As body ascends height increases from the formula $mgh$ the increasing height should increase magnitude of P.E. but some say we should take height negative as it is going up against gravity.
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$\begingroup$ The people who say that the height should be negative, might be combining gravity and buoyancy into one potential energy. But if you just look at gravity, then its potential energy will always go up if the height is increased. $\endgroup$– fibonaticCommented Dec 18, 2015 at 6:19
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$\begingroup$ How it is possible to combine them $\endgroup$– SireesCommented Dec 18, 2015 at 6:24
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2 Answers
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Going up, h increases and so does your potential energy. This makes sense: A body at a greater height has more energy it can convert to something else (e.g. into kinetic energy if it falls down, or eventually heat energy after it crashed the ground).
By the way, mgh is an approximation valid only near the surface of the Earth. Going further up, you would use the formula $E = -\frac{G M m}{R}$, where $G$ is the gravtitational constant, $M$ and $m$ the masses of earth and your test body, and $R$ the distance between the two. Using this, you will get zero energy for a body very far away from earth, and negative energy for all bodies closer to earth, including on the surface.
This doesn't change anything on the conclusion, however: Going up, the magnitude of your P.E. will always increase.
By the way, the gravitational force decreases while you go up- but that's an altogether different question.
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If you take the P.E. of the balloon alone, it does increase as it rises. But, the reason it rises is because air from above moves down to displace it, losing P.E. in the process. Air is heavier than hydrogen, so a given volume of air loses more potential energy over a certain distance sinking than the balloon gains over the same distance rising. Thus the potential of the entire system decreases as the balloon rises.
