Question

guys, why potential energy did't depend on the path
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Answer 1

The potential energy represents the work done on the spring and the energy stored in it as a result of stretching or compressing it a distance x. The potential energy of the spring PEs does not depend on the path taken; it depends only on the stretch or squeeze x in the final configuration.

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Answer 2

The work a conservative force does on an object is path-independent; the actual path taken by the object makes no difference. ... Conservative forces are easier to work with in physics because they don't “leak” energy as you move around a path — if you end up in the same place, you have the same amount of energy.

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