a) Imagine that a relativistic train travels past your lecture room at a speed o
ID: 1561862 • Letter: A
Question
a) Imagine that a relativistic train travels past your lecture room at a speed of 0.926 c. The passengers of the train claim that when they measure the length of the train using standard meter bars found on the train, the length comes out to be 73.8 m. What would be the length of the train in the frame of the lecture room if you measured it?
b)How long would a regular 50 minute long class in the lecture room last for the passengers of the train if they measured it while sitting on the train? (in min)
Explanation / Answer
from equation of length contraction ( Lorentz transformation)
L = Lo*sqrt(1-(v/c)^2)
Lo = length measure in moving frame
L = length measured in rest frame
L = 73.8*sqrt(1-0.926^2)
L = 27.8 m
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from equation of time dilation
T = T'/sqrt(1-(v/c)^2)
T' = time on space ship
T = time on earth = 50 min
v = 0.6c
50 = T'/sqrt(1-0.926^2) = 18.87 min
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