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Imagine that I lifted 100 kg object 1 cm above the ground and keep it there. I would like to know how much energy do I need to spend to keep this object there? I understand that in basic sense energy required is 0. But in reality, I spend energy to keep say my hand rigid to keep the object lifted. Or I can attach a drone to the object and burn gasoline to keep it afloat. Any formulas?

Qmechanic
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Morton Gelt
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2 Answers2

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Your question is clear.

The spending of energy comes about by doing work which has the same units as energy, and we know from elementary physics that work done in a gravitational field is simply the product of force and distance

$$W = Fd$$

So say for example you take your 100 kg mass and raise it from the ground and place it on a pedestal 1 meter high. The force you exerted is $mg$, so about 980 Newtons and the distance traveled, 1 meter so you spend about 980 Joules of energy. And that was done whether you did it with your muscles or with a drone. Furthermore after the object is set on the pedestal neither you nor the pedestal continue to spend energy. The energy did not disappear but was rather stored in the object and that's called potential energy.

What does continue to persist after the object is at rest is an upward force by the pedestal that is in equilibrium with the downward force (weight) of the object. But the pedestal does not spend energy doing that. If however you are holding the object, or a UAV is burning gasoline, energy is being spent to maintain that force equilibrium.

docscience
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The thing is that this question has different answers depending on context and exact setup.

If you hold up the weight with your arm, it would be incredibly tiring to hold in a horizontally stretched arm. I you instead hold your arm vertically, then you might be able to let bones carry the load instead of muscles, and your effort is much, much less.

The drone will spent fuel to supply the updrift needed against the total weight that pulls it down. But how much energy that takes depends on fuel, drone, the air, the wings' geometry and structure etc.

Put the weight onto a hook in the ceiling and no energy is spent at all - not by you or any drone, and not by the ceiling either. No energy is required for a force to be present. But such force may be the result of energy-requiring processes, which is the case in the human body with muscle contractions and biological processes, but not the case in the ceiling.

Steeven
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