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This issue continues to puzzle me. I just taught a lesson on the
work-energy theorem.
Net work = delta K.
delta K = Net work.
But did one CAUSE the other? Or are they only associated with each
other?
I think this may be a question about language and grammar, more than
about physics. Our language works this way: subjects of sentences
perform actions indicated by verbs. The engine did work on the
rocket. The kicker kicked the ball. It FEELS right to say that the
work caused the energy change. "How do I know" that the energy
changed is not the same question.
"How do I know that the rocket's energy changed?" ---> Because I
observe that v-final > v-initial.
"Why did the rocket's energy change?" ---> Because the engine did
work.
That the equations are symmetric seems undebatable. And yet...???