Energy to hold an object for a given time

K^2

If you put an object on the table, all of the above logic still applies. Yet, a table doesn't use up any energy to support an object. The above logic is, therefore, flawed.

The amount of energy required to support an object by a person has everything to do with biology of a muscle and cannot be resolved from physics considerations alone.

h1a8

I understand that. I was referring to a force that will create acceleration when no opposing force is acting (holding forces such as tables don't cause acceleration if no opposing force exists).

From my understanding, if a force (accelerating force) is acting on an object while the object isn't moving (due to some opposing force) then the energy fueling the force is being held (still potential energy). Once the other opposing force is eliminated the energy is now released and causes work to be done. A perfect example of what I'm talking about is a spring that is compressed and held.

Doc Al

As K^2 stated, the 'energy fueling the force' is a matter of biology, not physics. If you hold an object up using your muscles you will expend energy to maintain that muscular tension.
Again, what's holding the spring in its compressed state? You? A block resting on the spring?

ronaldleemhui

It's like a jet engine, or a rocket engine or throwing stones downward forcefully -- a certain momentum per unit time has to be shot down to overcome the effect of gravity on the helicopter. You can easily figure out what momentum flux is necessary, but depending on whether it is small amount of mass shot out fast, or large amount shot out slow, the energy required varies.

It is easier to conceive if you think of a glider in a steady glide. The steady drop rate times the weight of the glider is the power needed to achieve steady level flight. Only in the helicopter your "glide" is more like a corkscrew.

Think of those maple seeds that fall like little helicopters from the trees.

Drakkith

Energy is a measure of the ability to do work. In simple setups, such as a table holding up an object, it requires no energy to hold an object up because no work is being done. If you compare a table holding up a book to a rocket holding the book up instead, you will notice that the rocket is accelerating molecules which generates the force needed to hold the book up against gravity. (Because the rocket isn't resting on something that pushes back, like the ground) Similarly your muscles are not "simple" objects, they are complicated machines that constantly perform work (in the form of tensing muscle fibers) to hold something.

In my post above I explained that energy does not create forces, it is forces that create energy. In a complicated machine such as a jet engine or rocket engine, we use the fundamental force of electromagnetism to cause chemical reactions which result in an acceleration of molecules away from the rocket. This process results in the generation of a force against the rocket that pushes it forwards, aka thrust. But the ENERGY isn't causing this, our fundamental source or starting point is a FORCE. The EM force. How much force we can generate with the fuel we have is what energy measures and is purely a result of how many molecules we can react together.

Remember your basic definitions! Energy is the ability to perform work! It is not a force, it does not cause anything to happen. That, by definition, can only be done by a force.

Lsos

You're talking as if there is a distinction between an "accelerating force" and a "holding force". No such thing. A force is a force. For example, a table is also a spring, and if you somehow turned off gravity, whatever is resting on it would indeed accelerate upward. Perhaps not much, as it's just not a particularly good spring and so doesn't store as much energy.

Again, a force is a force. it's just a question of how efficient the machine that generates it is. Turns out that movnig around tons of air is not a particularly efficient method.

potatoecannon

This is the kind of fundamental question that really irritates high-school students when they are first told that carrying a box does no work, while lifting it does.

Try to think of it another way.

The goal is to levetate an object. The method chosen to do so will have the largest effect on the energy budget. This depends on the force producing mechanism, the device arrangement, and the force transmission method.

1) Fixed stable linkage:
Up to the compressive strength limit of the material, sticking something (ie table) underneath it gives your best (0 energy) result. Same holds for using a rigid bar mounted to the wall, etc.
(Makes for a pretty boring robot though).

2) Pinned linkage:
If you use a robot arm, human arm, etc., it is not designed to store a small amount of potential energy as strain energy to resist movement (resulting in the resisting force as per hooke's law).
For example, if you use a stepper motor on the joint, a holding current WILL be required to maintain the outstreched position. (Same applies to hydraulics/pneumatics etc where the system isn't pressure-locked).
The force required is based on the static moment balance (T=F*d), and thus changing the length of the arm will change your torque requirement, and thus the power required to maintain the holding torque on the motor.
Efficiency does come into play (ex battery life of your robot); you can design with shorter arms, more efficient motors, but you still aren't doing any mechanical work -> it's just the power cost of a unstable mechanism to develope a force. (By unstable, I mean it wouldn't maintain the position without a constant power supply).

3) No linkage:
Third class of levetation comes from things like magnetic levitation, helicopter rotors, jet engines, helium balloons etc.
Typically a system with no linkages would have the highest power requirement (ex helicopter pushing air) and you also need active stability compensation to maintain position, but the spinning magnetically levitating top (toy) hovers quite a while without "using" energy to maintain position (it falls when air friction has leeched enough angular momentum to reduce its gyroscopically-maintained stability below a critical point).

If you read all that, all I'm saying is that everybody above is technically correct - a stable system requires no energy to do work, but depending on the design it can take drastically different amounts of power to maintain stability.
The "theoretical minimum" only applies to the force-producing device you chose, and the configuration you use it it.

Side note:
The power requirement is easy to calculate with an electric motor's data sheet, but I haven't been able to find one for your arm yet...

sophiecentaur

There is a vital distinction between Work Done On and Work Done By. The work done By your muscles is all expended inside your arm by work done ON the internals as the muscle fibres tighten and then relax in sequence and none of it is expended on the supported mass.
Come on chaps. This is not difficult, is it?

In fact, as the table gradually creeps and sags, over the years, work is actually done ON the table by the falling mass.

DocZaius

A phrase I keep hearing OP say is "the energy fueling the force." I think this is where the misconception lies. His picture is of some energy being "trapped" in this static picture of two equal and opposite forces. Removing one of the forces suddenly "releases" the energy. He wants to know what that energy is.

Never mind that this is a wrong picture, let's try look at what actually does happen in terms of energy for the scenario. Say you have a body in free space that has two rockets pushing on it at either end with equal and opposite force. Now let's say that there is some energy associated with this static picture. Can we possibly tell what it is? Let's say we remove one of the rockets. The object now accelerates and gains kinetic energy. Do you not agree that the object's kinetic energy will go from zero to infinity based on how long (and more correctly, how far) we let this rocket act on the object? If there was a single value of energy associated with the static scenario, why are we getting every possible energy (0 to infinity) when we remove one of the rockets?

Drakkith

That is what I attempted to explain twice DocZaius.