I've read this question and answers, but neither of the posts does seem to address my concerns. The problem is as follows:
Assuming a device that keeps something in a gravitational field on a constant height, like an electromagnet, how does one measure the required power?
I'm stumbling on that because the equation $P = Fv$ would mean that, assuming the object stays in place, the power is zero. That might be true for, say, a rigid construction holding something up. What if I am actively trying to keep something up, like holding it in my hand, or powering an electromagnet to create an electromagnetic field to keep something in the air? I am applying a constant force, but the object doesn't move!
I've tried to imagine it from the point of theoretical loss of potential energy I'm preventing, but it only got me to something like $P = g^2 m t$, which depends on time. In fact, every attempt to tackle the energy was in vain, because the velocity of the object in a gravitational field, if left without the support, wouldn't be constant (thus making the power depend on time), and is apparently not fit to describe the problem formally.
