Why work is force times distance?

[fresh_42]

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[PeterDonis]

I am not sure I agree that to a physicist there is no work done when you strain against an immovable object.

There is no work done on the object, which was the point under discussion. It is true that your muscles are doing work if you include the internal motions of parts of your body in the model.

 

[Monsterboy]

After all, as my version of the question goes, if I am a first-grader standing near the top of a hill, pulling on my red wagon, where my little sister happens to be sitting, just enough to keep it from moving so it won't run downhill, because I'm too weak to pull it any farther uphill, then I am doing "work" as we normally understand it. My muscles certainly ache after holding on to that wagon until my dad comes along and takes over. I am applying a force to the wagon, I am expending energy to keep it from moving, my energy is running low, yet physics says I am only doing "work" when I pull the wagon up the hill. Why?

This has sparked of an interesting conversation although some might find it silly. It is difficult to explain this to a six year old without proper context.
Let me give an alternative solution. You are doing work by pulling the wagon but you are not doing work on the wagon, work is being done inside your own body by expending the internal energy present in your body to breathe air using your lungs and pump blood through your blood vessels to transport oxygen and glucose to your muscles. Now, that is considered as work because you are pumping the fluid throughout your body i.e flow work.

It is just like holding down the accelerator and applying the breaks fully at the same time, you are not any work but you are wasting the fuel i.e energy. But inside the car the crank shaft keeps rotating and that is rotational work being done inside the car body without the car as a whole doing any work.

You might argue that you are doing flow work in your body even while sitting still in your room, that is also correct, we are constantly consuming our internal energy in our body to run our internal organs and the body as a whole, that requires our blood to do flow work, but you will be doing less work in this case because your muscles aren't consuming as much energy.

 

[FactChecker]

Whatever the definition is, it must not say that a table holding up a book for a month is doing "work" all that time. If a spring is squeezed between two fixed surfaces, we must not say that both the spring and the fixed surface are doing (opposing??) "work". With a definition like that, "work" would be a useless concept.

 

[PeterDonis]

You are doing work by pulling the wagon but you are not doing work on the wagon, work is being done inside your own body

This is fine if your model includes all the internal motions of your own body, presumably because you are interested in them for some reason. But if all you're interested in is the motion (or lack thereof) of the wagon, talking about "work being done inside your own body" just adds unnecessary detail. That's why physicists will typically prefer to just say that if the wagon is not moving, no work is being done, and leave it at that.

 

[Monsterboy]

This is fine if your model includes all the internal motions of your own body, presumably because you are interested in them for some reason. But if all you're interested in is the motion (or lack thereof) of the wagon, talking about "work being done inside your own body" just adds unnecessary detail. That's why physicists will typically prefer to just say that if the wagon is not moving, no work is being done, and leave it at that.

Agreed, I was just addressing the question of "If I am not doing any work, why am I feeling tired ?" in the context of an overthinking 1st grader who asks too many questions and my answer is "you are feeling tired because you spending your internal energy to do internal work to apply a force on the wagon, but the force you are applying on the wagon is balanced by the force of gravity."

 

[Grinkle]

"you are feeling tired because you spending your internal energy to do internal work to apply a force on the wagon, but the force you are applying on the wagon is balanced by the force of gravity."

The first grader promptly kicks you in the shin. ;-)

 

[Aufbauwerk 2045]

Yes, It is often the case that science uses common words in different or more restrictive or differently defined ways than regular English does. Get used to it.

If it is "often the case," can you provide many other examples from classical physics at least? Modern physics is another story. But classical physics deals with our familiar macroscopic world.

I think the attitude of "get used to it" may work in some subjects, but to me it seems to be dismissing the OP's question in a way that is not appropriate for a science forum.

 

[russ_watters]

If it is "often the case," can you provide many other examples from classical physics at least?

Speed, velocity, weight, mass, elasticity. Basically all of the concepts in classical physics that are used colloquially are misused or used imprecisely.

Heck, in Pennsylvania, the answer to the question: "How far is it to Wawa?" is "5 minutes!"

I think the attitude of "get used to it" may work in some subjects, but to me it seems to be dismissing the OP's question in a way that is not appropriate for a science forum.

It's not [inappropriate]. "Get used to it" is the first barrier to entry to any serious subject. It means: this subject has a specific vocabulary that you must understand and use properly in order to even communicate with people about it.

 

[Aufbauwerk 2045]

There is no work done on the object, which was the point under discussion. It is true that your muscles are doing work if you include the internal motions of parts of your body in the model.

The point under discussion is the OP's question.

He begins as follows.

"So, here we are trying our best to describe physical universe. We start from displacement, time, velocity and then force, but I don't get why would we define a physical quantity called 'work' as force times distance?"

