Don't understand the choice of zero-potential level

[KFC]

Hi there, I textbook it said the zero potential level can be chosed arbitrarily. Let's take the gravity as example, if an box is moving from the top of a incline to the bottom without considering the friction, suppose the center of mass located in the geometric center of the box. Someone pick the horizontal level as the zero potential level. But if I setup my coordinate system with the origin attached to the top of the incline, x axis along the incline and y axis perpendicular to the incline, so every point the box moved to will have y=0, in this case, can I set everywhere on the surface of the incline (i.e. y=0) the gravity potential is ZERO? If no, how to find gravity potential in above-mentioned coordinate system?

Thanks

[Monocles]

No, setting the coordinate system like that will just mean that you will make potential energy a function of both x and y instead of just y. Potential is independent of the chosen coordinate system.

[KFC]

No, setting the coordinate system like that will just mean that you will make potential energy a function of both x and y instead of just y. Potential is independent of the chosen coordinate system.

Thanks. So after setting up the coordinate system, shall we always chose the origin as the zero potential point?

[Redbelly98]

Thanks. So after setting up the coordinate system, shall we always chose the origin as the zero potential point?

It's usually easiest to do that, but it is not necessary.