I am aware that there appear to be many similar questions on this site, but that is just because of the misleading title. I could not think of a better title that illustrates how different is this question, so if you could fix it - thank you very much.
My knowledge of physics comes down to kinematics and Newton's laws. I would like to get answers which do not deviate from this basic knowledge.
I am currently questing for exact definitions of work and energy, and what is behind these definitions . I searched in physics sites, and here in Physics in particular, but I have not found a satisfactory answer. Here is a list of the main resources I have reviewed:
Over the net:
Here on Physics:
To preface my question, I will explain the process I went through until I got my current understanding, which I want to sharpen. First, here are the main definitions of work and energy I found around the web:
Energy Is a property, or state of objects representing the ability to do work. It can be transferred to other objects, and it can be reflected in many forms, which are convertible.
Work is a transfer of energy from one object to another by applying force, and it is equal to $\vec{F_{x}}\cdot \vec{x}$ for a constant force, or to $\int_{x_{1}}^{x_{2}}\vec{F_{x}}\enspace d\vec{x}$ for a changing force.
These definitions seem circular because work is a transfer of energy, and energy is the ability to do work. To solve this problem I adopted NeuroFuzzy's approach:
Sometimes when you're stuck on things, it's helpful to look at the mathematics of what's being asserted.
A basic mathematical analysis of work definition $W=\vec{F_{x}}\cdot \vec{x}$ raises the following two points:
- When multiplying the force or the displacement by $k$, the work is also multiplied by $k$. For example, if I apply a force of $2\vec{F}$ on an object, the work will be twice as big as if I applied a force of $\vec{F}$. Also, if a given force on an object led to $\frac{1}{2}\vec{x}$ displacement, the work it did is twice as smaller as in a case it led to $\vec{x}$ displacement.
A force does a positive work when:
- The object displaces.
- The force on the object is in the direction of the displacement.
A force does negative work when:- The object displaces.
- The force on the object is in the opposite direction of the displacement.
A force does no work when:- The object does not displace.
- No force is applied to the displacement axis.
- Both of these conditions are met.
In other words, when I apply a force on an object in certain circumstances (environment, other forces, time period, etc.) and the object's displacement is different than the displacement in the same conditions, only without the force, I could say that the force has influenced the displacement. It can have a "positive" influence (if the displacement was larger than the displacement under the same conditions without applying the force) or have a "negative" influence (if the displacement was smaller than the displacement under the same conditions, without applying the force). If I applied a force, and the displacement was equal to the displacement under the same conditions, without applying the force, then the force did not influence the displacement.
My intuitive conclusion of this analysis is that work is the degree of influence a force has on an object's displacement. If we accept my definition, and we combine it with the definitions above, we could describe work and energy as follows:
Energy Is a property, or state of objects representing the ability to apply a force that will influence an object's displacement. It can be transferred to other objects, and it can be reflected in many forms, which are convertible.
Work is the degree of influence a force has on an object's displacement. When a force does work, besides the fact that it moves the object, it also transfers to the object the ability to influence other objects' displacement by applying force.
I have a few questions about these definitions I cannot find an answer. I do not know whether the definitions are correct and the questions have answers - and then I will be grateful for answers, or the definitions are incorrect in the first place - and then I will be grateful if you could correct my definitions.
Here are the questions:
- Does the definition of energy mean that all energy is potential energy? Because if energy describes the capability of an object to do work, doesn't it means that we are talking about the potential of the object to do work?
- I defined energy as a property, or state of an object representing the amount of work it can do. But how could we quantify it? If, for example, a man stores within itself $100J$ of energy, does that mean he is able to apply a force of $10^{100}N$ over $10^{-98}m$? Surely a human being is not capable of applying so much force, so why we still say he stores $100J$?
- How potential energy is reflected while being potential? Can we see a difference between a person that stores $x$ energy and a person consuming that $x$ energy? An answer I heard a lot is that the mass of the person is actually its potential energy, and therefore doing physical activities, for example, is consuming energy, and reducing the mass. But if it is correct, wouldn't we measure energy in $kg$ or mass in $Joule$?
- Although my definitions do explain the inner nature of work and energy, I could still mathematically describe this nature in an infinite number of ways. For example, if I describe work as $2\vec{F}_{x}\cdot \vec{x}$, I would still get to the conclusion that work is the influence a force has on an object's displacement. So why is that the equation?
