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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.

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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.

Yes, that's right.

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.

That's also right. Force isn't the only thing that determines how hard something feels; the power (force times velocity) is also important, since that is the rate you're transferring energy to the bar.

There are tons of examples where this is important. For example, hanging from a bar involves exerting a fairly large force (to cancel your weight). But hanging is not as hard as doing pullups, where you have nonzero velocity. Similarly, an object can hang from a crane basically forever, but the crane has to burn fuel to lift the object even at constant speed, and it burns fuel faster the larger that speed is.

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As you said, the force is the same, either with the weight at rest or going up at a constant velocity.

But lifting a weight requires work, and power (work / time): $P = F.V$ increases linearly with the speed.

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