This is a legitimate question. It is clear, from at least one previous thread on this forum, as well as from numerous discussions on this point on the internet, that it's not a rare question.

"Is it just some quantity we defined in physics because it turns out to be useful and it doesn't have much of reference with idea of 'work' in usual meaning itself?"

This is a two-part question. Do we define 'work' the way we do because it is useful? The answer is 'yes.' Does this usage not have much reference to the idea of 'work' in its usual meaning? It certainly has some reference, but our common understanding of the word does not match the way physics uses it.

This raises the question why do we use this word "work," which is so familiar to us, in a way that goes against our common idea of "work." It is obvious from the many discussions one finds on this issue, including an old thread on this forum, that this use of the word "work" in physics is problematic. It may not be the best terminology. This is not to say we can change it at this point. A curious person would want to know when was the word first used the way we use it. This is a history of science question. Some people may be curious about the history of one of the most basic terms we use in physics.

It is not a good answer to simply dismiss the question by saying that's just the way it is, so "get over it." That is not an attitude that respects someone's desire to understand why a certain word is used. "Get over it" is not the attitude that promotes curiosity and digging more deeply into why things are the way they are.

 

[Aufbauwerk 2045]

Of course the practical engineer and the compulsive questioners known as scientists may approach this whole subject in different ways. If I belonged to an engineering forum, I would not even bring the subject up. I would not say "get used to it" because it seems a bit rude. But I would not deviate from the program. I would just refer to the equations and say the important thing from an engineering standpoint is to be able to use the equations in the real world. I've studied and worked on problems from both viewpoints, so I do understand the difference. This just happens to be a physics forum.

 

[FactChecker]

If the OP thinks hard about the common definition that he is used to, he will see a huge number of problems. He would have to distinguish between a person holding a weight overhead (difficult), versus holding it in a horizontally extended arm (very difficult), versus holding it with his arm down (easy). He would also have to distinguish between a weight being held up by a person (doing work) versus by a desk (no work). There are endless problems with that definition. I think it is untenable.
And the OP would have to develop that theory enough to compete with the standard physics definition, which is intimately related to energy and is useful throughout physics.
As has been said, this question has been discussed before many times. We have accepted the use of the word "work" as it is currently defined in physics.

 

[PeterDonis]

It is obvious from the many discussions one finds on this issue, including an old thread on this forum, that this use of the word "work" in physics is problematic.

No, what is obvious is that, as you say, the physicist's usage of the word "work" is different from the ordinary language usage of the word "work". But that's true of pretty much every substantive term used in physics. And it's that way for a very good reason. Physicists don't use words with technical meanings different from their ordinary ones just to be difficult. They do it because the ordinary language meanings of words are not suitable for describing physics. A key part of learning physics is unlearning intuitions, and many of those intuitions come from ordinary language and the meanings it gives to words.

It may not be the best terminology.

But here's the problem: there is no best terminology in the sense you are using the term. There is no way to either pick words whose ordinary language meanings will work for describing physics, or find words that are rare enough in ordinary usage that giving them technical meanings in physics won't impact the usage in describing physics of any common ordinary words. That is part of what I was referring above when I said that the ordinary language meanings of words are not suitable for describing physics.

It is not a good answer to simply dismiss the question by saying that's just the way it is, so "get over it."

That's not what people are saying. What people are saying is what I said above.

 

[Aufbauwerk 2045]

A question for the elementary school and middle school science teachers out there. Are the topics of work and conservation of energy taught in your school? Is it part of Common Core? If they are taught, how are they taught? What do you think about the Feynman essay I linked to about math and science textbooks? I like his point about not using certain standard physics terms to explain things to kids, because in fact it does not really explain anything.

 

[PeterDonis]

What do you think about the Feynman essay I linked to about math and science textbooks?

Since that link was actually in a post that got deleted, I am re-posting it here:

https://fs.blog/2016/07/richard-feynman-teaching-math-kids/

 

[Aufbauwerk 2045]

I found at least part of the answer I was looking for. I asked a few posts ago whether our definition of work originated with the study of machines. People a few centuries ago obviously did not come up with the definition based on Noether. They were looking for something useful in their own time based on the physics they knew.

It seems that Coriolis is responsible. "Calculation of the Effect of Machines, or Considerations on the Use of Engines and their Evaluation. (1829)"

Since I'm so interested in how ideas develop, I'll add that to my reading list. The engineers are free to ignore it and get on with their work!

:)

 

[PeterDonis]

I like his point about not using certain standard physics terms to explain things to kids, because in fact it does not really explain anything.

