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Can anyone suggest me some book/article explaining how and why the quantity named 'Energy' made its way into physics?

I have gone through "Lectures on Physics" (Vol. 1) by R.P. Feynman and have been convinced that at first scientists were in search of a quantity which remains constant w.r.t. any other internal change,in a closed system.The quantity later turned out to be 'Force x displacement'.

But we know that momentum is also conserved in closed systems. So why don't we invent a scalar 'mass x speed' (in order to fix the problem that momentum is a vector) and use this instead of 'Energy'? While we could take the advantage that 'mass x speed' is much simpler than '1/2 (mass x square of velocity)'.

One of my teachers, on being asked this question, said that energy is more fundamental than momentum. And giving the example of a field force, he wrote:

$$\vec{F}=\frac{\partial \varphi}{\partial x}\hat{\imath}+\frac{\partial \varphi}{\partial y}\hat{\jmath}+\frac{\partial \varphi}{\partial z}\hat{k}$$

And showed that the quantity $\varphi$ turns out to be the potential energy of a particle (e.g. a point mass in case of a gravitational field) in the field at the point $\vec r = (x,y,z)$. But what is the thought behind the approach to find out such a quantity whose change w.r.t. position will describe the force? And at which point 'Force x displacement' becomes more fundamental than momentum?

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    $\begingroup$ You can see : Yehúda Elkana, The discovery of the conservation of energy (1974). $\endgroup$ – Mauro ALLEGRANZA Mar 14 '15 at 14:03
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    $\begingroup$ Note that we have MathJax support on this site, so you should just type out the math instead of pasting an image. Please do so next time :) $\endgroup$ – Danu Mar 15 '15 at 13:09
  • $\begingroup$ It's not correct that force x displacement equals energy, nor is it true that force x displacement is conserved. Force x displacement is a method for calculating a certain type of transfer of energy (one that occurs through a mechanical force). $\endgroup$ – Ben Crowell Mar 15 '15 at 19:43
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    $\begingroup$ The question is largely answered here hsm.stackexchange.com/questions/596/…, there is also a link there to Mach's book The Science of Mechanics whose ch.II gives details on the early history of kinetic energy and momentum. $\endgroup$ – Conifold Mar 17 '15 at 23:46
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    $\begingroup$ Possible duplicate of What is the history of the energy concept and its measurement? $\endgroup$ – Francois Ziegler Jun 22 '18 at 21:11
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This is a very interesting and complex topic that is far from closed. Here are some of the sources I have found.

Energy the subtle concept, by Jennifer Coopersmith, is probably the book you are looking for. However, if you get interested in more critical accounts, continue reading. http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198716747.001.0001/acprof-9780198716747

Energy conservation as an example of simultaneous discovery, a classical (and very critical for its time) article by Thomas Kuhn and a good place to start understanding the subtleties of the history of energy. It has been published in the following:

M. Clagett (Ed.), Critical problems in the history of science (pp. 321-356). Madison: University of Wisconsin Press. (Proceedings of the Institute for the History of Science at the University of Wisconsin, September 1-11, 1957); Th. S. Kuhn, The essential tension (pp. 66-104).

More Heat than Light, an extraordinary book by Philip Mirowski. Warning: Mirowski is interested in the link between the conservation of energy in Physics and the conservation of value in neoclassical economics, but its treatment of energy conservation is very useful for your purpose. https://www.cambridge.org/core/books/more-heat-than-light/4CD2ADE8D5DE8665E43E2922D7E360B3

The Science of Energy, by Crosbie Smith. While your question is coming from Mechanics, this book is focused on Thermodynamics. However, the first chapters could provide some valuable information and insights. https://www.press.uchicago.edu/ucp/books/book/chicago/S/bo3628434.html

As said in comments the work of Mach and Elkana are other important sources but I have not had time to read them.

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