Solving Two Hours of Christmas Arguing: PE on a Cliff and Ramp?

[jimprince]

Simple Question??

Here is a question I argued with my family for over two hours Christmas evening...
If a man is standing on the edge of a plateau overlooking a 1000' cliff, does he have the SAME potential energy of a man of the same mass at the same elevation on the plateau but 2 miles from the cliff?
Now, what if you put an object on the edge of a ramp, does it have the same PE as an object of the same mass on the edge of the ramp but inside of an immovable box? Would the box change the PE?
We have an "airline ticket to Florida" wager on this argument so any details would be appreciated.
Thanks!

 

[jimprince]

PS: Our reference point is the bottom of the cliff.

 

[Doc Al]

Near the Earth's surface, the gravitational PE is just mgh: it just depends on the height with respect to some arbitrary reference point. So, ignoring any trivial differences in g from place to place, if two equal masses have the same height then they have the same PE.

If a man is standing on the edge of a plateau overlooking a 1000' cliff, does he have the SAME potential energy of a man of the same mass at the same elevation on the plateau but 2 miles from the cliff?

Sure, why not?

Now, what if you put an object on the edge of a ramp, does it have the same PE as an object of the same mass on the edge of the ramp but inside of an immovable box? Would the box change the PE?

Makes no difference.

 

[Saketh]

Now, what if you put an object on the edge of a ramp, does it have the same PE as an object of the same mass on the edge of the ramp but inside of an immovable box? Would the box change the PE?

If the box is assumed to be massless (or at least of negligible mass), then there would be no change in PE. Otherwise, the box could be contrived to have its own, non-negligible gravitational field, in which case the potential energy of the object on the ramp would change.

Barring such an odd situation, there would be no change in the PE of the box.

 

[disregardthat]

You shouldn't add more than the strictly needed factors. At least not when they hardly makes a difference.

 

[russ_watters]

I predict that you will not be able to resolve the dispute due to an inability to agree on how irrelevant factors being added to the scenario confuse and change the actual scenario.