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Consider a spring block system . The surface on which the block moves is frictionless and the air resistance is nil . Suppose the block is at the mean position in it's natural length . By hookes law , ( PE ) = 0 because x = 0 . Also , the ( KE ) = 0 because block is at rest . Hence , total mechanical energy = KE + PE = 0 . Now , suppose it is elongated to maximum elongation . Then , at the point of maximum elongation ; KE = 0 and PE = k.a² / 2 , where a is the maximum displacement of elongtion . Hence , at this point , Mechanical energy = KE + PE = 0 + k.a²/2 = k.a²/2 . It is evident that initial mechanical energy ( = 0 ) is not equal to final mechanical energy ( ka²/2 ) . But how ?

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  • $\begingroup$ The two situations are different, the total energy of the first is not related to the second situation. You added energy to the system in the second. $\endgroup$
    – Triatticus
    Commented Jan 16, 2022 at 8:37
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    $\begingroup$ How is the spring elongated? $\endgroup$ Commented Jan 16, 2022 at 8:37
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    $\begingroup$ Does this answer your question? Different Spring constant when calculating different ways? $\endgroup$ Commented Jan 16, 2022 at 9:23
  • $\begingroup$ Hello! It is preferable to use MathJax (LaTeX) to display formulas. You can find a tutorial at MathJax basic tutorial and quick reference. Please edit your question accordingly. Thanks! $\endgroup$
    – jng224
    Commented Jan 16, 2022 at 10:50
  • $\begingroup$ Suppose I added energy externally through a conservative force . Then , mechanical energy must be conserved even when external forces are applied because only conservative forces are involved $\endgroup$
    – Abbas
    Commented Jan 19, 2022 at 5:36

1 Answer 1

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Energy is added to the system by the force that pulled the mass to position $a$.

Using conservation of energy to make predictions about a system requires the concepts of “closed” and “open” systems.

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  • $\begingroup$ No, just look at system , not external $\endgroup$
    – Abbas
    Commented Jan 16, 2022 at 7:51
  • $\begingroup$ No , just look at system . There are only conservative forces . So mechanical energy should be conserved $\endgroup$
    – Abbas
    Commented Jan 16, 2022 at 7:51
  • $\begingroup$ @Abbas In your post, you said, "Also , the ( KE ) = 0 because block is at rest." If the block starts at rest with the spring at natural equilibrium length and if your system is isolated with no external forces, then the spring is never elongated because the block would continue to be at rest for all time. By Newton's first law, if something is at rest, it continues to be at rest unless there are external forces. $\endgroup$ Commented Jan 16, 2022 at 8:41
  • $\begingroup$ Assume that the external forces are conservative . Then ? $\endgroup$
    – Abbas
    Commented Jan 19, 2022 at 5:37
  • $\begingroup$ @Abbas then there would be a potential energy associated with that force. $\endgroup$
    – cms
    Commented Jan 20, 2022 at 0:22

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