How did we come to know that, for example, the quantity Work=Force*distance is conserved?
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You can see : Yehuda Elkana (1974), The discovery of the conservation of energy. – Mauro ALLEGRANZA Jan 02 '17 at 18:17
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Old, but freely available : Ernst Mach, (German ed,1872), History and Root of the Principles of the Conservation of Energy. – Mauro ALLEGRANZA Jan 02 '17 at 18:52
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2This took centuries to sort out, because in the real world mechanical energy is usually not conserved, and it is not at all obvious that there is any relationship between mechanical work and heat, for example. Most historical scientists and mathematicians with familiar names (and a few unfamiliar ones) had something to say about this question. See https://en.wikipedia.org/wiki/Conservation_of_energy for a very brief summary. – Jan 02 '17 at 12:30