Energy to hold an object for a given time

[Drakkith]

In other words, We all can simply calculate the minimum Energy that it will take to generate a force of magnitude 'mg' in order to move an object of mass m over the distance X. This is because energy generated the force that did work on the object. But since we know the object's acceleration over the distance X (it was g) we can calculate the time t it took to travel X distance by using the equation Energy= mgX=1/2m(gt)^2. Now in the scenario where both opposite forces are acting on the object and the object isn't moving, this same equation can also be used to calculate the minimum energy that's fueling each force over time t, since it is a function of time only.

Energy does not create force, instead it is force that creates energy. If I place an electron near another electron, the two will experience a repulsive force and be accelerated away from each other and in the process they will gain kinetic energy. The force is why the electrons gained energy, and it does not require energy to function.

Now, the situation is much more complicated if we get into things like rocket engines which have to go through chemical reactions to generate their thrust, but the basics are still the same. A force is what accelerates something and gives it energy.

 

[Dale]

The moment that one force was released doesn't mean that energy is NOW fueling the acting force, when before it wasn't.

Actually, it does. The minimum amount of energy required is equal to the work done on the object, by conservation of energy. If the work done is 0 then the minimum energy is 0.

Consider your example where the forces are provided by a pair of springs at equilibrium under a compression force F. If one spring is used the object accelerates, but if both springs are used the object does not. Use the standard spring formulas to calculate the energy used in each case.

 

[Lsos]

The laws of physics are not being violated in any way in the scenario I'm thinking of but not explaining correctly. It's my fault and not others. I'm talking about the minimum energy needed to fuel the force, not the energy the force creates. And I'm talking about forces that actually create movement if no opposing forces existed (not holding forces). And I'm not talking about forces from the human body anymore.

I'm trying to understand what you're asking...

Is it this: How much minimum energy would it take to, for instance, keep a spaceship motionless in one point above the earth?

Or, How much minimum energy would it take, for instance, to keep a helicopter hovering motionless?

If that's what you're asking, then that is no different a question than asking how much energy would it take for a human or table to hold the object in place. Whether on the ground, on a rock, or in space fighting against a black hole's gravity (outside of the event horizon), as long as there is no acceleration the answer is ZERO. All you have to do is break up the problem into a simple free-body diagram. You will notice that all these examples have two equal but opposite forces acting on an object. Whatever is is that applies those forces is irrelevant. As long as the forces are balanced, the energy requirement is none.

Now, realistically if we want a helicopter to hover we need a lot of energy. But that's just a limitation of our technology. The fact is that theoreticaly we shouldn't need any energy. For example, if we made the rotor blades longer (thereby moving more air), they would be more efficient at providing lift, and the energy requirement would drop. Make them infinitely long and perfect blades, and we need no energy. Obviously we don't know how to do that, but physics doesn't prevent us from accomplishing an equivalent thing.

A spacehip hovering in space: obviously we need to fire a rocket to keep it from falling, requiring lots of energy. But again, depending on the rocket we could use more or less fuel. An ion engine, firing a little mass but very quickly requires much more energy than a chemical rocket engine firing lots of mass but slower. The more mass we expel, the less energy we need, so we could always use bigger engines to fire more and more mass and require less and less fuel. The minimum is, again, zero. Of course no reasonable rocket we can build could fire mountains of mass, but that's just an engineering limitation of rocket engines. There's no reason, for example, why we couldn't place a great big magnet on the Earth that keeps the spaceship hovering. Or place another Earth behind it, balancing out the forces and, again, keeping it hovering. These are all just technological limitations. The theoretical limitations and the answer to your question is, to reiterate, zero.

 

[ronaldleemhui]

To hover, a helicopter needs to provide a thrust by accelerating air downward. The thrust is proportional to the mass of downdraft per unit time times the velocity of the flow. If the rotors are extremely long and wide, the volume of downflow can be great. This allows the velocity to be low and still achieve the same thrust. In the extreme, the work required would approach zero, apart from parasitic drag of the rotors, the effects of turbulence, friction and the inefficiencies inherent in the need for a tail rotor.

Another way to look at things is to view the rotors just like wings on an airplane. In this case, however, the wings move while the helicopter stays put. One can think of a glide ratio for a glider, or of an airplane without power. Typical ratios can run from 1:8 for a small plane to 1:50 for a highly efficient glider. Now let us assume that the rotors are safely subsonic at the tips and perhaps 100 mph somewhere near the effective middle. A 1:8 glide ratio for the airfoil would therefore lead to a natural sink rate of 100/8 mph without power. The sink rate times the weight of the helicopter becomes the power consumption required to hover. (That is, if that amount is applied to the rotors, the natural sink rate will be neutralized.) As an order of magnitude,

weight of helicopter 1800 lb
sink rate as estimated above = 12.5 mph = roughly 18 ft/sec

so power requirement = 1800 * 18 / 550 hp or about 60 hp.

Power requirement would be less, perhaps by 50% close to the ground.

Just order of magnitude estimates.

 

[K^2]

Nevermind I think I know how to calculate it. All I have to do is calculated the distance the object will move if gravity wasn't acting on it. Let's say I hold a m kg object for t seconds. Then I would need to apply a force of mg netwons. Now the distance an object at rest will travel if mg force was applied to it over t seconds is d=1/2at^2 = 1/2gt^2
So the work done or energy used would be W=mg x 1/2gt^2 = 1/2mgt^2

So the energy required to hold an object with weight w for t time is
E=1/2wt^2.

Is this correct?

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]

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.

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]

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).

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.

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.

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]

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.

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]

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.

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.