View source for Specific potential energy

{{Infobox physical quantity
| bgcolour={default}
| name           = Specific potential energy
| image          =
| caption        =
| basequantities =  m<sup>2</sup>/s<sup>2</sup>
| unit           =  J/kg
| symbols        = pe, or ''e''<sub>u</sub>
| derivations    = ''e''<sub>u</sub> = ''[[Gravitational_acceleration|g]]'' [[height|h]]
}}
In [[classical mechanics]] and [[gravitational physics]], '''massic gravitational potential energy''' (MGPE) is a fundamental concept that relates to the [[gravitational potential]] a body possesses due to its position in a [[gravitational field]] relative to a [[Frame of reference|reference point]]. This energy is associated with the [[gravitational force]] acting on a body and its displacement within the gravitational field. It depends on the height of a body and the strength of the gravitational field. The term "massic" in this context refers to the [[gravitational energy]] per unit [[mass]].<ref>Serway, Raymond A., and Jewett, John W. Physics for Scientists and Engineers. Cengage Learning, 2013</ref><ref>Halliday, David, Resnick, Robert, and Walker, Jearl. [[Fundamentals of Physics]]. John Wiley & Sons, 2013.</ref>
==Overview==
===Definition===
The massic gravitational potential energy (MGPE)  of an object is defined as the [[gravitational potential]] at a location which is the [[gravitational potential energy]] (GPE) at that location per unit mass (m):
:<math>MGPE = {GPE\over m}</math>

In some situations, the equations can be simplified by assuming a field that is nearly independent of position. For instance, in a region close to the surface of the Earth, the [[gravitational acceleration]], ''g'', can be considered constant. In that case, the difference in potential energy from one height to another is, to a good approximation, linearly related to the difference in height (∆h):
<math display="block">MGPE \approx g\Delta h.</math>

Massic gravitational potential energy is typically measured in [[Joules]] per [[kilogram]] (J/kg) in the International System of Units. The [[dimensional formula]] for massic gravitational potential energy is [L]²[T]<sup>-2</sup>, consistent with energy measurements.
===Key Concepts===
*[[Frame of reference]]: The choice of reference point is arbitrary but is crucial for determining the potential energy. Commonly, the Earth's surface is chosen as a reference, and heights are measured vertically above it.
*Zero Potential Energy at Infinity: As an object moves infinitely far away from the gravitational source, its potential energy approaches zero. This choice simplifies calculations and is a convention in many physics problems.
==Mathematical form==
{{Excerpt|Gravitational potential|Mathematical form}}
==See also==
* [[Specific mechanical energy]]
==References==
{{Reflist}}
[[Category:Energy (physics)]]