A sealed cabin is carried by a rocket in empty space
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 sealed cabin is carried by a rocket in empty space, far from every gravitating mass. The rocket's engines give the cabin a constant proper acceleration of 20.0ms−2, and the crew call the direction of that acceleration "up". A laser fixed to one wall fires a short pulse exactly "horizontally" (perpendicular to the acceleration) across the cabin, whose width is 5.00m, to the opposite wall. Work to first order in aL/c2.
((a)) Predict the reading of an accelerometer bolted to the cabin floor.
((b)) Predict how far below the firing height the pulse strikes the far wall, as measured in the cabin.
((c)) Predict the angle, measured in the cabin, through which the beam's direction has been turned by the time it reaches the far wall.