Potential difference vs Potential energy

AI Thread Summary
The discussion emphasizes the distinction between potential difference and potential energy, highlighting that only changes in potential energy are physically significant. The value of potential energy is dependent on the chosen reference point, but the change in potential energy remains constant regardless of that reference. For instance, lifting a mass from a desk to a shelf results in the same change in potential energy, irrespective of whether the reference point is the floor or the desk. Additionally, gravitational potential is typically negative, with variations indicating how much less negative it is in different locations. Understanding potential difference is crucial for practical applications in physics.
Tommy1995
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G'day!
I was looking over my notes about gravitational potential energy and I came across the graphs that I drew in class of the gravitational potential energy of a mass with reference point at infinity compared with the potential energy of a mass with reference point at the surface of the earth. They had totally different potential energies, one was negative, the other was positive. And then I jotted down a little side note saying, "potential difference is important, not potential energy". School isn't until another 6 weeks so could someone please help me justify why its more important to observe a mass' potential difference rather than its potential energy? I sort of have the idea in my head but I just can't express it in words...
 
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The point being made is that only changes in potential energy (from one point to another) have physical significance. The particular value you may assign at some location depends on where you choose your reference point, but the change in PE when going from point A to point B does not.

For example: If a mass m is lifted from a desk to a shelf, it doesn't matter if you take the reference point (where PE = 0) to be the floor or the desk or anywhere else. The change in PE will be mgΔh no matter what.
 
With gravity, the Potential is always Negative. It's just a matter of 'how much negative'. In some places, the potential will be Higher (less negative) than in others.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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