Want to understand ke formula without having to accept any assumptions

[jtbell]

I don't know enough about the history of classical mechanics to say which experiments historically came first. There is a recent thread in our Science & Math Textbooks forum about books that deal with the history of physics. I think at least one of the books mentioned focuses on the development of classical mechanics.

However, I can describe such an experiment using equipment commonly available in a first-year undergraduate physics laboratory.

Set up a level, frictionless air track. On it, place a glider of mass m. Tie a string to the glider, drape the string over a pulley at one end of the track, and hang another mass on it. As the hanging mass falls, it exerts a constant force on the glider via the string, producing a constant acceleration.

Place two photogates along the air track, separated by a distance Δx. Connect them to a timer, configured to display the speeds of the glider through each photogate. Call these two speeds v₁ and v₂.

Set up another photogate at the pulley, and configure it to display the linear acceleration, a, of the rim of the pulley.

[Instructors and students who have done similar labs may recognize the Pasco smart timer and accessory pulley here.]

Let the hanging mass fall, and measure a, v₁ and v₂.

Calculate the force on the glider from F = ma. Calculate the work done on the glider from W = FΔx. Calculate the kinetic energies at each photogate from K₁ = mv₁²/2 and K₂ = mv₂²/2.

Verify that W = K₂ - K₁, to some degree of precision.

 

[mattt]

I am continuously surprised by the inability to understand and answer a very simple question.

How would you answer this question "What is the experimental proof that "the natural number 2" is just "the natural number 2" and not something else?

I just want to examine the experiment that scientists used to decide that work is force x distance

That shows an important problem in your understanding. There is nothing "experimental" about the following:

People (mathematicians, physicists) realize that the mathematical object

$$\int_{t_0}^{t_1}\vec{F}(t)\cdot\vec{v}(t)dt$$

is very useful, so they put a name to it, "Work", just like my mother thought it would be useful to put a name on me, "Matt".

That mathematical object is what it is, no matter how we call it, just like I am what I am, no matter if they call me "Matt" and or any other name.

And it happens that this useful mathematical object

$$\int_{t_0}^{t_1}\vec{F}(t)\cdot\vec{v}(t)dt$$

interpreted physically has dimension of F.L = M.L^2/T^2.


By the way, there are obviously many other mathematical objects that we consider useful, for example

$$\int_{t_0}^{t_1}\vec{F}(t)dt$$

we consider very useful, and so we put a name on it, "Impulse", and this mathematical object happens to have dimension F.T = M L/T.

I know that every website and book on intro physics says it is true but they do not show why it is scientifically true.

If you mean the mathematical theorem "work-energy theorem", then it is not exactly "scientifically true", but MATHEMATICALLY true, just like "a + b = b + a in the natural numbers" is not "scientifically true" but MATHEMATICALLY true.

Why is work defined as force x distance?

Ahhhh, so you are asking "Why we use the word "work" to refer to the mathematical object

$$\int_{t_0}^{t_1}\vec{F}(t)\cdot\vec{v}(t)dt$$

?"

Is that what you ask? Why did my mother use the word "Matt" to refer to me?

I am getting the feeling that everyone who has studied physics just accepts what they are told and are very good at explaining everything except why it is true experimentally. I have been told that I'm a strange person. I guess Galileo was strange too because he asked questions like mine. I'll bet some of the other notable physicists of the past also asked "strange" questions. Does anyone know the answer to mine?

Galileo never asked the kind of question you are asking. He understood perfectly well how physics should work and we are following that model (mathematical structures + interpretation of some of its mathematical objects by means of experimental setup and measure procedures).

 

[speedingelf]

No one has answered my question and if anyone thinks differently, they may not be as bright or educated as they think.

If no experiment exists that proves mechanical energy is defined by force x distance, then physics is based, at least partially, on faith. A subject that requires faith to some degree is a religion. I thought all modern sciences, and especially physics, are based on the scientific method where a scientist notices certain patterns or other things, formulates a hypothesis, and tests his ideas by experimentally checking any predictions that the hypothesis might have.


If you personally don't know the answer to my question, fine. Not everyone is as curious as I am about physics and how the universe functions. If I am going to study Relativity and Quantum Mechanics in the future. I want to understand, not believe, things.

