A lift cage is released from rest and falls freely down a tall evacuated shaft in a…
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · The equivalence principle and gravity as geometry · The equivalence principle and gravity as geometry
Relativity and Gravitation, Ch Accelerated observers, hyperbolic motion and the equivalence principle
Problem
A lift cage is released from rest and falls freely down a tall evacuated shaft in a building on Earth. Take the gravitational field in the shaft to be uniform with g=9.81ms−2 downward, ignore air resistance and ignore tidal effects across the cage. A laser fixed to one wall of the cage fires a short pulse horizontally across the cage, a width of 2.50m, while the cage is falling. Work to first order in gL/c2.
((a)) Predict the reading of an accelerometer inside the falling cage, and the reading of an identical accelerometer bolted to the shaft wall.
((b)) Predict how far below the firing height the pulse strikes the far wall of the cage, as measured by an observer inside the cage.
((c)) Predict how far the pulse falls below the horizontal straight line it started along, as measured relative to the building.