Work Origins: Searching for the Proof Behind the Equation

[Nano-Passion]

Where did the concept and equation of work come from? It was introduced in Physics 1 with absolutely no background or proof. It was just: " we physicists define work to be force times distance." It seemed to pop out of thin air, and I gulped my pride/hate and accepted it in hopes that it would be explained later. Unfortunately, it resurfaced in physics II with electrical potential energy. And frankly, I'm going crazy not knowing the proof or how it came to be.

 

[gmax137]

Well, it is always dangerous to give examples that involve the human body (witness any of waynexk8's threads), but... suppose you are sitting in your tree-house and you need to pull the basket of food up from the ground through the trap door. How 'hard' it is depends on how high you have to raise the load (that's the distance) and how heavy the basket is (that's the force). So, raising a ten-pound basket ten feet is the same work as raising a five-pound basket 20 feet. That's all there is to it.

 

[jtbell]

In Physics 1, were you also introduced to kinetic energy and the work-energy theorem? And to at least a few forms of potential energy (gravitational and springs come to mind), and to the concept of conservation of energy that ties all of these together?

 

[OldEngr63]

To put it in mathematical form, the differential work is dw,

dw = f (s) ds

where

f(s) = force acting through the differential displacement ds

To get to the finite form, integrate to get

W₁₂ = ∫ _s1^s2 f(s) ds

 

[Nano-Passion]

Well, it is always dangerous to give examples that involve the human body (witness any of waynexk8's threads), but... suppose you are sitting in your tree-house and you need to pull the basket of food up from the ground through the trap door. How 'hard' it is depends on how high you have to raise the load (that's the distance) and how heavy the basket is (that's the force). So, raising a ten-pound basket ten feet is the same work as raising a five-pound basket 20 feet. That's all there is to it.

So physicists sat down and thought of it conceptually? I want to see how it actually came to life. Is there any proofs, any scientific papers or writings behind the concept when it first started?

In Physics 1, were you also introduced to kinetic energy and the work-energy theorem? And to at least a few forms of potential energy (gravitational and springs come to mind), and to the concept of conservation of energy that ties all of these together?

Yes, yes, and yes.

To put it in mathematical form, the differential work is dw,

dw = f (s) ds

where

f(s) = force acting through the differential displacement ds

To get to the finite form, integrate to get

W₁₂ = ∫ _s1^s2 f(s) ds

That didn't really answer my question. You just showed me the form of work where you take very very small pieces, the differential form if you will.

 

[OldEngr63]

You ask for proofs; proofs of what? I get the impression that underneath this all you are asking what is it used for. To understand that, you need to work more problems. After you work a number of problems where it turns out to be a short, handy way to get a result, then you will appreciate it very much. Until that time, not so much.

 

[AlephZero]

The history of the idea of "energy" in physics isn't straightforward. There were many scientists involved with it between about 1800 and 1850, mostly working on thermodyamics, and the relation between mechanical work and heat energy.

Arguably, it wasn't really sorted out until Emmy Noether's paper published in 1918. Without going into the details, this showed that there are some properties that are conserved (including energy) because of the basic structure of time and space. In simple terms, since the same physical process produces the same results independent of when and where it happens, it follows that there must be some mathematical properties that are unchanged by any physical process, and one of those properties is what was already called "energy".

But since "physics 101" doesn't usualy start with thermodynamics, and it certainly doesn't start with Noether's theorem () you probably just have to accept the simple definitions of energy and work without any deep explanation of "why".

 

[Dale]

It was just: " we physicists define work to be force times distance." ... I'm going crazy not knowing the proof or how it came to be.

There is no proof. Your physics 1 class is correct, it is just defined.

What typically happens is that people play around with some equations and they find out that they have to keep on writing equations with terms of f.d. After writing f.d the tenth time they get tired of it, so they just make the substitution w=f.d, call it work, and presto work is defined. No proof is needed, it is just a definition.

What would be proven would be something like the relationship between work and energy.

 

[jtbell]

So physicists sat down and thought of it [work] conceptually? I want to see how it actually came to life. Is there any proofs, any scientific papers or writings behind the concept when it first started?

