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Work energy theorem states that $$W_{total}=\Delta K_{system}$$ From this basic equation we can derive the following equation $$\Delta E_{mechanical}=W_{external}+W_{non-conservative}$$ The above equation is time independent and forms the basis of mechanical energy conservation law.I know the mathematical derivation. I am not sure but I want to know Does nature prefer time-independent mechanical energy equations?

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Nature is. It does not use equations as these are mere approximate descriptions of nature. Physicists prefer to write time independent definitions since these reflect the observation that energy, momentum, charge, angular momentum, spin etc are conserved.

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