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I was reading the discussion here: Why does holding something up cost energy while no work is being done?

I feel as though the question is being avoided. Suppose instead of holding an object by hand we would attach some machine which burns fuel and converts it to force. This force is equal to mg. We would like to predict how much fuel is being burnt (how much energy is spent) in order to hold the object for a time of T seconds. The attached link does not give any clue how one can approach this problem. Furthermore, and this is what bothers me most, suppose that while the machine holds the object perfectly still someone would miraculously turn off the earth's gravity. The machine still creates a force of mg. Suppose that after time of T seconds the object is at height h (relative to its starting position). Would we then be able to say the amount of energy spent by the machine is mgh? Maybe one would say it depends on how the machine works and how much energy is converted to heat. So suppose the machine has perfect efficiency (equals or very close to 1), i.e. every joule spent by the machine is dedicated to hold the object.
For me it seems the 2 scenarios are exactly alike, since the machine is indifferent to gravity. Please be the devil's advocate when answering this question :)

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Nadavb
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    Your perfect machine would expend no energy to maintain the force. This is no different from the way a static vice maintains a force on a clamped object without energy input or the way a steel column continuously exerts a reaction force on a heavy object balance on top, without energy input. Both are examples of your machine. – RedGrittyBrick May 04 '16 at 09:52
  • It does not take any energy to hold something in place, your body is simply not evolved to be a static load bearing structure, so it doesn't have the necessary passive locking mechanism in its joints. Tension in the mammalian anatomy requires energy. If you have ever seen a person faint, you will know just how completely soft we go when the brain stops controlling muscle tension. It is, if you want, a biological "problem", the physics of it is trivial, though: the work performed on a body is $dW=Fds$. If $ds=0$, then no work is being performed, and that takes zero energy. – CuriousOne May 04 '16 at 09:53
  • You can design a machine that sort of mirrors the imperfection of the human body. E.g. place the object on one arm of a lever, an electromagnet at the other end, and an iron plate right beneath it. Drive a current through the electromagnet and it will be attracted to the iron plate, thus supporting the object. The problem with this reasoning is that the machine can be designed to be arbitrarily efficient, depending on the lengths of the lever arms, the resistance of the electromagnet, etc etc. How much energy the human body expends is a question for biologists, though. – LLlAMnYP May 04 '16 at 10:04
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    Possible duplicate of Why does holding something up cost energy while no work is being done? – Joce May 17 '16 at 11:50
  • @LLlAMnYP The fun thing about a machine that mimics the human body's inefficiency is that all of the energy it expends to hold something up is waste. In your electromagnetic lever-lock, the only mechanism for energy expenditure is resistive losses in the coil, for example. If the lever stays the same height, no work is being done and thus the energy of the lever is unchanged. – Asher May 17 '16 at 21:37
  • @Asher Ok so what if the object is moving at a constant acceleration? Still no energy is wasted? According to you answer "If the lever stays the same height, no work is being done and thus the energy of the lever is unchanged". If it does consume energy then why does the movement of the object affects the energy consumption of the lever? – Nadavb May 19 '16 at 09:42
  • @Nadavb If the object is accelerating, its energy is changing. That energy has to come from somewhere so your machine will now need a source of energy to deposit into the object. How much is wasted is entirely dependent on the design of the machine doing the lifting – Asher May 19 '16 at 13:16
  • @asher Ok so why does the energy consumption of the machine depends on whether the object is moving or not? In both cases the machine does exactly the same thing i.e. activates force of mg. Remember that we assume that when the object is moving the gravity is 'turned off'. As for the question of how the machine is designed then as I wrote in my question the machine has perfect - or near perfect - efficiency – Nadavb May 22 '16 at 07:59
  • @Nadavb "moving" and "accelerating" mean two different things in physics. An object can move at constant velocity for free, but accelerating requires energy. We've known this since Newton. It stems from the law of conservation of energy. If you could accelerate something without expending energy, you could accelerate water to the top of the dam for free and extract energy from it as it fell; you'd get energy for free. – Asher May 22 '16 at 18:13
  • @Asher But in both cases the machine does EXACTLY the same thing. In both cases it produces force of size mg If the machine runs on fuel then the EXACT amount of fuel is used in both cases It doesn't make any sense that a different amount of energy will be consumed in the EXACT same case – Nadavb May 22 '16 at 22:47
  • @Nadavb if the machine accelerates an object in one case and does not accelerate it in another, it's not doing "exactly the same thing." Unless of course you start changing the initial conditions, such as "miraculously turning off the Earth's gravity." I'd like to point out though that there's no way to create a machine with "perfect efficiency" which dynamically holds an object in place against gravity: if it's expending energy without doing work, it is 0% efficient. Your question cannot be answered within your expectations because it is nonphysical. – Asher May 22 '16 at 23:15
  • @Asher So when the gravity is turned off then the machine becomes physically possible? – Nadavb May 23 '16 at 10:13

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To understand why holding objects costs energy even though the work appears to be zero, you have to understand how muscles work. When you are holding an object, your muscles are contracted. The process of muscle contraction consists in a protein filament called Myosin pulling another filament, called Actin. Since this is a dynamical process (the Actin filaments are moving because the Myosin filaments exert a force on them), you can see how the work is not zero.

In this video you can get a fairly good idea of the process: https://www.youtube.com/watch?v=Cjx3vSm54N8

As for your thought experiment, you should be clearer on how the machine works. Of course you don't really need a machine, since a piece of rope will basically serve the purpose perfectly. But let's say you want to do it with a machine, because you have a lot of fuel to spare.

We can imagine, for example, an "artificial muscle" that basically works like ours. In this case, when gravity is switched off, if the muscle stays contracted, work will still be done, even if nothing will take off or start to move; but of course, you can just relax the muscle and still be able to hold the now weightless object.

But we can imagine different kinds of machines: maybe a levitating machine using jet propulsion to counterbalance the force exerted by the object. In this case, your reasoning will be basically correct: when gravity is switched off, the machine will take off, reaching a certain height in a certain amount of time and giving us an idea of the amount of work necessary to hold the object using this particular machine (but in this case, remember to take also kinetic energy into account!).

valerio
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  • I think te underline "problem" relates to whether there is contact with whatever is holding the object. If there is contact then one can apply Newton's 3rd law and say that no energy is used to generate the force. By "inventing" a machine which generates power without touching the object I side stepped this problem. Alternatively, LLlAMnYP side stepped the problem by using electromagnetic force. – Nadavb May 05 '16 at 11:18
  • To all those who say it's a bio-mechanic issue or 'F dot ds' with ds=0, it seems to me kind of ignoring the problem – Nadavb May 05 '16 at 11:27