Special Relativity - Length Contraction

Questions 69-71

A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.

The length of the garage in the car’s rest frame is

A. 2.4 m
B. 4.0 m
C. 5.0 m
D. 8.3 m
E. Not determinable from the data given

(GR8677 #70)

Solution:

Length contraction: L = L₀/γ

Given for the garage, L₀ = 4 m
From problem GR8677 #69 → γ = 5/3

L = 4/(5/3) = 12/5 = 2.4 m

Answer: A