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If anything is at a ground level then does it have potential energy? Since the formula for potential energy requires height and height is zero in this case, so is potential energy zero in this case?

P.E= mgh.

Now in the next scenario: I am at my bungalow and there is a room upstairs 10 ft above the ground floor. On this room upstairs I have kept a book on the floor. Does the book have potential energy even though it is at the floor of the room upstairs. Mass of the book is 1 kg.

So will the potential energy of the book be 1 kg x 9.8 m/s2 x 10 ft= 98 Joules.

Or will the potential energy be zero since it is at the floor of this room that is upstairs?

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The zero of potential energy is arbitrary, strictly speaking it only makes sense to talk about differences in potential energy. This is because the physical relevance of potential energy is that its derivative gives a conservative force, but derivatives don't care for constants that we may add to the potential energy function.

That is, when you say "the book has $98\ \mathrm{J}$ of potential energy", you really mean "the book has $98\ \mathrm{J}$ of potential energy more than one on the ground floor", and when you say "the book has zero potential energy" you mean "the book has zero potential energy compared to another book at the same position".

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  • $\begingroup$ Can we calculate potential energy without knowing the height? $\endgroup$ – avito009 Feb 12 '17 at 16:12

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