Somebody has to know why physics defines work as force x distance. I suppose I could continue to surf the internet till I find that person. Maybe, I'll have to go to various libraries dig through books that are at least 100 years old to find clues as to where the work energy theorem came from. It might take a while but I will find out why it became an accepted theory.

 

[mattt]

You should read the previous posts, if you really want to understand something, seriously. It is not that difficult, but...you have to try to read it.EDIT: Newtonian Mechanics is just amazingly simple and beautiful, you will love it when you understand it well, you'll be able to appreciate it.

One day (I hope) you'll remember this day and think "Wow, now I see why it all makes perfect sense" and you'll feel great :-).

Then you will want to know more, you'll learn (I hope) Lagrangian Mechanics, Hamiltonian Mechanics and you will be able to appreciate such books as:

Classical Dynamics: A Contemporary Approach (Jose and Saletan)
Mathematical Methods of Classical Mechanics (Arnold)

and of course:

Foundations of Mechanics (Abraham and Marsden)And then you will want to know more, you will study ( I hope ) quantum physics, quantum field theory,...and you will be forever trapped in this beautiful and strange conceptual mathematical-physical universe...

 

[russ_watters]

We can help you, but only if you want help. Please take a step back, breathe, maybe sleep on it, then come back and actually read, consider and respond to the answers you were given.

Also, because you are young, I'm willing to go private and give you some help via PM. At this point, you may have gotten overloaded with information and need it in smaller bites to process it. PM me if interested.

 

[speedingelf]

I have tried and tried to understand why work is force x distance. The closest anyone comes is the experiment with air track. That experiment, when you boil it down, is like dropping a object of known mass. The force acting on it is F=ma which in this case a = g (acceleration due to gravity) and that gives F=mg. When you multiply the distance the object falls due to the effect of gravity by it's mass you wind up with the work that is done on it. You then take the velocity of the object as it reaches the ground and plug that value along with the mass of the object into the kinetic energy formula. When you compare the work done with the ke formula, they are the same. That's great but if you do the same experiment, in exactly the same way but measure different things you get an equally impressive result. In other words, measure how long the object takes to hit the ground and multiply that by the force acting on it and you wind up with a value for force x time. You then take the speed of the object as it hits the ground and multiply that with the amount of mass and you wind up with the situation of force x time = mass x speed.

That experiment, depending on what you measure or how, proves that four different equations are true. force x distance = one half mass x speed x speed, force x displacement = one half mass x velocity x velocity, force x time = mass x velocity (impulse momentum equation), and force x time = mass x speed (scalar version).

So, which one of those four equations is the one scientists should use? All the "evidence" from the last 100 plus years is based on force x displacement = one half mass x velocity x velocity. If the scientists of the past choose the scalar version of force x time, things would be a little different today but I would still be asking the same question except everyone would be telling me there is a natural link between force and time, the one that Newton's 3rd Law demonstrates.

I have asked a very legitimate question that has not been answered. Am I required to accept work = force x distance because "everyone knows it is true" except me? Didn't everyone at one time "know" that heavier objects fell faster than lighter ones? Where is the science? I don't need to have the work energy theorem explained to me. I just want to know where it came from and why it is true? Is that too much to ask on a physics forum?

 

[speedingelf]

Can you not see that no one has answered the question? I will go for a run or a walk with my dog but, come on. Think about it, the air track experiment only proves that the math is good but, it also proves that other math is good. If I came up with a "discovery" that was as simple as force x distance, physicists would demand proof, wouldn't they?

I'm going to walk away for a while and come back to this later. I know of one other situation where force x distance does not seem to work well. I don't want to say it because I can't get a straight answer and I know that my example will be rejected just like the astronaut ball example was. By the way, one of the responses said the ke for both situations are the same, but they are not. I worked it out and it ain't so.

 

[russ_watters]

That experiment, depending on what you measure or how, proves that four different equations are true. force x distance = one half mass x speed x speed, force x displacement = one half mass x velocity x velocity, force x time = mass x velocity (impulse momentum equation), and force x time = mass x speed (scalar version).

Yes!

So, which one of those four equations is the one scientists should use?

Whichever one answers the question they are being asked/asking! Any can be useful depending on the situation.

I have asked a very legitimate question that has not been answered. Am I required to accept work = force x distance because "everyone knows it is true" except me? Didn't everyone at one time "know" that heavier objects fell faster than lighter ones? Where is the science? I don't need to have the work energy theorem explained to me. I just want to know where it came from and why it is true? Is that too much to ask on a physics forum?

