Action (physics) - Wikipedia
Power | Energy flux, kg.m2.s-3, J.s-1, W, watt. [ΔEnergy]/[ΔTime]. Action, kg.m2.s- 1, J.s, [Energy]*[Time], [Moment of motion]*[Distance]. Angular. Watt-hours are a measurement of energy, describing the total amount of electricity used over time. Watt-hours are a combination of how fast the electricity is used. In physics, power is the rate of doing work or transferring heat, the amount of energy transferred The dimension of power is energy divided by time. . The similar relationship is obtained for rotating systems, where TA and ωA are the torque and angular velocity of the input and TB and ωB . kg m s · action: 𝒮, actergy: ℵ.
An object moves with different speed in different frames, depending on the motion of the observer, so the kinetic energy in both Newtonian mechanics and relativity is frame dependent. This means that the amount of relativistic energy, and therefore the amount of relativistic mass, that an object is measured to have depends on the observer.
The rest mass is defined as the mass that an object has when it is not moving or when an inertial frame is chosen such that it is not moving. The term also applies to the invariant mass of systems when the system as a whole is not "moving" has no net momentum.
The rest and invariant masses are the smallest possible value of the mass of the object or system. They also are conserved quantities, so long as the system is isolated. Because of the way they are calculated, the effects of moving observers are subtracted, so these quantities do not change with the motion of the observer.
The rest mass is almost never additive: The rest mass of an object is the total energy of all the parts, including kinetic energy, as measured by an observer that sees the center of the mass of the object to be standing still.
The rest mass adds up only if the parts are standing still and do not attract or repel, so that they do not have any extra kinetic or potential energy.
The other possibility is that they have a positive kinetic energy and a negative potential energy that exactly cancels.
Power (physics) - Wikipedia
Binding energy and the "mass defect"[ edit ] This section needs additional citations for verification. July Learn how and when to remove this template message Whenever any type of energy is removed from a system, the mass associated with the energy is also removed, and the system therefore loses mass.
However, use of this formula in such circumstances has led to the false idea that mass has been "converted" to energy. This may be particularly the case when the energy and mass removed from the system is associated with the binding energy of the system.
In such cases, the binding energy is observed as a "mass defect" or deficit in the new system. The fact that the released energy is not easily weighed in many such cases, may cause its mass to be neglected as though it no longer existed.
This circumstance has encouraged the false idea of conversion of mass to energy, rather than the correct idea that the binding energy of such systems is relatively large, and exhibits a measurable mass, which is removed when the binding energy is removed.
The difference between the rest mass of a bound system and of the unbound parts is the binding energy of the system, if this energy has been removed after binding. For example, a water molecule weighs a little less than two free hydrogen atoms and an oxygen atom.
The minuscule mass difference is the energy needed to split the molecule into three individual atoms divided by c2which was given off as heat when the molecule formed this heat had mass.
Likewise, a stick of dynamite in theory weighs a little bit more than the fragments after the explosion, but this is true only so long as the fragments are cooled and the heat removed. Such a change in mass may only happen when the system is open, and the energy and mass escapes. Thus, if a stick of dynamite is blown up in a hermetically sealed chamber, the mass of the chamber and fragments, the heat, sound, and light would still be equal to the original mass of the chamber and dynamite.
If sitting on a scale, the weight and mass would not change.
This would in theory also happen even with a nuclear bomb, if it could be kept in an ideal box of infinite strength, which did not rupture or pass radiation.
If then, however, a transparent window passing only electromagnetic radiation were opened in such an ideal box after the explosion, and a beam of X-rays and other lower-energy light allowed to escape the box, it would eventually be found to weigh one gram less than it had before the explosion.
This weight loss and mass loss would happen as the box was cooled by this process, to room temperature. However, any surrounding mass that absorbed the X-rays and other "heat" would gain this gram of mass from the resulting heating, so the mass "loss" would represent merely its relocation.
