Negative Gravity? Is GPE Really -mgh?

[conquerer7]

This has been bothering me, since I just realized I've never really thought about it. What's the correct sign of gravity? Of course, it's supposed to be negative, since it points down, but in GPE (mgh) it seems to be positive. GPE is positive above the zero level, and so g must be positive as well, right? Is GPE really -mgh, or does the g really mean the magnitude of gravity, without counting its sign?

I'm asking this now because I'm doing a question where I need to find KE and GPE in terms a few common variables, one of which is gravity, which in the problem clearly has to point down. The only way I can get KE to have the right sign is to make gravity positive throughout the whole problem (or put it in absolute value bars?), which doesn't make sense to me after being told it's always negative.

 

[Phyisab****]

Hmmm, I am about to graduate with a physics degree and I am wondering about the answer to this. I could go on, but in other words, tag.

 

[K^2]

Potential energy is measured relative to some arbitrary starting point. If you set GPE to zero at ground level, then GPE becomes positive as you move up. If you set GPE to zero at "infinity", as is often done with gravity, then GPE at ground level is negative and becomes less negative as you move up. In either case, however, it is increasing as you go up.

The force of gravity is negative of the rate of change of GPE with respect to position, as with any conservative force. So if your GPE is mgh, F = -d(mgh)/dh = -mg, which automatically has the correct sign. In simpler terms, if potential energy increases as you go up, force points down.

Of course, the sign depends on the choice of the coordinate. Sometimes it may be convenient to measure "depth" as the positive coordinate. In that system, gravitational force will have a positive sign, but only because you flipped coordinate system upside down.

Hmmm, I am about to graduate with a physics degree and I am wondering about the answer to this.

That's a really bad sign. You are supposed to be able to deal with generalized forces in generalized coordinates. So deriving a force vector from given conservative potential should be something you could do in your sleep. Have you not had a descent mechanics course?