That sort of thing just isn't taught in "straight" physics courses. You'll have to look for books and papers about the history of science. For example, there's Rene Dugas's "History of Mechanics" which I have in my office so I can't lay hands on it right now, but you can view pages on Google Books:

http://books.google.com/books/about/A_history_of_mechanics.html?id=jmKxffjQtasC

On page 128, he mentions Solomon of Caux, who published a book in the early 1600s. "It is to this author that we owe the term work in the sense that it is used now." From the book's title, it appears to have been about the design of various types of machines, so I speculate that the notion of work as force times distance originated with the use of levers and other simple machines, which "convert" a small force acting over a large distance to a large force acting over a small distance.

 

[Nano-Passion]

The history of the idea of "energy" in physics isn't straightforward. There were many scientists involved with it between about 1800 and 1850, mostly working on thermodyamics, and the relation between mechanical work and heat energy.

Arguably, it wasn't really sorted out until Emmy Noether's paper published in 1918. Without going into the details, this showed that there are some properties that are conserved (including energy) because of the basic structure of time and space. In simple terms, since the same physical process produces the same results independent of when and where it happens, it follows that there must be some mathematical properties that are unchanged by any physical process, and one of those properties is what was already called "energy".

But since "physics 101" doesn't usualy start with thermodynamics, and it certainly doesn't start with Noether's theorem () you probably just have to accept the simple definitions of energy and work without any deep explanation of "why".

Your post had such big-picture perspective that I wrote it down in my physics notebook. I always appreciate the insight, thanks!

You ask for proofs; proofs of what? I get the impression that underneath this all you are asking what is it used for. To understand that, you need to work more problems. After you work a number of problems where it turns out to be a short, handy way to get a result, then you will appreciate it very much. Until that time, not so much.

I've did countless problems including work and work-energy theorem, solving them is one of the skills I perfected. But it really just left me in a bigger puzzlement of where it came from. I guess I'm thinking too theoretically, perhaps because I'm comparing it to other things that had a deep history and included a proof (f=ma, etc.)

There is no proof. Your physics 1 class is correct, it is just defined.

What typically happens is that people play around with some equations and they find out that they have to keep on writing equations with terms of f.d. After writing f.d the tenth time they get tired of it, so they just make the substitution w=f.d, call it work, and presto work is defined. No proof is needed, it is just a definition.

What would be proven would be something like the relationship between work and energy.

Really??

Do you have an idea of what factors were subject to the habitual appearance of f*d?

That sort of thing just isn't taught in "straight" physics courses. You'll have to look for books and papers about the history of science. For example, there's Rene Dugas's "History of Mechanics" which I have in my office so I can't lay hands on it right now, but you can view pages on Google Books:

http://books.google.com/books/about/A_history_of_mechanics.html?id=jmKxffjQtasC

On page 128, he mentions Solomon of Caux, who published a book in the early 1600s. "It is to this author that we owe the term work in the sense that it is used now." From the book's title, it appears to have been about the design of various types of machines, so I speculate that the notion of work as force times distance originated with the use of levers and other simple machines, which "convert" a small force acting over a large distance to a large force acting over a small distance.

Interesting. Thanks for the link, I'll read it in a bit.

 

[MrRobotoToo]

Where did the concept and equation of work come from? It was introduced in Physics 1 with absolutely no background or proof. It was just: " we physicists define work to be force times distance." It seemed to pop out of thin air, and I gulped my pride/hate and accepted it in hopes that it would be explained later. Unfortunately, it resurfaced in physics II with electrical potential energy. And frankly, I'm going crazy not knowing the proof or how it came to be.

The product of force and distance has always been an important quantity in the design of machines. It has been known since ancient times that in any machine there exists a trade-off between distance and force. Specifically, the product of the effort and the distance through which it is exerted is always greater than or equal to the product of the load and the distance through which it moves. This is just a consequence of the conservation of energy, although it wasn't recognized as a universal law of nature until relatively recently. Archimedes' law of the lever, for example, is just a special case of the more general principle. It is for this reason that work is such an important concept in physics.

 

[kweba]

So physicists sat down and thought of it conceptually? I want to see how it actually came to life. Is there any proofs, any scientific papers or writings behind the concept when it first started?

I'm sorry not sure what exactly do you mean by "proofs" but if I'm not mistaken, Physics and physicists do not use proofs to develop and "prove" theories. Proofs (along with deductive reasoning) are only used by mathematicians to make mathematical theorems. Physics, like any other natural science, only confirm theories and physical equations by (real-world) experiments. So yes, theoretical physicists just commonly thought of these ideas conceptually and then be later tested with experiments. (Although sometimes observations from experiments comes first before a theory that describes the phenomenon is developed, i.e the photoelectric effect.)

