Okay I’m having a little problem with non conservative forces, why are their signs different? Aren’t they basically the same equations?
In: 1
Lets use W and I for to separate them, W= -MmG/R, U= mgh
U= mgh is an approximation for elevation close to the surface of the earth. for masses a lot smaller than then earth and describe the potential energy in a point relative to the surface
g =f/m = MG/r^2 with earth mass and earth radius and is the surface acceleration
So mgh =mhg =mhf/m =hf. That is force times distance and it works (energy)
The real potential energy would be integral to the force from the top to bottom location. Because elevation changes are usually very small compared to Earth’s radius
W is the energy that is required to go from an infinite distance from the earth to the surface. You gain energy so the required energy is negative. U is the energy release if the election change is h
You get it by integrating GMm/r^2 from infinity to R which is Earth’s radius.
So it is not exactly the same thing, one is an approximation close to the surface and one is from the surface to infinity. Because of the slight difference in definition, the sign is the opposite.
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