Many theories use something called energy to explain reason behind certain phenomenon, but I have not been able to grasp the idea of energy. Maybe it is because I have grown in a society where the word energy has a completely different meaning, I don't really care about that though.
When I started studying about energy, I got acquainted to a physical quantity called Work, which is defined as $W = F . s$. I never really understood why this quantity was defined. And moving on, I got to know that "Energy is the ability of a system to do work". After reading this relationship, I certainly didn't have any sense, any reason behind this relationship between energy and work. I simple mechanics, I always thought that if an object has energy, it can provide a force. But never understood why we say that "if an object has energy, then it can provide not just force, but $F . s$ , which is work". So my first question is: Why have we defined work to know what energy is? And why only $W = F . s$?
Then, when I accepted this unusual fact(to me atleast), I encountered the equation $E = mc^2$, or mass-energy equivalence. I have read many resources stating the mass can be converted to energy and vice-versa (even my book uses this statement), which seems highly against my intuitive sense of what energy is.
I know this question has been asked at Phys. SE previously, I have also read the answer to it. But still, there is a confusion in my mind as to what energy is.
Before asking my main question, I would like to share my thoughts as to what energy seems to me. When I think of energy, I think that if an object has energy, it can provide a force. That's it. What else it can do, because all forms of energy that we have, whether its Kinetic, Potential, Electric, even Heat(in which particles vibrate and thus exert a force on near particles), all of them exert a force.
I also read an answer on Phys. SE regarding this question, in which an answerer put on the views of Feynman, which stated that "energy is something that is conserved, it is a numerical value that remains constant, no matter what process has occurred. It is a law of nature".
So my final question: With all these confusions regarding what is energy, why do we use Work to define energy Mathematically(like energy has unit Joule, the same unit as work)? And why are my thoughts regarding energy are not true, even when we encounter forces with most of the energies? Or even simply, not including any mathematics, what is the idea behind energy?