That is something you will just need to get over: Not all questions are good/legitimate. You asked a bad question.

And just in case you missed it, you just explained pretty well why a particular experiment shows it is true, then asked why it is true. Don't you see that you are contradicting yourself? You have the answer in your head already and are just refusing to accept it.

 

[mattt]

I have tried and tried to understand why work is force x distance. The closest anyone comes is the experiment with air track. That experiment, when you boil it down, is like dropping a object of known mass. The force acting on it is F=ma which in this case a = g (acceleration due to gravity) and that gives F=mg. When you multiply the distance the object falls due to the effect of gravity by it's mass you wind up with the work that is done on it. You then take the velocity of the object as it reaches the ground and plug that value along with the mass of the object into the kinetic energy formula. When you compare the work done with the ke formula, they are the same. That's great but if you do the same experiment, in exactly the same way but measure different things you get an equally impressive result. In other words, measure how long the object takes to hit the ground and multiply that by the force acting on it and you wind up with a value for force x time. You then take the speed of the object as it hits the ground and multiply that with the amount of mass and you wind up with the situation of force x time = mass x speed.

That experiment, depending on what you measure or how, proves that four different equations are true. force x distance = one half mass x speed x speed, force x displacement = one half mass x velocity x velocity, force x time = mass x velocity (impulse momentum equation), and force x time = mass x speed (scalar version).

So, which one of those four equations is the one scientists should use?

You use all that is useful :-)

If you want to know the linear momentum at the end and they give you as data: F and t_1-t_0 then you use the "Impulse-linear_momentum" theorem.

If you want to know the velocity at the end and they give you as data: F, t_1-t_0 and m, then you use again the "Impulse-linear_momentum" theorem and then you compute v=p/m

If you want to know the kinetic energy at the end and they give you as data: F, h, then you use the "work-energy" theorem.

If...


There are thousands of things you may want to know, and depending on what the available data is, you may use one or another of a thousand of useful correct expression/theorems/formulas...

All the "evidence" from the last 100 plus years is based on force x displacement = one half mass x velocity x velocity. If the scientists of the past choose the scalar version of force x time, things would be a little different today but I would still be asking the same question except everyone would be telling me there is a natural link between force and time, the one that Newton's 3rd Law demonstrates.

Both

$$\int_{t_0}^{t_1}\vec{F}(t)\cdot\vec{v}(t)dt = \frac{1}{2}mv^2(t_1) - \frac{1}{2}mv^2(t_0)$$

and

$$\int_{t_0}^{t_1}\vec{F}(t)dt = \vec{P}(t_1)-\vec{P}(t_0)$$

are mathematical theorems, so they are mathematically true statements.

Because Newtonian Mechanics is a very good model for all this type of real experiments, you can check that their physical interpretation is satisfied in the real experiments.

I have asked a very legitimate question that has not been answered. Am I required to accept work = force x distance because "everyone knows it is true" except me? Didn't everyone at one time "know" that heavier objects fell faster than lighter ones? Where is the science? I don't need to have the work energy theorem explained to me. I just want to know where it came from and why it is true? Is that too much to ask on a physics forum?

Now again you miss the point. "Work" is the word we use to refer to what you call "Force x distance", we could just call it "Force x distance", but you have to acknowledge that the word "work" is shorter.

 

[Doc Al]

I have tried and tried to understand why work is force x distance. The closest anyone comes is the experiment with air track. That experiment, when you boil it down, is like dropping a object of known mass. The force acting on it is F=ma which in this case a = g (acceleration due to gravity) and that gives F=mg. When you multiply the distance the object falls due to the effect of gravity by it's mass you wind up with the work that is done on it. You then take the velocity of the object as it reaches the ground and plug that value along with the mass of the object into the kinetic energy formula. When you compare the work done with the ke formula, they are the same. That's great but if you do the same experiment, in exactly the same way but measure different things you get an equally impressive result. In other words, measure how long the object takes to hit the ground and multiply that by the force acting on it and you wind up with a value for force x time. You then take the speed of the object as it hits the ground and multiply that with the amount of mass and you wind up with the situation of force x time = mass x speed.

OK.

