Potential gravitational energy coordinate axis

[Bunny-chan]

Homework Statement

I know that potential gravitational energy is relative to the reference point that I decide to choose (like in the picture below).

But then if, for instance, I set my reference point in the ceiling and my vertically down y-axis to be positive. What would the potential gravitational energy of an object falling from the ceiling and an object moving towards the celing be? This kind of makes me confused. I'd appreciate some insight on this matter.

Homework Equations

The Attempt at a Solution

 

[PeterDonis]

In order for us to help you, you need to at least make an attempt to write down the relevant equations and try a solution.

 

[Bunny-chan]

In order for us to help you, you need to at least make an attempt to write down the relevant equations and try a solution.

But I don't know how equations will help me to visualize this? I know that the work done on the mass in an object-Earth system is W = - \Delta U, and that in the reference point, the potential energy is 0, since what matters is actually the difference in potential energy.

In a vertically up y-axis, If I throw an object in the air, the gravitational potential energy of the object-Earth system will increase as it rises, and decrease as it falls down, considering the ground as reference, right? And if I consider the reference as a point as a certain height from the ground, and I drop an object from that point, the gravitational potential energy of the system will decrease too.

But now, I don't know if taking the positive y-axis to be vertically down will change the way this works. If I consider the same situations as above, dropping an object from the elevated point would actually mean I'm throwing it up? (Even though it's obvious I'm not, because the displacement it's in the same direction as gravity...).

 

[haruspex]

set my reference point in the ceiling and my vertically down y-axis to be positive. What would the potential gravitational energy of an object

You need to be consistent in the assignment of the positive direction, same for displacements, velcities, accelerations and forces.
Since W=∫F.ds, switching the positive direction for F and s leaves W unchanged.

 

[Bunny-chan]

You need to be consistent in the assignment of the positive direction, same for displacements, velcities, accelerations and forces.
Since W=∫F.ds, switching the positive direction for F and s leaves W unchanged.

So gravitational potential energy would still be negative when the object is falling?

 

[haruspex]

So gravitational potential energy would still be negative when the object is falling?

The change would still be negative, yes.

 

[Bunny-chan]

The change would still be negative, yes.

Thank you!