a) An earth observer measures the length of a rod to be one meter with her measu
ID: 1326825 • Letter: A
Question
a) An earth observer measures the length of a rod to be one meter with her measuring stick. What would the earth observer measure for this length if the rod were on a spaceship moving at a constant velocity of 0.5 c relative to the earth? Assumed the rod is aligned along the direction of motion.
b) An earth observer measures a time interval of one hour(=3600s) on her clock. What would be the earth observer measure for this time interval if the clock were on a spaceship moving at a constant velocity of 0.5 c relative to the earth?
Explanation / Answer
(a)
from the lenght contraction
L = L' root (1- (v/c)^2
= ( 1.0 m) root ( 1- ( 0.5c/c)^2
=0.866 m
(b)
from the timdilation equation
t = t'/root (1- (v/c)^2
=( 3600 s) /root ( 1- ( 0.5c/c)^2
=4156.92 s
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