That experiment, depending on what you measure or how, proves that four different equations are true. force x distance = one half mass x speed x speed, force x displacement = one half mass x velocity x velocity, force x time = mass x velocity (impulse momentum equation), and force x time = mass x speed (scalar version).

OK.

So, which one of those four equations is the one scientists should use?

Use them all! The force x distance version is quite limited; force x displacement (scalar product of two vectors) has proven to be the most useful. It's what we call "work". Similarly, the vector version of force x time, which is called impulse, is the one that is most useful.

All the "evidence" from the last 100 plus years is based on force x displacement = one half mass x velocity x velocity. If the scientists of the past choose the scalar version of force x time, things would be a little different today but I would still be asking the same question except everyone would be telling me there is a natural link between force and time, the one that Newton's 3rd Law demonstrates.

Both work and energy and impulse and momentum are used all the time! And yes, there is a natural connection between Newton's 3rd law and force and time and thus momentum. So?

I have asked a very legitimate question that has not been answered. Am I required to accept work = force x distance because "everyone knows it is true" except me?

Work = force x displacement is a definition. Do you mean to ask is: Why is such a definition useful?

Didn't everyone at one time "know" that heavier objects fell faster than lighter ones? Where is the science? I don't need to have the work energy theorem explained to me. I just want to know where it came from and why it is true? Is that too much to ask on a physics forum?

Your question remains unclear. Are you looking for a history lesson on how the concept of energy was first figured out? That will be long and drawn out! You seem to accept Newton's laws. And if you understand the work-energy theorem you must realize that it follows from Newton's laws.

 

[AlephZero]

So, which one of those four equations is the one scientists should use?

They use all of them. You seem to be arguing about a straw man, by not recognizing that "momentum" and "energy" are two different things.

Historically, it took several hundred years after Newton before ideas about energy were properly sorted out, but it doesn't make much sense to learn modern physics by going through that long history lesson, and learning about all the wrong ideas that were tried before physicists got to the right one.

 

[speedingelf]

I understand that force x distance has it's uses, and the same is true for force x time. The question is which one is correct for representing mechanical energy.

Electrically, we use watts (volts x amperes) and I have personally witnessed that watts is valid. I have yet to see any experimental proof that force x distance is the correct way to represent energy.

I can imagine a scientist taking a known quantity of electrical energy and converting that into mechanical. If he used 1000 watts to make a 1 kilogram mass accelerate from 0 m/s to a velocity "v", the work energy theorem tells us that he would need 4000 watts (or a little more due to any inefficiencies) to accelerate the same 1 kilogram mass from rest to a velocity twice as great (2v). So, who did this experiment? Did anyone do it?

If no one ever converted electrical or some other form of energy INTO mechanical energy, how do we know that force x time does not function better? Please, do not bring impulse or momentum into the discussion. I KNOW it cannot be used in that way and why.

Did someone one day say, let's define energy by force x distance? If someone did, there had to have been someone who said, why not force x time. In that situation, the scientists would have conducted an experiment. Who did it? What was it?

Why is this such a tough question to get answered? I am even more determined to find out because it seems that no one knows. My grandpa saws that if I see smoke, there could be a fire. Well, there seems to be a lot of smoke turning up by me asking a simple question and I want to see if it is a fire or just dust.

Would it be the end of the world if the work energy theorem is not right? I'm thinking a lot of people would be upset even though it would mean a lot of work for physicists.

Please think about this and let me know. I've got chores to do and I got to start making dinner cause I promised I would. I'll check back tomorrow.

 

[A.T.]

Please, do not bring impulse or momentum into the discussion
...
why not force x time.

You bring it into the discussion.

 

[russ_watters]

I understand that force x distance has it's uses, and the same is true for force x time. The question is which one is correct for representing mechanical energy.

The one that is energy. The units tell you that! And you already acknowledged that it works, so why ask again?

Electrically, we use watts (volts x amperes) and I have personally witnessed that watts is valid.

I doubt that: how did you do it?

I have yet to see any experimental proof that force x distance is the correct way to represent energy.

Again, you acknowledged above that it works. I don't understand why you are saying this.

I can imagine a scientist taking a known quantity of electrical energy and converting that into mechanical. If he used 1000 watts to make a 1 kilogram mass accelerate from 0 m/s to a velocity "v", the work energy theorem tells us that he would need 4000 watts (or a little more due to any inefficiencies) to accelerate the same 1 kilogram mass from rest to a velocity twice as great (2v). So, who did this experiment? Did anyone do it?