A great example would be Newton's Law of Gravitation. Isaac Newton himself had developed a new kind of math called Calculus, to mathematically describe his ideas. But even with his great use of Calculus, his Universal law of gravitation still had problems in experiments. His math used to describe Mercury's orbit did not correspond well with reality (experimental observations). This was later on fixed by Einstein's general relativity, which would be another example. GR was ultimately proved by Sir Eddington's photograph of a solar eclipse that showed that light around the sun was "bent". (But despite of even with Einstein's elegant/complex mathematical description of GR, and Eddington's experimental evidence, the Science community at the time still had not fully accepted his theory.)

The point is that in Physics, physical theories along with its maths, are only "proved" and accepted if it matches with physical reality and experiments, not with the proofs of math.

Here are some links and other threads regarding Proofs in Math and Physics:

http://en.wikipedia.org/wiki/Mathematical_proof

https://www.physicsforums.com/showthread.php?t=373388

https://www.physicsforums.com/showthread.php?t=149605

Anyways, sorry if I kind of went out of the OP's main question. :)

 

[aim1732]

"It is important to realize that in physics today, we have no knowledge of what energy is.We do not have a picture that energy comes in little blobs of a definite amount.Is is not that way.However, there are formulas for calculating some numerical quantity, and when we add it all together it gives "28"-always the same number.It is an abstract thing in that it does not tell us the mechanisms or reasons for the various formulas."
(Reference:Feynman Lectures,Vol.I,Conservation of Energy)

If energy is only a number,why should it be difficult to see that work and heat(with their differences) are mere mathematical expressions with no mechanisms or reasons?(after all the first law says that energy moves about as work and heat only so the three are equivalent in this respect of being abstract)

 

[OldEngr63]

Wow! Those poor physicists! Engineers have had a satisfactory understanding of what energy is (the ability to do work) for ages, but the physicist seem to be regressing!

In the search for purity of understanding, you risk losing all understanding, or so it seems. Think I'll stick with my simple understanding.

 

[kweba]

...had a satisfactory understanding of what energy is (the ability to do work)...

Exactly. The unit for the scalar quantity/magnitude of Work is a Joule. Just as it is for Energy. So it's safe to say that Work is Energy. Right?

 

[inelwk22]

Well if you are looking for experimental "evidence" look at books for Joule's old machines to "confirm" conservation of energy (oh sorry I meant heat, just as joule called by then).

Maybe we should review some of them.

P.S. please do not scary when you can't find machines to confirm energies like electromagnetic, solar, wind, magnetic, etc, all together. Physicists surely are building them in the backstage to convince you! hehehe

 

[aim1732]

Wow! Those poor physicists! Engineers have had a satisfactory understanding of what energy is (the ability to do work) for ages, but the physicist seem to be regressing!

Disagree.I ain't a physicist yet but maybe it is this search for purity that has kept us from losing track.(*Smugly*)Don't you engineers depend on us for everything?
I am just joking..

Now for the understanding part..the point is we do not need to understand energy anymore than that Feynman says..it is just a number that is magically conserved.All laws are in a way magical.I do not feel any sense in trying to find a mechanism for them.I can go on to quote Feynman again but I am lazy so just look up the chapter on Gravitation in Vol.I(Feynman Lectures of course) and see how he again talks of no known mechanism on how gravitation works(I do not know about GTR so let's stick to classical Newtonian gravitation).He gives an example of a suggested mechanism and then goes on to disprove it and then says that a lot have been proposed but none have accounted for everything without predicting something that does not happen.

So my simple answer is there is no need for any mechanism so far as energy or work is concerned.It is much better to live with the incomplete than think of something wrong or twisted.

Exactly. The unit for the scalar quantity/magnitude of Work is a Joule. Just as it is for Energy. So it's safe to say that Work is Energy. Right?

Well,not quite.A lot of quantities have same unit but vastly different meanings.I can give you a lot of differences between heat and work and energy..just to spur you--work is a path function and energy a state function.That means you have X JOULE of energy but can never have X JOULE of work.

 

[Lsos]

Perhaps OP's problem is that he has an "everyday" understanding of what work is, which doesn't necessarily seem to coincide with "energy=force x distance".

For example, holding up a heavy book seems to require energy, whereas according to strict definition it appears that it would require none.