What Is Energy Really?

[kishtik]

<br /> v_f^2-v_0^2=2ax<br />
Multiplying by m,
<br /> \frac{mv_f^2-mv_i^2}{2}=max<br />
<br /> \frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2=Fx<br />
This equation is true for all of the motions which include a force. Therefore we call the left side KE difference, and the right side work done.
Is energy a thing which can only be defined mathematically? Or are there any other ways to define it? If yes, why did Euler call it vis viva? Was it only because of KE? If no, what leads us to conclude that there is a thing called energy?
For almost every physical definition, we have an imagination, a perception, a conception, something inexplicable. Where is this coming from? When we were babies, playing with Legos (K'Nex for me) we learn about dynamics and perhaps energy. I've read that smells, tastes and views were perceived the same by a little baby. Perhaps we develop that conciousness at that age.

 

[turin]

This only works if a, m, and F are constant, in general. Otherwise, you have to integrate.

 

[Arcon]

Originally posted by kishtik

Is energy a thing which can only be defined mathematically?

For the most part that is true. Recall what Feynman said on this point

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. It is not that way. However, there are formulas for calculating some numerical quantity, and 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 mechanism or the reasons for the various formulas.