I'm sure that is way too boring for a physicist, but I'm an engineer and I do that every day when I work with fans. I have yet to incorrectly select a motor to run a fan due to making such an error!

…how do we know that force x time does not function better?

FT doesn't work at all: the units are wrong!

Did someone one day say, let's define energy by force x distance? If someone did, there had to have been someone who said, why not force x time. In that situation, the scientists would have conducted an experiment. Who did it? What was it?

Once again, you are looking at it backwards. They didn't say let's define energy as force times distance, they said let's call force times distance energy. (Work)

Why is this such a tough question to get answered?

Because asking a bad question over and over will never turn it into a good question.

Would it be the end of the world if the work energy theorem is not right?

Quite literally, yes, it would mean the end of the universe if the work-energy theorem suddenly became wrong.

 

[mattt]

I understand that force x distance has it's uses, and the same is true for force x time. The question is which one is correct for representing mechanical energy.

Electrically, we use watts (volts x amperes) and I have personally witnessed that watts is valid. I have yet to see any experimental proof that force x distance is the correct way to represent energy.

I can imagine a scientist taking a known quantity of electrical energy and converting that into mechanical. If he used 1000 watts to make a 1 kilogram mass accelerate from 0 m/s to a velocity "v", the work energy theorem tells us that he would need 4000 watts (or a little more due to any inefficiencies) to accelerate the same 1 kilogram mass from rest to a velocity twice as great (2v). So, who did this experiment? Did anyone do it?

Of course, you can do thousands of that kind of experiments at University.

If no one ever converted electrical or some other form of energy INTO mechanical energy

What do you think an electric motor does? http://en.wikipedia.org/wiki/Electric_motor

What do you think a chemical motor does?

How do you think a car works, a rocket works, etc?

how do we know that force x time does not function better? Please, do not bring impulse or momentum into the discussion. I KNOW it cannot be used in that way and why.

Did someone one day say, let's define energy by force x distance? If someone did, there had to have been someone who said, why not force x time. In that situation, the scientists would have conducted an experiment. Who did it? What was it?

All this already answered in previous posts.

Why is this such a tough question to get answered? I am even more determined to find out because it seems that no one knows. My grandpa saws that if I see smoke, there could be a fire. Well, there seems to be a lot of smoke turning up by me asking a simple question and I want to see if it is a fire or just dust.

Are you seriously saying you did not know that the type of experiements you talk about (converting electric energy or chemical energy, into mechanical energy) are done by thousands every day at Universities and of course our technology (cars, motorcycles, airplanes, rockets,...) use it every day?

Are you seriously saying you did not know these mathematical theorems are used every day in the industry (to make electric motors, chemical motors, cars, rockets,...) ?

Would it be the end of the world if the work energy theorem is not right? I'm thinking a lot of people would be upset even though it would mean a lot of work for physicists.

You still don't understand that a mathematical theorem CAN NOT be suddenly "not right", just like "a + b = b + a for natural numbers" can't be suddenly "not right".

Please think about this and let me know. I've got chores to do and I got to start making dinner cause I promised I would. I'll check back tomorrow.

Good luck tomorrow :-)

 

[speedingelf]

I explained earlier that I saw an electrician wire a motor at 120 volts and 240 volts, the same motor. At 120 volts, the motor used about 10 amperes and at 240 volts it used about 5 amperes. That tells me that the formulas for electrical power are probably right. It also tells me you didn't read my responses. The thing is that someone said I wasn't reading them but I did. It is my question that is not being understood.

As for the units for mechanical power, they are what they are because physics defines mechanical energy in units as Newton x meters or kilogram x meters per second x meters per second. So who decided that it should be that way? That is all I'm trying to find out and no body seems to be able to answer. Telling me that the scalar versions of impulse and momentum have different units is not helpful. I already know the units are different but that does not mean they are wrong if no one ever verified mechanical energy just as it says to do with the scientific method.

I know impulse and momentum cannot represent energy but that does not mean that the scalar versions of them could not. Isn't energy scalar? So, why can't the variables in a scalar concept be scalar?

I don't like it when people criticize me for asking questions. I only ask because I don't know. How can it be wrong to find out why something is a certain way? Isn't that what a scientist is supposed to do? Why is no one answering the question?

