The height in the potential gravitational energy

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Discussion Overview

The discussion revolves around the interpretation of height in the context of gravitational potential energy (GPE) calculations, particularly for a sphere. Participants explore whether height should be measured from the bottom of the object or from its center of gravity, and how this affects the calculation of potential energy.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question whether the height in the GPE formula should be the vertical distance from the bottom of the object to the reference point or from the center of gravity.
  • There is a suggestion that for a sphere, the height could be measured from the bottom, but others argue that it is more common to measure from the center of mass due to symmetry.
  • One participant emphasizes that the reference point for measuring gravitational potential energy is arbitrary, and what matters is the change in potential energy rather than the absolute height.
  • Some participants propose that when an object reaches the Earth's surface, it has no gravitational potential energy, regardless of how height is defined.

Areas of Agreement / Disagreement

Participants express differing views on how to define height in the context of gravitational potential energy, with no consensus reached on the correct approach. The discussion remains unresolved regarding the implications of measuring height from different points.

Contextual Notes

Limitations include the ambiguity in defining the reference point for height and the implications of measuring from the center of gravity versus the bottom of the object. The discussion does not resolve these ambiguities.

terryds
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Is the height in the formula the vertical distance from the bottom to the center of gravity of object, or is it just the vertical distance from the bottom to the very top of the object.

I mean..
If there is a sphere with mass m and radius r and placed at height h, what is its potential gravitational energy ?
Is it just mgh or mg(h-r) ?
 
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terryds said:
If there is a sphere with mass m and radius r and placed at height h
Height "h" measured from what point? Also, is that the height of the center of the sphere or the bottom?

Realize that the reference point for measuring the gravitational PE is arbitrary. What really matters is the change in PE.
 
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Doc Al said:
Height "h" measured from what point? Also, is that the height of the center of the sphere or the bottom?

Realize that the reference point for measuring the gravitational PE is arbitrary. What really matters is the change in PE.

So, it is the vertical distance from Earth surface to the very bottom of an object, right ?
I think when I refer the height to the center of gravity or anything that is above the very bottom of an object, when it reaches the Earth surface, it'll still have the height (measured to the center of gravity or radius in a sphere). But, the fact is that it has no potential gravitational energy since it has reached the Earth surface.
Am i right?
 
Last edited:
terryds said:
So, it is the vertical distance from Earth surface to the very bottom of an object, right ?
As I said before, the GPE = 0 point is arbitrary.

terryds said:
I think when I refer the height to the center of gravity or anything that is above the very bottom of an object, when it reaches the Earth surface, it'll still have the height (measured to the center of gravity or radius in a sphere). But, the fact is that it has no potential gravitational energy since it has reached the Earth surface.
Am i right?
If you want to measure the GPE from some reference level (using the Earth's surface is fine) one usually measures the height of the center of mass with respect to that reference. But for a sphere, it doesn't matter, since it is symmetric.

Again, what matters is the change in GPE when the object moves from one point to another.
 
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