Q81 · Practice questionComplex unfamiliar5 marks
QUESTION 81 (5 marks)
Muons created high in Earth’s atmosphere travel at . Their proper mean lifetime is . Calculate the mean lifetime and mean travel distance in the Earth frame. Compare the result with a classical calculation that ignores time dilation.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
and ; classically the distance would be only .
Worked solution
Therefore
Earth-frame distance:
Without time dilation,
Relativistic time dilation therefore explains why many more muons can reach low altitude than a classical lifetime estimate suggests.
Calculates gamma.
Calculates dilated lifetime.
Calculates relativistic distance.
Calculates classical distance.
Compares and interprets results.
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