An office worker has his lunch on the 53rd floor of an office building. In which case is the gravitational potential energy of t
he lunch-Earth system greatest? An office worker has his lunch on the 53rd floor of an office building. In which case is the gravitational potential energy of the lunch-Earth system greatest? The worker carried the lunch up to the 53rd floor in the elevator. The worker got a ride in a helicopter to the top of the 68-floor building and then carried the lunch down in the elevator to the 53rd floor? The Worker carried it up the stairs to the 53rd floor. Gravitational potential energy does not depend on the path taken.
Answer: In all cases, gravitational potential energy, respect from a common reference level (street level for instance) is the same.
Gravitational potential energy, comes from the action of the gravitational field, which is a conservative one.
This means, that if someone does work against the field (for instance lifting a weight from the ground to a given height), and then drops the weight, the work done by the field will be exactly the same.
Otherwise, the object would have remaining energy after returning to the starting point, which would violate the laws of physics, specially Thermodynamic's 2nd Law.
For this reason, the gravitational potential energy only depends from the height, and is independent from the path taken to reach there.