (or: momentum upwards increased, momentum downwards increased).
here's my question: at first I have to accelerate the weight (v=0 to v>0). lets say I then manage to keep the velocity constant. at this time, what does the scale show? my current conclusion: it shows the same weight as when standing still.
reasoning: when I move the weight at the same pace, I actually don't apply any more force to it than when I just hold it (i.e. same force as G). I once overcame the gravitational pull, but now that the weight is in motion, cancelling out gravitation is sufficient (the weight will stay in motion according to the first law). this is the same situation as just holding the weight. regarding conservation of momentum: the additional momentum got cancelled out by the scale/floor when acceleration occurs, thus the spike, and then it goes back to normal.
if my reasoning is correct however, this means that if I do a bench press with very different constant bar speeds, I both times apply the same forces (except at the beginning). this seems kind of counter intuitive to me, so I wanted to ask you guys.