Work function: zero movement=zero energy, is it true?

[vakundok]

I have just started to read the book "The final theory". Do not laugh at me, I bought it because I thought it would make me do some thinking. And I was right.

So, the work function states that work (energy) equals the force multiplied by the distance (the distance of the movement in the same direction as the force). Based on this, it is stated that it requires no energy to hold the moon on orbit.

1. Imagine an electromagnet holding something. Since, it is just holding, but not moving that thing, according to the current definition, it requires no (usefull) work (and as such, energy), so the whole (electrical) energy input (IUt) is just a waste. However, if you switch off the energy supply, the thing will start to fall, so part of the energy input MUST be used to hold that thing in place. How does this match to the conservation of energy law?

2. The distance of a movement can be described based on the acceleration. For the sake of simplicity let's see only a basic linear acceleration from a standstill: d (for distance) = a (for acceleration) * t (for time) ^2 / 2.
If you put this into the work function, it will give the same results when used normally, however, it will give an extremely different result in an energy field, like gravity.
According to the conventional form, holding something against gravity requires zero energy (work) because W = F * d and d = 0. However, according to the converted form, it requires W = F * a * t^2 / 2 where a = g. Why the two forms are not interchangeable?

3. Why neither form of the work function describes what we experienced in the starting scenario of question 1? (You can see that the converted form of the work function would suggest that it requires energy growing exponentially by time to hold something in place against gravity.)

[Surlethe]

So, the work function states that work (energy) equals the force multiplied by the distance (the distance of the movement in the same direction as the force). Based on this, it is stated that it requires no energy to hold the moon on orbit.

Correct.

1. Imagine an electromagnet holding something. Since, it is just holding, but not moving that thing, according to the current definition, it requires no (usefull) work (and as such, energy), so the whole (electrical) energy input (IUt) is just a waste. However, if you switch off the energy supply, the thing will start to fall, so part of the energy input MUST be used to hold that thing in place. How does this match to the conservation of energy law?

That doesn't mean it doesn't have energy. The object has potential energy U equal to the force of magnetism at that point (F = k * q1 * q2/r^2, IIRC; k is the proportionality constant, the charges are q1 and q2, and r is the distance from the magnet) multiplied by the distance, which comes out to U = (k*q1*q2)/r. This energy is converted into kinetic energy K as the object falls, but the total energy E in the system stays constant. We say E = K + U (assuming frictionless objects, airless, no heat, yadda yadda yadda...). In this particular starting point, K just happens to equal 0.

2. The distance of a movement can be described based on the acceleration. For the sake of simplicity let's see only a basic linear acceleration from a standstill: d (for distance) = a (for acceleration) * t (for time) ^2 / 2.
If you put this into the work function, it will give the same results when used normally, however, it will give an extremely different result in an energy field, like gravity.
According to the conventional form, holding something against gravity requires zero energy (work) because W = F * d and d = 0. However, according to the converted form, it requires W = F * a * t^2 / 2 where a = g. Why the two forms are not interchangeable?

If an object is being held still, how fast is it accelerating?

3. Why neither form of the work function describes what we experienced in the starting scenario of question 1? (You can see that the converted form of the work function would suggest that it requires energy growing exponentially by time to hold something in place against gravity.)

No, there is no energy required to hold something against gravity because that object is not accelerating. You only require a constant force to hold an object in place against gravity. Since the net force is 0, there is no acceleration, and W = (F * a * t^2)/2 = (F * 0 * t^2)/2 = 0.

Again, holding an object still in a gravitational field requires only a constant force, and not constant energy. Since the two forces balance each other, neither force is doing any work; thus, the energy change will be zero.

However, the object will have potential energy determined by G * m1 * m2 /r, which, if the stabilizing force is turned off, will convert into kinetic energy.

[Illuminatus Primus]

Think of a pressurized matress holding up a person against gravity. Is the matress constantly expending energy? No. Is it constantly pushing against your weight? Yes. Now, if it was to push you up, against gravity another inch, that would require the application of more energy. If you fell another inch, the loss in pressure would amount to a loss of energy in the system.

[Lord of the Abyss]

So, the work function states that work (energy) equals the force multiplied by the distance (the distance of the movement in the same direction as the force). Based on this, it is stated that it requires no energy to hold the moon on orbit.

Correct.

?? I always understood the Moon was constantly losing energy via gravity waves ( in analogy to synchrotron radiation ). Also, the tides means it's exchanging energy with Earth. After googling, I found this.

I recall reading years ago that the Moon, given enough time would first spiral out, then spiral in until it broke up.

1. Imagine an electromagnet holding something. Since, it is just holding, but not moving that thing, according to the current definition, it requires no (usefull) work (and as such, energy), so the whole (electrical) energy input (IUt) is just a waste. However, if you switch off the energy supply, the thing will start to fall, so part of the energy input MUST be used to hold that thing in place. How does this match to the conservation of energy law?

I suspect ( wild guess alert ! ) that the energy loss is due to electrical resistance; plain old magnets can hold something without an energy input after all.

