Unraveling the Mystery of Work Done & Energy Transfer

[Frigus]

I was reading the chapter kinetic energy and work where I saw a derivation in which it was proved that work done=change in kinetic energy, so i understood from this derivation that work done is energy transfer by means of force but in this book kinetic energy is introduced earlier so as to find derivation of kinetic energy I start reading another book in which kinetic energy was derived from work and their it was written work done is in general force times displacement.
•Now my question is that which is the foundational thing of finding all other types of energy or is it something else and my another question is that

•why work done is (force)(displacement),I know we can derive it from other kind of energy and find it but it confuses me as "if work done is derived from another kind of energy then how do we find formula for another kind of energy(which we will find in future) and connects it all other kinds of energy if it is work done from which all other kinds of energy is derived then it makes sense to me as all things will be connected.
It would help me me if you try to explain it with historical context.

 

[davenn]

•why work done is (force)(displacement),I know we found it from other kind of energy but it confuses me as If work done is derived from another kind of energy then how do we find another kind of energy(which we will find in future) and connects it all other kinds of energy if it is work done from which all other kinds of energy is derived then it makes sense to me as all things will be connected but then how do we get (force) (displacement).

Am trying to make sense of that statement.
But I think you have a wrong understanding of what energy is
Energy ISN'T a thing, It is a property of a thing
Therefore "different types" of energy isn't an issue.
There's potential energy, kinetic, electrical energy, nuclear energy among others

 

[Frigus]

Am trying to make sense of that statement.
But I think you have a wrong understanding of what energy is
Energy ISN'T a thing, It is a property of a thing
Therefore "different types" of energy isn't an issue.
There's potential energy, kinetic, electrical energy, nuclear energy among others

In short I want to know that how do we find equations of different kinds of energy.

 

[davenn]

In short I want to know that how do we find equations of different kinds of energy.

OK , Google potential energy and kinetic energy and come back with what you discover

 

[Frigus]

OK , Google potential energy and kinetic energy and come back with what you discover

Firstly I searched kinetic energy,I readed introduction then I readed derivation and in most sites it was derived from work done so I thought I should search for work then there was written that work is defined as force times displacement and then I searched for potential energy which I got is -(work done). I also find that leibniz found an equation that living force $\alpha$ mv². But I didn't got my answer how do we find equation for a particular type of energy.i also read about energy from which I came to know that it is not easy to define it and it is an number which remains constant. So how can we find an equation for energy without even knowing what it is.

 

[anorlunda]

I still don't understand what you are asking about.

Consider electrical energy. Electric power is voltage times current, and electric energy is the time integral of power. We routinely transform electric energy into other forms of energy. That is what the power grid is all about.

A more fundamental unifying principle is the principle of least action, and Noether's theorem, which can be used to show why energy is conserved; but those are not B level topics.

How would that relate to your question?

 

[Frigus]

I still don't understand what you are asking about.

Consider electrical energy. Electric power is voltage times current, and electric energy is the time integral of power. We routinely transform electric energy into other forms of energy. That is what the power grid is all about.

A more fundamental unifying principle is the principle of least action, and Noether's theorem, which can be used to show why energy is conserved; but those are not B level topics.

How would that relate to your question?

Can you please tell me the part in which I am unable to explain my question well or should I retry to explain whole question in my mind.

 

[anorlunda]

Can you please tell me the part in which I am unable to explain my question well or should I retry to explain whole question in my mind.

Try to simplify by considering only two forms.

Mechanical power is $\frac{force*distance}{time}$
Electric power is $voltage*current$

Are you looking for an equation to unite those two?

 

[Dale]

Now my question is that which is the foundational thing of finding all other types of energy or is it something else and my another question is that

It is a little hard to understand what you are asking, but I am going to assume that this is your basic question. The idea of energy is confusing to you because it seems like a complicated mess of interrelated ideas and you don’t know which comes first. If that is not your underlying question then please simplify/clarify.

The answer is that it doesn’t matter. There may be a historical “which came first” but not a logical one.

Suppose you have five true statements and given any two of them you can derive the other three. One author might take statements 1 and 2 as the foundation and derive the others, while a different author might take statements 4 and 5 as the basic ones and derive the others. Both authors are justified in doing it their way.

Often in mechanics you start with a definition of work as force times distance. From that you derive kinetic energy and potential energy and then conservation of energy. Often in thermodynamics you start with kinetic energy and then you show that work is a transfer of energy and derive potential energy and show conservation.

All of the concepts are simultaneously true, but different authors will start with different ones first. There is nothing wrong with that. There is no physical reason we can select one as the foundation, only aesthetic reasons.

That said, the modern preference is to treat symmetries as the foundational principles. So in later courses you will learn about Noether’s theorem, which says that for every symmetry of the Lagrangian there is a corresponding conserved quantity. A time-symmetric Lagrangian leads to conservation of energy and then the rest follows. So in these earlier courses don’t worry too much about which concept comes first: it doesn’t matter, and there are other concepts like the Lagrangian symmetries that will be added later.

 

[Frigus]

It is a little hard to understand what you are asking, but I am going to assume that this is your basic question. The idea of energy is confusing to you because it seems like a complicated mess of interrelated ideas and you don’t know which comes first. If that is not your underlying question then please simplify/clarify.

