Question

A barn of length 10m in its own rest frame sits on the earth. A 10m proper length rocket attempts to fly through the barn at a speed of 0.8c, but the doors on both ends of the barn close simultaneously trapping it inside.

a) What is the length of the rocket measured in the barn reference frame? What is the length of the barn measured in the rocket reference frame?

b) How far out of syncronization are the door closings in the rocket reference frame? Which one appears earlier? How far would the barn travel in the rocket reference frame in this amount of time?

Answer 1

Cinen the bann The bann l=lom l=10m in its . The proper length of own frame / earth frame. ' Rocuet's Propen length Speed V-0.86, space time diagn ane 62 = 10m, which moves with - use bann reference Frame: Lorentz transformation of length contraction. length of recuet l = ln fr ve l2 = 1om fl- og?' B lom x 0.6 = 6m * In Rocket Reference frame: Here the obsenver at rocket frame saw that the barn moves towards with V=90:8( so, Length of the bonn i = l T - V? ů= 10m VT-o.ge ☺ = 10m x0.6 = 6 m Fenste O In the rocket's reference frame : Here the - Por to nochet's is length lo- com, but - the length of bam is contracted le. = 6m (10) ele. lz > ei

Diagrame 2 w smo L ' - - In figure o is the - The syncronization of point doons of center of coincidence. - are closing is (ere both the doons 0.8% 3 1. The front doon - At this time Open is an event appears earlier, the barn would travel (10-6)= ym.