[Surlethe]

So, the work function states that work (energy) equals the force multiplied by the distance (the distance of the movement in the same direction as the force). Based on this, it is stated that it requires no energy to hold the moon on orbit.

Correct.

?? I always understood the Moon was constantly losing energy via gravity waves ( in analogy to synchrotron radiation ). Also, the tides means it's exchanging energy with Earth. After googling, I found this.

I recall reading years ago that the Moon, given enough time would first spiral out, then spiral in until it broke up.

If you want to be technical, the Moon is constantly losing energy via gravity waves, but that's a relativistic effect, and I assumed he was just curious about mechanics. In both cases (tides exchanging energy with the Earth and gravity waves), the effects are not pertinent to the basic issue of gravitational potential energy, the force of gravity, and the difference therebetween; therefore, I cut them from the explanation.

[Lord of the Abyss]

If you want to be technical, the Moon is constantly losing energy via gravity waves, but that's a relativistic effect, and I assumed he was just curious about mechanics. In both cases (tides exchanging energy with the Earth and gravity waves), the effects are not pertinent to the basic issue of gravitational potential energy, the force of gravity, and the difference therebetween; therefore, I cut them from the explanation.

Ok; thanks for explaining.

[Kuroneko]

1. Imagine an electromagnet holding something. Since, it is just holding, but not moving that thing, according to the current definition, it requires no (usefull) work (and as such, energy), so the whole (electrical) energy input (IUt) is just a waste. However, if you switch off the energy supply, the thing will start to fall, so part of the energy input MUST be used to hold that thing in place. How does this match to the conservation of energy law?

You're completely correct in all of your statements. In regards to your question, the electrical energy is converted to heat due to the internal resistance in the electromagnet. That is the only reason that the electromagnet requires continuous power in order to maintain its magnetic field; a superconducting electromagnet, on the other hand, could maintain its field virtually forever with no power input. While actually lifting the object, the power drain would be greater than while the object is stationary, simply because work is being done in that case.

According to the conventional form, holding something against gravity requires zero energy (work) because W = F * d and d = 0. However, according to the converted form, it requires W = F * a * t^2 / 2 where a = g. Why the two forms are not interchangeable?

This is confused; if the object is held stationary, then there is a counterforce to make a = 0.

[Darth Wong]

1. Imagine an electromagnet holding something. Since, it is just holding, but not moving that thing, according to the current definition, it requires no (usefull) work (and as such, energy), so the whole (electrical) energy input (IUt) is just a waste. However, if you switch off the energy supply, the thing will start to fall, so part of the energy input MUST be used to hold that thing in place. How does this match to the conservation of energy law?

Do you realize that the electrical energy going into the electromagnet becomes heat? Or are you honestly so ignorant that you think it just disappears into nothing because there's no work involved in holding up the object? Do you think that a rope must require energy in order to hold something up?

2. The distance of a movement can be described based on the acceleration. For the sake of simplicity let's see only a basic linear acceleration from a standstill: d (for distance) = a (for acceleration) * t (for time) ^2 / 2.
If you put this into the work function, it will give the same results when used normally, however, it will give an extremely different result in an energy field, like gravity.
According to the conventional form, holding something against gravity requires zero energy (work) because W = F * d and d = 0. However, according to the converted form, it requires W = F * a * t^2 / 2 where a = g. Why the two forms are not interchangeable?

The object is not accelerating, dumb-ass. You are confusing the rate at which it would accelerate if released with the rate at which it is actually accelerating.

3. Why neither form of the work function describes what we experienced in the starting scenario of question 1? (You can see that the converted form of the work function would suggest that it requires energy growing exponentially by time to hold something in place against gravity.)

I strongly suggest that you go to school to learn physics rather than trying to muddle through it yourself by looking at websites and asking questions on webboards.

[vakundok]

Sorry, I was quite busy in the previous few days (a wedding and a birthday party).

Thanks for the help (especially to Surlethe). Actually, I followed the logic that if something has weight and mass it has acceleration as well and if it does not move an opposite acceleration (an opposing force to weight) have to apply. I missed that this opposing acceleration and the acceleration in the movement part of the work function are not the same, as the latter is the resulting ("real") acceleration of the object. So, yes I confused the would and does accelerations.

Dear Darth Wong,

I knew that in question one the energy input became heat, I just thought that writing only that the energy input became a waste instead of writing "waste heat" was enough. It was not.

Thanks for the rope example (it is much better than the example IP brought up as it has no physical support underneath), despite by the time I read it I already found out where I was wrong (with the example of a nail holding a lamp).

Sadly, it is not that easy to go back to elementary or even secondary school and learn the basic physics again around here. Actually it is not even possible due to age limitations (not to mention size limitations for example). So, I have only the oppurtunity to read books about it and ask other people about it.

[TheDarkOne]

So, I have only the oppurtunity to read books about it and ask other people about it.

So get a textbook. That would probably be the best thing to learn the basics of physics from.