Yes this was my question and I got answer from you but can you please also tell me why work done is force times displacement.
From one of the earlier thread I got an answer that scientist defines things after some intelligent guesses and after many hits and trials. But In this case energy is very vast concept so how they defined it with these methods. I feel their should be some idea behind it why it is defined as this.

 

[Dale]

can you please also tell me why work done is force times displacement

This comes from the work energy theorem which shows that the change in kinetic energy is equal to force times displacement. Since changes in energy are important we want to give the force times displacement a name. So someone decided to call it work and the name stuck.

https://phys.libretexts.org/Courses/University_of_California_Davis/UCD:_Physics_9A_–_Classical_Mechanics/3:_Work_and_Energy/3.1:_The_Work_-_Energy_Theorem

 

[Frigus]

This comes from the work energy theorem which shows that the change in kinetic energy is equal to force times displacement. Since changes in energy are important we want to give the force times displacement a name. So someone decided to call it work and the name stuck.

https://phys.libretexts.org/Courses/University_of_California_Davis/UCD:_Physics_9A_–_Classical_Mechanics/3:_Work_and_Energy/3.1:_The_Work_-_Energy_Theorem

Thanks.

 

[jtbell]

why work done is force times displacement.

I suspect that this definition of work originated in the study of simple machines such as levers, which "convert" a small force acting through a large distance to a large force acting through a small distance. See this post which I made several years ago:

https://www.physicsforums.com/threads/what-is-up-with-work.584812/#post-3804085

 

[Frigus]

I was reading about experiment of James Prescott Joule in which he proved that certain amount of work produce specific amount of heat.So from this result they concluded that energy is conserved but according to my reasoning energy is conserved if their is decrease in one energy then it should be increased in another. So it doesn't makes sense to me. Can you please tell me the point I am missing from this experiment.

 

[Herman Trivilino]

I was reading about experiment of James Prescott Joule in which he proved that certain amount of work produce specific amount of heat.

Yes, it's a unification of sorts, showing that work and heat are both transfers of energy.

So from this result they concluded that energy is conserved but according to my reasoning energy is conserved if their is decrease in one energy then it should be increased in another. So it doesn't makes sense to me. Can you please tell me the point I am missing from this experiment.

Conservation of energy applies to closed systems. If you add energy to a system you increase its internal energy. There are two ways of doing this, a mechanical transfer is work and a thermal transfer is heat. The idea is that if the internal energy of a system increases by some amount, then somewhere outside the system energy decreases by an equal amount.

You may find it interesting to note even as recently as the 1890's the notion of conservation of energy was in serious jeopardy. Researchers like the Curies were placing pieces of radium ore in insulated cups of water and noticing that the temperature rose. Eventually, of course, it was realized that a new form of energy had to be invented, called nuclear energy, to account for the increase.

This is really the answer to most of the questions you're asking in this thread. Researchers have been able to define different types of energy in such a way that energy is conserved. At first this may seem like some kind of a cheat, but in reality it's not. The fact is that Nature allows for these types of constructions to be made for some quantities but not for others. Energy is one that Nature seems to allow.

 

[Frigus]

Eventually, of course, it was realized that a new form of energy had to be invented

there was a question somewhere in my mind that how do we know that this specific phenomenon involves energy. This line gave me an eureka moment. Thanks a lot!
I don't why but it never came to my mind.
Can you please also share some thought process of scientists that they used to find new equation of energy or refer some article like that because historical context helps me a lot to understand concept which lacks in many study materials.

 

[Herman Trivilino]

Can you please also share some thought process of scientists that they used to find new equation of energy or refer some article like that because historical context helps me a lot to understand concept which lacks in many study materials.

The clues are in those textbooks. When you see a concept that interests you, do some research on the scientists who developed the concept. That is what scholarship is all about. One thing that fascinates me is that when I study a scientist's work I often run across loads of stuff that they got wrong. They're famous for the stuff they got right, so often that's all we see reported in the textbooks. Look deeper.

I know that visiting a library is becoming an outdated practice, but it really is a valuable experience for this kind of thing.

 

[jbriggs444]

In short I want to know that how do we find equations of different kinds of energy.

The empirical method.
https://www.feynmanlectures.caltech.edu/I_04.html

 

[Frigus]

The empirical method.
https://www.feynmanlectures.caltech.edu/I_04.html

Thanks.
Truly speaking it refined my concepts a lot.

 

[Frigus]

Conservation of energy applies to closed systems. If you add energy to a system you increase its internal energy. There are two ways of doing this, a mechanical transfer is work and a thermal transfer is heat. The idea is that if the internal energy of a system increases by some amount, then somewhere outside the system energy decreases by an equal amount.

I think I have not posted my question clearly,my question was that how did James Joule concluded that energy is conserved when specific amount of work produces specific amount of heat.

 

[Herman Trivilino]

I think I have not posted my question clearly,my question was that how did James Joule concluded that energy is conserved when specific amount of work produces specific amount of heat.

What he showed was that a specific amount of work $W$ caused the temperature to rise by the same amount as a specific amount of heat $Q$. Thus demonstrating that $W$ and $Q$ were equivalent, that is, that they are both transfers of energy. This is the so-called mechanical equivalent of heat.

Conservation of energy is a different issue.