Wells sets a 4.0 kg toolbox on a workbench 1.0 m above the garage floor. He works out its GPE from the floor and gets 39.2 J. Xenia measures the same toolbox from the benchtop instead, and gets 0 J.
Same toolbox, same bench, two different answers. Who is wrong?
Check Wells first. The weight: 4.0 × 9.8 = 39.2 N. From the floor, h = 1.0 m, so GPE = 39.2 × 1.0 = 39.2 J.
Check Xenia. From the benchtop, the toolbox sits at h = 0, so its GPE is 0 J.
Both used GPE = mgh correctly. They chose different places to call h = 0.
Now lift the toolbox from the bench to a shelf 2.0 m above the floor, and run the numbers both ways.
Wells's ledger: GPE goes from 39.2 J to 39.2 × 2.0 = 78.4 J. The gain is 78.4 − 39.2 = 39.2 J.
Xenia's ledger: the shelf sits 1.0 m above her zero, so GPE goes from 0 J to 39.2 × 1.0 = 39.2 J. The gain is the same 39.2 J.
The gains agree because only the change in height enters them. The starting level cancels out.
Pick the floor, the benchtop, or the sidewalk outside. Say which level you chose, then track changes from it.
Vada computes a hanging lantern's GPE measured from the porch floor. Yael computes the same lantern's GPE measured from the garden path below the porch. Their values differ. Who is wrong?
A gym stores a 10 kg ball on a rack 1.5 m above the gym floor. Taking the rack shelf itself as h = 0, what is the ball's GPE?
The chosen zero level is the rack shelf.
The ball sits at that level, so h = 0 m.
GPE = mgh with h = 0 gives 0 J.
GPE = (10 × 9.8) × 0 = 0
The ball's GPE, measured from the rack shelf, is 0 J.
The same 10 kg ball is lifted from the 1.5 m rack to a 2.0 m rack. Take g = 9.8 N/kg. How much GPE does it gain?
Only the change in height matters: 2.0 − 1.5 = 0.5 m.
The weight: 10 × 9.8 = 98 N.
The gain: 98 × 0.5 = 49 J.
The ball gains 49 J, whichever zero level is chosen.
A 3.0 kg planter is lifted from a 1.0 m bench to a 2.0 m shelf. Take g = 9.8 N/kg. Enter the planter's GPE gain, in J.
Wells records his backpack's GPE as 0 J while it sits on a 1.2 m table. Can his record be right?
A drone hovers 10 m above a hilltop park lawn. The park sits 40 m above a river. Taking the lawn as h = 0, which value is the drone's h?
A 7.0 kg toolbox is raised from a 0.5 m shelf to a 1.5 m workbench. Take g = 9.8 N/kg. Enter its GPE gain, in J.
Two students compute the GPE of the same hanging sign. One measures from the sidewalk and gets 150 J. The other measures from a balcony and gets 60 J. Why can both be right?