That's not the point he was making. The point he was making was that if you use a term, whether it's a "standard physics term" or not, you should link the term to something the child can observe and understand. In the example of the toy, saying "energy makes it move" tells the child nothing because he can't observe energy making it move and can't understand how "energy makes it move" links to anything he can observe. That's not a problem with the word "energy"; it's a problem with the general method of teaching that Feynman is describing, and would be the same even if technical physics terms were carefully avoided.

To illustrate a different way, suppose that the examples of the wind-up toy dog, the real dog, and the motorcycle were presented as follows:

"If we look inside the wind-up toy dog, we see that winding it up coils up a spring, and then when we release the dog the spring uncoils and makes the toy dog move."

"We can't take the real dog apart, but if we could, we would see that there are muscles inside the dog that are something like the spring in the toy dog: they pull on the dog's bones and move his legs and make him move. And for the dog's muscles, and all the other things inside him like his heart and his lungs and his brain, to work, the dog has to eat and has to breathe; in other words, food and air has to be put into the dog from the outside. That's something like the winding up of the toy dog."

"If we take the motorcycle engine apart, we see pistons inside that get pushed by tiny explosions inside the cylinders, and turn a shaft that turns a chain that turns the wheels and make the motorcycle move, just like the coiled spring uncoils and makes the toy dog move or the real dog's muscles pull on his bones and make him move. And for all that to work, the motorcycle has to have gas put into its gas tank from outside. That's something like the real dog eating and breathing and the toy dog being wound up."

"So in all three of these cases, we see that, in order for the thing to move, something from outside has to be put in and stored inside the thing: the spring coiled up in the toy dog, the food and air inside the real dog, and the gas in the motorcycle's gas tank. The actual things that are stored look very different, but they all have something in common: making things move. Scientists have a word for this common property of making things move: energy. So the scientists would say that the coiled up spring, the food and air inside the dog, and the gas in the motorcycle's gas tank, all contain energy."

Here I've still used the physics word--energy--but presented at the end, as a name for something already illustrated by the examples.

 

[russ_watters]

T
This raises the question why do we use this word "work," which is so familiar to us, in a way that goes against our common idea of "work." It is obvious from the many discussions one finds on this issue, including an old thread on this forum, that this use of the word "work" in physics is problematic. It may not be the best terminology. This is not to say we can change it at this point. A curious person would want to know when was the word first used the way we use it. This is a history of science question. Some people may be curious about the history of one of the most basic terms we use in physics.

It is not a good answer to simply dismiss the question by saying that's just the way it is, so "get over it." That is not an attitude that respects someone's desire to understand why a certain word is used. "Get over it" is not the attitude that promotes curiosity and digging more deeply into why things are the way they are.

This is just so wrong. It's like going to a baseball game and instead of learning how the game works, starting an argument with the umpire about his usage of the word "ball". The audacity one has to have to tell him he's using it wrong!

 

[russ_watters]

But here's the problem: there is no best terminology in the sense you are using the term. There is no way to either pick words whose ordinary language meanings will work for describing physics, or find words that are rare enough in ordinary usage that giving them technical meanings in physics won't impact the usage in describing physics of any common ordinary words.

Well, as @jbriggs444 said: We could call it "grobnitz". That's only half a joke. It means that words are just a jumble of letters that we assign a meaning to, by convention. So why didn't/don't physicists invent new words instead of co-opting existing words? Because there's no harm in using a word that's almost used the way they need it and modifying it just slightly to make it what they need it to be. And it's so much easier to remember an already existing word.

This is a feature, not a bug!

 

[PeterDonis]

This is a feature, not a bug!

I agree. I was just pointing out that, whether you take this obvious route (of co-opting existing words for all the good reasons you give) or invent new words like "grobnitz", you're never going to get to the point @Aufbauwerk 2045 seems to want to get to, where you can somehow just use ordinary language and still have an accurate description of the physics.

 

[FactChecker]

If the unmodified original language was a perfect fit with physics, the principles of physics would have been discovered by primitive mankind the first time a true sentence was formed.

 

[Vanadium 50]

 

[Dale]

It is not a good answer to simply dismiss the question by saying that's just the way it is, so "get over it." That is not an attitude that respects someone's desire to understand why a certain word is used. "Get over it" is not the attitude that promotes curiosity and digging more deeply into why things are the way they are.

Nobody else in this thread besides you ever said "Get over it". @phinds said "get used to it", meaning that giving ordinary words a specific technical meaning is a very common practice in all fields of science. So any student must get used to the fact that this will happen frequently and learn that in science you need to use the corresponding scientific definition and not the ordinary definition. His comment was instructive (and brief), not dismissive.

Since we are now digressing and having an argument about non-existent slights, it is past time to close this thread.