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The Work Energy(WE) equation in Mechanics says that the net total work done on an object due to various conservative and non-conservative forces equals the change in kinetic energy of the body. This above theorem is usually derived simply from Newton's laws in the EARTH Frame. Now, consider a variant ( actually a no. of variants! ) :-

1) Consider the analysis of motion of the body in the frame which is moving with a constant velocity [tex] \vec{u} [/tex] in the earth frame. Now, what does the Work Energy equation look like when a person in THIS frame tries to analyse the motion of the body? i.e. does the KE term include relative velocities and even the Works done change etc... basically, please derive the final, exact Work Energy equation in this frame..... is it possible to apply WE theorem in this frame?

2) I ask the exact same question as above when the frame of reference is moving with an acceleration ( uniform or even time varying!) [tex] \vec{a}[/tex] wrt the EARTH??

3) Now, let's come back to the EARTH Frame. The work done , when derived using Newton's equations DOES NOT contain terms for heat energy exchanged etc. Where do these come from when we consider the Law of conservation of energy??? Do Heat related terms appear in the work energy equation?

4) Finally, I ask the same question as (3) above when our frame of reference is moving relative to the earth with a constant velocity or some acceleration?? What happens to the 'Heat' terms now?

Basically, my last two questions ask this :- Do heat exchange terms come in the WE theorem as derived from Newton's 2nd law? How do we correlate the WE eqn and the First Law of Thermodynamics? Why doesn't heat appear as the 'work of some force'??? If it does, which force is it???

I shall strongly prefer suggestions to this problem that have a proper mathematical basis and are derived rigorously!