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[I have changed the title and also edited the question in other ways to make it clearer what I am asking. I hope it no more reads like a duplicate. Nor it remains any more a history question.]

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-

enter image description here

And showed that the quantity phi 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 (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?

Ayan Biswas
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    $\phi$ is the potential energy of a field, not just energy! – Hritik Narayan Mar 14 '15 at 05:02
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    relevant: http://en.wikipedia.org/wiki/Vis_viva#History –  Mar 14 '15 at 05:33
  • But the Wikipedia article doesn't carry much detail. – Ayan Biswas Mar 14 '15 at 05:35
  • "It was largely engineers such as John Smeaton, Peter Ewart, Karl Holtzmann, Gustave-Adolphe Hirn and Marc Seguin who objected that conservation of momentum alone was not adequate for practical calculation"(As the wiki article says).....Why??? – Ayan Biswas Mar 14 '15 at 05:42
  • Do you mean energy as in $L = T -V$? – Stan Shunpike Mar 14 '15 at 06:21
  • The above equation is new to me. Would you please mention what L, T and V stand for? – Ayan Biswas Mar 14 '15 at 06:49
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    Would [hsm.se] be a better home for this question? – Qmechanic Mar 14 '15 at 12:51
  • Thanks for the suggestion. I have asked this question on History of Science and Mathematics also. – Ayan Biswas Mar 14 '15 at 13:17
  • For future reference, the moderators can move question to another site (this is called migration), and it is generally better to use that mechanism than to ask the same question on multiple sites. I'm going to close this instance of the question, so that the [hsm.se] version will be the version. – dmckee --- ex-moderator kitten Mar 14 '15 at 15:27
  • I'm voting to close this question as off-topic because about the history of a physical concept. – dmckee --- ex-moderator kitten Mar 14 '15 at 15:27
  • This doesn't seem off topic to me. He seems to be asking why the concepts are useful. It seems to me that this question would be answered by Noether's theorem -- as such, it's a physics question. – Leandro M. Mar 14 '15 at 17:14
  • @LeandroM. It reads to me like he is asking after the historical thinking that led to use of the concepts. And the OP's move seems to agree. If your interpretation is correct, then I think that http://physics.stackexchange.com/questions/21669/on-what-basis-do-we-trust-conservation-of-energy?lq=1 is relevant and may be a duplicate. Possibly also http://physics.stackexchange.com/questions/19216/why-cant-energy-be-created-or-destroyed – dmckee --- ex-moderator kitten Mar 14 '15 at 17:55
  • Sometimes people don't even know enough to ask the right question. Teachers often tell students that the conservation of energy is just an experimental fact, so many don't even know to ask there's a deeper justification. In that mindset it makes sense to ask why people just made up this odd looking "energy" function. But I agree that, if this interpretation is correct, it is a duplicate. – Leandro M. Mar 14 '15 at 18:00
  • OK, removing the portion regarding the quest for history, I have made it a purely physics question, and it now only deals with basic concepts. I'm only asking about the usefulness of taking 'work' as measure of energy. And to say about the duplicity, the two questions mentioned by dmckee doubts the conserved nature of energy, while mine does not. As I said that I was convinced that energy is conserved, by Feynman – Ayan Biswas Mar 15 '15 at 06:06

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