The height in the potential gravitational energy

[terryds]

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) ?

 

[Doc Al]

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.

 

[terryds]

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?

 

[Doc Al]

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.

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.

 

[PJC01]

I can clarify that the height in the formula for potential gravitational energy refers to the vertical distance from the bottom to the center of gravity of the object. This is because the center of gravity is the point at which the gravitational force acts on the object. Therefore, the potential gravitational energy is given by the formula mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the vertical distance from the bottom to the center of gravity.

In the case of a sphere with mass m and radius r placed at height h, the potential gravitational energy would be mgh, where h is the vertical distance from the bottom to the center of gravity of the sphere.

It is important to note that the potential gravitational energy is a measure of the energy an object has due to its position in a gravitational field. It does not depend on the size or shape of the object, only its mass and the distance from the center of gravity. Therefore, the potential gravitational energy for an object placed at a certain height will be the same regardless of whether it is a sphere or any other shape.

I hope this clarifies any confusion regarding the height in the formula for potential gravitational energy. As scientists, it is important to use precise and accurate language to avoid any misunderstandings.