How did the notion of mechanical energy emerge? I know how it's defined and the implications we exploit as tools to analyze physical systems. What remains unclear to me is how people arrived at the conclusion that the force times the distance over which it acts is such a fundamentally linked quantity, quantitatively linked to all forms of energy. To give a clearer picture: think of us as early humans just starting to explore nature. In our analysis of mechanics, we come across the quantity force times over which the distance it acts. Now we successfully link this quantity to it's affect on the body under consideration by using our mathematical knowledge: F•S = ∆mv²/2 , but when we come to name this quantity, it can be anything- say momentum. This, of course, does not affect our usage of this quantity and the conservative laws we come up with. How is it that it was established that the mechanical form of energy was the quantity ∆mv²/2 and not something else, like ∆mv. Was this deduction solely based on experimental evidences that linked this to the other forms of energy or was there something else that led to this as well?

I would really like somebody to provide me with intuitive, historical and other insights that can help me see why this must be so. I've tried the internet, and my physics textbooks, including Sears and Zermansky's University Physics, with not much luck. I've come up with a few arguments of my own which I'll share later in the comments. I hope the question's construct isn't too messy. :)


I would like to emphasize the intuitive part of my question, for anyone to whom it appears that my intentions are to solely know of the history. :)

  • $\begingroup$ I can barely remember, but I learned about how scientist thought about the question of what makes objects move, and the quantity $mv$ was one of the best candidates. However, I think it was Leibniz the first one who thought about $mv^2$ as that "quantity", he called it "vis viva". MAyeb you can find something with that. $\endgroup$
    – FGSUZ
    Commented Sep 2, 2017 at 18:33
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    $\begingroup$ If you don't get an answer here you can try the History of Science and Mathematics stack exchange. $\endgroup$
    – M. Enns
    Commented Sep 2, 2017 at 18:35
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    $\begingroup$ I'm voting to close this question as off-topic because it concerns the historical development of physics rather and belongs on History of Science and Mathematics SE. $\endgroup$ Commented Sep 2, 2017 at 18:43
  • $\begingroup$ My intentions are not to know of just the history, it is to gain an intuitive insight into the notion as well. $\endgroup$
    – ditsuke
    Commented Sep 2, 2017 at 18:47
  • $\begingroup$ That seems too broad. It is best to only ask only 1 subquestion per post. $\endgroup$
    – Qmechanic
    Commented Sep 2, 2017 at 19:33