- How is consuming energy in other forms than motion work? How are heat energy, or sound waves, for example, work?
Thanks.
Answer
Don't be surprised that physics has a lot of definitions that are circular. Ultimately, we are just describing the universe.
Work and energy have been defined in a certain way in newtonian physics to explain a kinematic model of reality. This is a model, not reality - you will find no such thing in reality. However, in many scenarios, it is close enough to reality to be useful.
For example, let's say that a human has a 10% efficiency at converting food to mechanical work. So if you spend 1000 kJ of food energy to press against a wall, are you doing 1000 kJ of work, or 100 kJ of work, or 0 kJ of work?
In strict mechanical sense, you did no work whatsoever, and all of the energy you used was wasted as heat. If you instead used this energy to push a locomotive, you would have wasted "only" 900 kJ of the energy as heat, with 100 kJ being work. But the locomotive has its own friction, and it wil stop eventually, wasting all the energy as heat again. And overall, you did expend all those 1000 kJ of food energy that is never coming back.
All of those are simplifications. Kinematics is concerned with things that move. Using models is all about understanding the limits of such models. You're trying to explain thermodynamics using kinematics - this is actually quite possible (e.g. the kinematic theory of heat), but not quite as simple as you make it. Let's look at the fire example. You say there is no displacement, and therefore no work. Now, within the usual context kinematics is used, you are entirely correct - all of that energy is wasted, and you should have used it to drive a piston or something to change it to useful work.
Make a clear note here: what is useful work is entirely a human concept - it's all 100% relevant only within the context of your goals; if you used that "waste" to heat your house, it would have been useful work. It so happens that if you look closer, you'll see that the heat from the fire does produce movement. Individual molecules forming the wood wiggle more and more, some of them breaking free and reforming, and rising with the hot air away from the fire, while also drawing in colder air from the surroundings to feed the fire further. There's a lot of displacement - individual molecules accelerate and slow down, move and bounce around... But make no mistake, the fact that kinematics can satisfactorily explain a huge part of thermodynamics is just a bonus - nobody claimed that kinematics explains 100% of the universe. It was a model to explain how macroscopic objects move in everyday scenarios. It didn't try to explain fire.
For your specific questions, you really shouldn't ask multiple questions in one question. It gets very messy. But to address them quickly:
- There is no potential energy in the kinematic model. The concept is defined for bound states, which do not really exist as a concept in kinematics. In other models, you might see that there's a difference between, say, potential energy and kinetic energy - no such thing really exists in reality. You need to understand the context of the model.
- In a perfectly kinematic world, this is 100% correct. However, as noted before, kinematics isn't a 100% accurate description of reality, and there are other considerations that apply, such as the fact that humans have limited work rate, limited ability to apply force, and the materials we are built of aren't infinitely tough, perfectly inflexible and don't exist in perfect isolation from all the outside (and inside) effects. In real world applications of models, these differences are usually eliminated through understanding the limits of given models, and using various "fixup" constants - and if that isn't good enough, picking (or making) a better model.
- You're mixing up many different models at different levels of abstraction and of different scope so confusion is inevitable. Within the simplified context of kinetics, there is no concept of "potential energy". You simply have energy that can be used to do work, and that's it; it doesn't care about how that energy is used to do work, about the efficiency of doing so etc. In another context, it might be very useful to think of energy and mass as being the same thing - and in yet another, they might be considered interchangeable at a certain ratio, or perhaps in a certain direction, or at a certain rate. It's all about what you're trying to do.
- How is that equation useful? That's the only thing that matters about both definitions and equations. I can define a million things that are completely useless if I wanted to - but what's the point?
- Within the original context, those aren't considered at all. Within a more realistic context, both heat and sound are also kinematic.
The reason you have so much trouble finding the answer to your questions on physics sites and forums is that the question doesn't make much sense in physics. It's more about the philosophy of science, and the idea of building models of the world that try to describe reality to an approximation that happens to be useful to us. You think that those words have an inherent meaning that is applicable in any possible context - this simply isn't true. From the very inception of the idea of physics, people have known that it isn't (and never will be) an accurate representation of reality; and we've known for a very long time that, for example, different observers may disagree on the energy of one object. You just need to understand where a given model is useful, and pick the right model for the job. Don't try to drive a screw with a garden rake.
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