Thus, no mass or, in the case of a nuclear bomb, no matter would be "converted" to energy in such a process. Mass and energy, as always, would both be separately conserved. Massless particles[ edit ] Massless particles have zero rest mass. This frequency and thus the relativistic energy are frame-dependent. His definition is almost the same as our current definition of kinetic energy.
He's missing a one-half multiplier out front that makes the energies intercovertable.
The same idea is somewhat more concisely expressed by the term energy, which indicates the tendency of a body to ascend or to penetrate to a certain distance, in opposition to a retarding force. William Rankine — Scotland: Since kinetic energy was the first form identified, he attached a modifier to the form of energy he discovered. Thus the unfortunate notion that kinetic energy is actual energy and potential energy is energy that has the potential to be actual energy.
No form of energy is any more or less "actual" than any other. Philosophy is not science although there is such a thing as philiosophy of science. But at a minimum, a tiny motion away makes, in the first approximation, no difference Fig. If we have the true path, a curve which differs only a little bit from it will, in the first approximation, make no difference in the action. Any difference will be in the second approximation, if we really have a minimum. If there is a change in the first order when I deviate the curve a certain way, there is a change in the action that is proportional to the deviation.
But then if the change is proportional to the deviation, reversing the sign of the deviation will make the action less. We would get the action to increase one way and to decrease the other way. It can differ in the second order, but in the first order the difference must be zero.
With that condition, we have specified our mathematical problem. Here is a certain integral. You will see the great value of that in a minute.
There are formulas that tell you how to do this in some cases without actually calculating, but they are not general enough to be worth bothering about; the best way is to calculate it out this way. I can do that by integrating by parts. It is always the same in every problem in which derivatives appear. Then I must have the integral from the rest of the integration by parts. The last term is brought down without change. In fact, if the integrated part does not disappear, you restate the principle, adding conditions to make sure it does!
So the integrated term is zero. We collect the other terms together and obtain this: The action integral will be a minimum for the path that satisfies this complicated differential equation: The first term is the mass times acceleration, and the second is the derivative of the potential energy, which is the force.
The fundamental principle was that for any first-order variation away from the optical path, the change in time was zero; it is the same story. In the first place, the thing can be done in three dimensions. And what about the path?
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The path is some general curve in space, which is not so easily drawn, but the idea is the same. Since only the first-order variation has to be zero, we can do the calculation by three successive shifts. We get one equation. Or, of course, in any order that you want.
Anyway, you get three equations. I think that you can practically see that it is bound to work, but we will leave you to show for yourself that it will work for three dimensions. If you have, say, two particles with a force between them, so that there is a mutual potential energy, then you just add the kinetic energy of both particles and take the potential energy of the mutual interaction.
And what do you vary? You vary the paths of both particles. Then, for two particles moving in three dimensions, there are six equations. But the principle of least action only works for conservative systems—where all forces can be gotten from a potential function.
You know, however, that on a microscopic level—on the deepest level of physics—there are no nonconservative forces. Nonconservative forces, like friction, appear only because we neglect microscopic complications—there are just too many particles to analyze.
But the fundamental laws can be put in the form of a principle of least action. Suppose we ask what happens if the particle moves relativistically. Is there a corresponding principle of least action for the relativistic case? The formula in the case of relativity is the following: Of course, we are then including only electromagnetic forces. This action function gives the complete theory of relativistic motion of a single particle in an electromagnetic field.
I will leave to the more ingenious of you the problem to demonstrate that this action formula does, in fact, give the correct equations of motion for relativity. The variations get much more complicated. But I will leave that for you to play with. The question of what the action should be for any particular case must be determined by some kind of trial and error. It is just the same problem as determining what are the laws of motion in the first place.
You just have to fiddle around with the equations that you know and see if you can get them into the form of the principle of least action. So now you too will call the new function the action, and pretty soon everybody will call it by that simple name. There is quite a difference in the characteristic of a law which says a certain integral from one place to another is a minimum—which tells something about the whole path—and of a law which says that as you go along, there is a force that makes it accelerate.
The second way tells how you inch your way along the path, and the other is a grand statement about the whole path.