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# An interesting question about potential energy watch

1. Ok the latest thing to rack my brain has been the idea of potential energy

E = mgh

So when h = 0, GPE = 0, yes ?
However, when h = infinite, GPE = 0 as well. This is because the g in that equation also tends to 0 as h gets large.

Intuitively this leads you to believe (it led me in any case) that there was a point somewhere between 0 and infinity where GPE was greatest. Trying to find it led me nowhere so i now question my instincts on whether GPE actually is 0 at those aforermentioned points.

I mean, at h=0, when dealing with a model of point masses, g is infinite. (g= something/r^2 gets large as r gets small) And as h gets large, we notice g decreasing to 0. In both cases we end up with weird maths involving infinities multiplied by zeroes.

These are my jumbled thoughts, so can anyone shed some light on what's going on before i end up confusing myself even more ?
2. gpe = o either at infinity or at the surface of the earth, not at both.

gpe = o at the surface comes in handy for problems involving local changes in GPE, i.e. in the region where g = 10 N/kg

when you leave the surface and venture into space it is more convenient to say GPE = 0 at infinity. All potential energies closer to the Earth are therefore negative.
3. Gravitational potential is taken as zero only at infinity. Therefore, at your h=0, this is height relative to infinity. So yes, potential is zero here. At h = infinity, the potential would be "something". Beware however, when using E=mgh, as this is only for a constant field. As gravitational fields are not constant, that means mgh is only an approximation really for potential, and only works with any success when close enough to a body that the field appears to be constant.

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