A lift runs in a tall building where the gravitational field strength is directed…
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 runs in a tall building where the gravitational field strength is g=9.80ms−2 directed downwards. An accelerometer is bolted to the lift floor; it reads the magnitude of the proper acceleration of the lift, that is, its acceleration measured in the momentarily comoving freely falling frame. All speeds are tiny compared with c, so relativistic corrections are ignored, and air resistance and friction are ignored. Give the accelerometer reading for each case.
((a)) The lift accelerates upwards at 2.50ms−2 relative to the building.
((b)) The lift accelerates downwards at 2.50ms−2 relative to the building.
((c)) The lift descends at a constant 3.00ms−1 relative to the building.
((d)) The cable snaps and the lift falls freely.
((e)) A windowless cabin far from all masses in deep space runs its engine so that no local experiment inside can tell its interior from the interior of the lift in case (a). What proper acceleration must the cabin have?