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How did people come up with various expressions for energy? By this I mean the expression or formulas for kinetic energy, gravitational potential energy etc. and the intuitive guiding principles to arrive at them.

Energy seems to be too abstract a quantity and with also a very loose definition. If energy was an abstract quantity which when calculated, always remained constant and no one really knows what it is, as Feynman puts it, how do you come up with mathematical expressions for it.

I guess a better way would to put it would be, that if you have identified a form of energy, how do you come up with a way of calculating it ?

Also, I would also like to know why work is defined as force times distance and how is this definition of work equivalent to change in the energy of a system. A historical and intuitive explanation would be appreciated.

PS: I am not just asking why work is defined to be force times distance, but how overall work is considered to be a change in the energy of a system and how this fits in the complete picture of energy as an abstract quantity.

Frankly speaking if someone can just shed light on this whole energy thing, it would be helpful as I am having nightmares trying to grasp this.

SaitamaSensei
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    For why work is force time distance see Why does work equal force times distance?. – John Rennie Jan 21 '16 at 08:06
  • I saw that....but as I said ...I was looking for a more comprehensive answer as to how work and energy correlate and are measures of the same quantity. – SaitamaSensei Jan 21 '16 at 08:07
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    Welcome to Physics Stack Exchange. To get good answers on this site, please ask specific questions. Asking how people came up with "various expressions for energy" is too broad. – DanielSank Jan 21 '16 at 08:23
  • Energy is conserved, so the energy done as work has to go somewhere and unless something leaves the system that somewhere is into internal energy. It isn't clear to me what the rest of your question is getting at. – John Rennie Jan 21 '16 at 08:23
  • No offense, but if you think the definitions of various forms of energy are "abstract and very loose", then you simply didn't take the time to read them. The definition of energy as "the ability of a system to perform work" is anything but abstract and the particular forms of energy are extremely well defined. You may not understand the definitions and their functions, yet, and that is a problem that can be solved by education, but please do not project your state of mind about a subject onto the subject itself. – CuriousOne Jan 21 '16 at 09:19
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    Ooo...that was harsh. Lol...well yes, I am not the brightest bulb here....and I am not PROJECTING anything...I was looking if someone can correct my misconceptions and provide clear explanation,THUS educating me. Energy is, as you said, ability of a system to do work and work is energy expended on or by a system. This sort of circular definition is bugging me. Further I never meant "various forms of energy are abstract and loose", I intended to mean the concept of energy appears abstract and loose TO ME, and how can we derive concrete expressions in terms of work, and why work is defined so. – SaitamaSensei Jan 21 '16 at 09:41

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