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Say I wanted to keep a body of 10kg at a certain altitude above the ground. If I elevate it 1m with my own arms or by any other means (with a drone, pulley system...) I'm spending energy in the form of work in order to bring it to that altitude.

Given work's expression: $W=F*Δr$ . The amount of energy would be given by the distance I move it (1m) and the amount of force I apply to it. Now, if the applied force equals the gravitational force, the net force applied to the body will be zero and thus it wont move at all. Meaning that for $F≤P ⇒ Δr=0$ . Where P is the weight of the body. This means that, unless the applied force is greater than the body's weight, the displacement and thus the work made over the body is zero. The problem (or rather what I can't get my head round) is that in the process of applying ANY amount of force I do use energy, even if it is lost as heat and does not translate to work (be it electrical in the case of the drone or chemical if I'm the one pulling).

The same goes for keeping the body in place once it was been moved to the 1m altitude. To keep it there $F=P$, so once again the forces neutralise each other and the body stays put, but since there is no displacement the force fighting gravity isn't doing work, even if it is consuming energy in the process.

My question is: in order to know the energy consumption of maintaining the body at the 1m elevation, would I only have to consider the efficiency of the machine used? Be it a drone, human muscles, or a pulley system pulled by either of both? Or is there certain energy use intrinsically related to the weight of the body?

El Nitromante
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As you say, supporting an object at a constant height above the ground does no work on the object. And there are certainly ways of supporting the object (e.g. on the end of an inextensible rope or on top of a rigid pillar) which consume no energy at all (at least, as long we allow idealisations like inextensible ropes and rigid pillars).

But there are other ways of supporting the object at a constant height (e.g. muscles, hovering drone, jet propulsion) which do consume energy. However, none of this energy represents work done on the object. All of this energy is lost to the surrounding environment in the form of heat, sound waves or other atmospheric motions (and even the sound waves etc. eventually end up as heat).

gandalf61
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in the process of applying ANY amount of force I do use energy

This is actually a misconception from the way our muscles work. Fundamentally, there's no reason why applying a force without moving needs to take any energy. In fact, there are a few muscles in the body, I think in the digestive tract, that actually work like that, they can apply a constant force for a long time without using any energy.

You could keep it 1m up by just resting it on a 1m high table. No energy needed.

Martin C. Martin
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