I think if we found out that the work energy theorem was wrong that it would be a wonderful thing for physicists. I'll bet there would be all kinds of opportunities to re-write books, and make discoveries. It would be good for physics but it would be even better for me if I just found out why work is related to force x distance instead of force x time (scalar).

Why won't anyone answer my question? Does anyone know who came up with the idea and who did the experiment that showed everyone it was so? I hope my teacher, whoever he might be knows, because no one is helping me.

One last thing before I check on dinner, why am I the only one talking about the scientific method? Yeah, why? I may not have any degrees but I do know that physics is supposed to be about the scientific method. I don't care if you all accepted the work energy theorem without proof. That don't matter a lick. But I want to know.

 

[Nugatory]

Why won't anyone answer my question?

I thought I gave it a pretty good try back in #25 in this thread... If you could tell me what part of it is not responsive I might understand your question better.

 

[russ_watters]

I explained earlier that I saw an electrician wire a motor at 120 volts and 240 volts, the same motor. At 120 volts, the motor used about 10 amperes and at 240 volts it used about 5 amperes. That tells me that the formulas for electrical power are probably right.

That tells you volts*amps is conserved: it doesn't tell you that it's power.

As for the units for mechanical power, they are what they are because physics defines mechanical energy in units as Newton x meters or kilogram x meters per second x meters per second. So who decided that it should be that way? That is all I'm trying to find out...

It isn't really true that that's all you are trying to find out. But if all you want is a name, try Gottfried Leibniz. His idea was most of the way to what is the modern version of energy (he almost got it right) and is the originator of the basic concept. The wiki has some history:
http://en.wikipedia.org/wiki/Energy#History

Telling me that the scalar versions of impulse and momentum have different units is not helpful.

It should be. I recognize that you are at the beginning of your journey with physics, but one of the first things you need to learn is that with math, the units on both sides of an equation must match.

I already know the units are different but that does not mean they are wrong...

They are wrong if you try to put it into an equation where they don't fit. That's a basic concept in math. It doesn't mean they aren't valid for other, different equations, though. Like momentum = mv. But having momentum be useful doesn't mean energy isn't and vice versa -- and again, you already acknowledged that you know that it works. And it doesn't mean you can plug energy into a momentum equation and have it work. It won't.

...if no one ever verified mechanical energy...

You need to take a step back and consider just how asinine that statement is -- an also go back and read through the thread to all of the examples already provided of how it gets verified. There's been half a dozen at least so far.

I know impulse and momentum cannot represent energy but that does not mean that the scalar versions of them could not.

It does if it means that when you plug them into the energy equations, the equations don't work.

I don't like it when people criticize me for asking questions. I only ask because I don't know.

We don't like it when people ask questions and then don't try hard enough to understand and accept the responses.

How can it be wrong to find out why something is a certain way?

It isn't. But not accepting the answer is wrong. Saying you want to learn and then fighting against learning is wrong.

Why is no one answering the question?

We don't like it when people ignore our answers and then say no one answered. There are dozens of quality answers in this thread and you haven't directly addressed (by quoting the relevant part) any of them.

I think if we found out that the work energy theorem was wrong that it would be a wonderful thing for physicists. I'll bet there would be all kinds of opportunities to re-write books, and make discoveries. It would be good for physics but it would be even better for me if I just found out why work is related to force x distance instead of force x time (scalar).

Because you are a kid, I'll say that's cute. But you need to recognize that because you are a kid, that's all it is. Coming from an adult, it would be laughable for you to think that the first thing you learned in physics is something that every physicist and engineer (millions of them) for hundreds of years got wrong.

One last thing before I check on dinner, why am I the only one talking about the scientific method?

Because you don't yet know enough about science to start learning the scientific method. What you are asking and not understanding over and over again is more basic even than the scientific method is. Your issue is essentially a communication issue: you have to learn how to talk about science before you can learn science.

 

[Dale]

why am I the only one talking about the scientific method?

You are not. I told you why your question was scientifically wrong back in post 2. What you are complaining about is simply not science.

In the theory part of science you make assumptions. If you are not making assumptions then you are simply collecting data without any theory and therefore you are not doing science.

Also, in any field of study, including science, you define terms. There is no proof or justification or faith or anything else that you have mentioned involved in defining terms. A definition is simply a convention, and like all conventions it could be different, but we use the agreed upon convention because it makes something easier. In the case of definitions, using the convention makes communication easier.

