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Relativistic Mechanics

Problem 1.360

Two rods having the same proper length \(l_{0}\) move lengthwise toward each other parallel to a common axis with the same velocity \(v\) relative to the laboratory frame of reference. What is the length of each rod in the reference frame fixed to the other rod?

Reveal Answer
l=l0(1−β2)/(1+β2), where β=v/cl=l_{0}\left(1-\beta^{2}\right) /\left(1+\beta^{2}\right), \text { where } \beta=v / c
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