speedingelf said:
I appreciate the effort everyone is giving but the only thing I need is the experimental proof that scientists used to verify the idea that work (force x distance) should represent energy.
As I said before, "energy", "linear momentum", "force", "angular momentum" are exactly what we decide them to be, and we make it by means of a mathematical definition and then an experimental setup to be able to interpret it and measure it.
It just happen that in many mathematical structures we use in Physics, there are some mathematical objects (some functions in Classical Mechanics, Self-Adjoint Operators in Quantum Mechanics, but it does not matter now for you, just some mathematical objects) that are constant during the evolution of that system. One of them, that is mathematically related to the time-translation symmetry of that mathematical structure, we decide to call it "Energy".
It happens that that concrete mathematical object we decide to call "Energy" has dimension ML^2/T^2.
For example:
System = one point-particle with mass m that moves in one dimension under the force F(x) = -kx
In this mathematical model, the function
f(x(t),v(t)) = \frac{1}{2}mv^2(t) + \frac{k}{2}x^2(t)
is constant, does not vary with time.
There are other functions in this model that are also constant, for example
g(x(t),v(t)) = \frac{1}{2}mv^2(t) + \frac{k}{2}x^2(t) + 42
does not vary with time.
We call the first one expression "Mechanical Energy of the particle", the second one expression is just as good, and it is exactly just as useful as the first one. Why useful?
Because if you call
\frac{1}{2}mv^2(t)
"kinetic energy of the particle" and you call
\frac{k}{2}x^2(t)
"potential energy of the particle", then you can know a lot of useful things about this system just by those two quantities.
For many important questions, you don't have to solve the (usually) difficult system of differential equations that would let you know what happens (the value of each physical magnitude of the system at each and every moment of time), but simply doing some arithmetic computations (addition and subtraction) with those two "energy terms" between some initial and final state, you can know important things about how the system changes between those initial and final states. (when you are interested only in those initial and final states, but not in every intermediate state).
I have put you the simplest model, but it is exactly the same in any other mechanical model. So now you know why those mathematical quantities we decide to call "Energy" are extremely important.
So I hope you now undertand why it is very useful and important, in a "real" experiment or observation (for example, when analyzing/observing the trajectory of a planet in the solar system, or when observing/studing this real tennis ball during a tennis match, etc) to calculate those quantities we call "energy". It simplifies the computation of many important things.
I understand that energy is thing that changes forms and so on. There is no argument with that.
The scientific method requires that a hypothesis be independently tested.
You create a mathematical model (a mathematical structure plus an interpretation of some of the mathematical objects in terms of some experimental setup and measure).
Then what we test is the mathematical predictions of that mathematical model (and it is possible to do it precisely because of the interpretation in terms of experimental/observational setup and measure process).
Someone must have come up with the idea of energy and other scientists confirmed it I know the air track experiment well but it does not prove the work energy theorem is valid unless you assume work is valid.
I really don't understand what you mean here. To test a model you just have to do the following:
1) Compute the mathematical expressions of the relevant mathematical objects of the model.
2) Measure, in the real experiment, those magnitudes that correspond by means of the interpretation of the model, to these mathematical objects.
3) See if it match.
For example, if you are going to do the following real experiment:
A tennis ball of mass m falling from h meters to the ground.
One useful mathematical model will be a point particle of mass m and a force F= -mg (along the vertical axis).
You compute whatever you want in the mathematical model that has an interpretation in terms of real measures (final speed of the tennis ball, for example, any other observable).
You measure the real final speed of the tennis ball.
You see if it match.
If you substitute force x time (a scalar expression), the air track experiment "proves" force time should represent energy.
Seriously, I don't have the slightest idea what you mean there. If you measure (in the real experiment) F.(t_1-t_0) you will get a number, if you also measure (in the real experiment) P(t_1) and P(t_0) you will get two more numbers. You can check that those three numbers satisfy
F.(t_1-t_0) = P(t_1)-P(t_0)
and you can mathematically prove in the mathematical model that for any two time points t_0 and t_1, the model implies F.(t_1-t_0) = P(t_1)-P(t-0)
So you have just witnessed that the model captures reality ( = is a good/useful model).
Obviously, or it should be, the air track experiment does not really test whether force x distance should represent mechanical energy.
I think you have a serious mess about how things work. There is no "should" anything.
"Mechanical energy" is what we decide it to be, and we have ALREADY decided that Mechanical Energy is "X-expression" depending on the mathematical model we are using (to modelize some real experiment) and I already told you the reasons why it is useful to put that name to those expressions of those models.
Please see that all I am asking for is the sort of experimental proof physicists would demand of me if I came up with something. For example, if I said that gravity is related not to mass but to the physical size of an object but offered no proof, no one would take me seriously. The work energy theorem came from somewhere and somebody showed it was true. By the way, if my last statement is proven true, I want credit. LOL
No, the more I read you, the more I see you have big problems understanding how it works. But I really not know what more to say to you (apart of all I have just written).
Seriously, what is the experimental proof that work should be used instead of force x time? As far as I know, work has been around for at least 100 years. Is it too much to ask to see it?
That question does not even make sense. "the work should be used instead of force x time"
I don't really know what you are asking, but something is seriously lacking in your understanding of physics.
I hope some other person gets what you mean.