In science, if you ASSUME Newton's laws and rigid bodies then you can prove the work energy theorem. (There is no chance for it to be wrong without all of math being wrong also). From the work energy theorem you find that $f\cdot d=\Delta(\frac{1}{2}mv^2)$. For convenience in communication we define "work" to refer to the quantity on the left and "kinetic energy" to refer to the quantity on the right. There is no proof or experiment involved.

Now, you can perform experiments and measure the relationship between work and kinetic energy. If you do that and get a result other than their equality then you have proven either that the objects are not rigid or that Newton's laws are wrong (or your experiment is flawed).

However, no matter how much experimental data you collect disproving the work energy theorem, you cannot ever even in principle prove that $W \ne f\cdot d$ nor $KE \ne \Delta(\frac{1}{2}mv^2)$ because those are tautologically true by definition.

 

[speedingelf]

No. You have to make assumptions. That is part of science. You make assumptions and then you test those assumptions against experimental evidence.

I am doing science, it is you who are not. If someone assumed that there was this called energy and came up with the work energy theorem, the scientific method requires checking any testable predictions.

What am I doing? I'm asking to see that experimental evidence. If that is not science, then I don't know what science is all about. What am I supposed to do, just accept it because everyone else does. I'm sure Galileo who showed that heavier objects fall at the same rate as lighter ones would take my side in this matter. Don't you?

 

[speedingelf]

In elastic collisions there are two conserved quantities: A vector whose magnitude is $mv$; and a scalar $mv^2/2$. That's the experimental fact that we have to start with.

We label one of them momentum (because we have to name it something) and the other kinetic energy; and we define force to be the time derivative of momentum because that's convenient and agrees with the experimentally confirmed result $F=ma$. It follows from this definition that we apply a given force for a particular length of time to change the momentum by a given amount - that's just doing math on the relationships we already have.

Now, if we turn our attention to that other conserved quantity, the scalar $mv^2/2$, and ask the question "What application of a given force will change the quantity $mv^2/2$ by a given amount... a bit of algebra and an easy integration will give you force times distance.

The discovery of kinetic energy and momentum, and the relationship of kinetic energy to potential energy (which comes directly from $W=Fd$) didn't follow exactly this path, of course. The history is full of misconceptions, false turns, and a even people expressing confusions similar to yours. It is only when we arrive at the end of the journey and look back that we are able to say "Oh - so that's the shortest route with the fewest wrong turns", and start writing the textbooks.

I understand what you are saying. I even did a bunch of collision problems myself and even worked out the formulas to do calculations for ideal elastic collisions.

I am not confused; all I want is the answer to a simple question.

I'm having trouble getting anyone to understand what I am after. We have the work energy theorem and it does have a testable prediction. According to the scientific method, whenever a hypothesis is proposed, it has no scientific value until it is confirmed experimentally. Today, I know there are scientists working on String Theory and they might even be teaching it, but String Theory is really only a hypothesis; it has not been proven. If it was, I'm sure that it would have been on the news. Don't ask me about it because I know very little beyond the fact that it is supposed to require more than 3 spatial dimensions. The point is, that today's physics community will not go out on a limb and grant String Theory (it should be called the String Hypothesis) the status of something like the Theory of Relativity.

The work energy theorem is at least 100 years old, probably a lot older, and if it has never been tested, that fact should be made known. I'm seriously beginning to believe that no scientist has ever tested the work energy theorem without assuming it is correct. The air track experiment suggests that. Is there some secret provision in the Scientific Method that says that something everyone agrees is true does not need experimental proof. Is there a provision that says anything older than a certain date does not require proof?

I don't understand why a simple question has generated all this noise. Am I being a b|^(h for wanting to know? It is as if the scientific method does not apply to students and the thing to do is to say all kinds of irrelevant things so the student forgets about the question. I really don't get why no one will answer the question of who came up with the work energy theorem and who proved it was right? Is it a secret that is only told to doctoral candidates or what? I'm getting a little upset right now and so, until tomorrow.

 

[russ_watters]

Ok, I think that's about enough. You've made it abundantly clear you don't want the answers you are being given, so this thread is closed. If you change your mind, my offer in post #40 still stands. In either case, if you ever decide to change your approach, please try rereading this thread and try to understand what you are reading instead of knee-jerk dismissing it.