Babumoshai: pleasedon\'t put your unjustified answer hereagain!!! Muons created
ID: 1757191 • Letter: B
Question
Babumoshai: pleasedon't put your unjustified answer hereagain!!!Muons created at rest in the laboratory are found to have a meanlifetime of 2s and the
average height of the outer edge of earth’s atmosphere is103km. Hint: Keep at least 6 decimal
places in your calculations. More is better in this case.
a) In order for a muon created in the upper atmosphere to reach theplanetary surface, what
relative velocity must it have? Express your answer as a fractionof c
b) How long does the trip take in the muon reference frame? Is thisa proper time? Explain.
c) Determine the atmosphere thickness in the muon reference frame.Is this a proper length?
Explain.
LIFESAVER rating will be awarded if you show ALLWORK, and explain your reasoning.
Explanation / Answer
Approximately 27 of the 560 muons sampled lasted for 6.3mseconds or longer. The incident speeds of the muons weredetermined using a specific thickness of lead plate before beingcaptured and brought to rest. The approximate speeds of the muonswere very close to the speed of light. (0.998c)
The lab was then moved to sea level and a muon count was takenfor 1 hour. A simple calculation was performed to determine theexpected number of captured muons using the time to reach theground from 1900m.
Approx muon speed of approx. 3 x108m/s
Vertical distance of 1900m.
The corresponding time = 6.3 mseconds.
This should correspond to approximately 27 muons captured in 1hour according to the data on top of Mt Washington.
However after a 1-hour count Frisch and Smith recordedapprox. 410 muons at sea level.
This suggests that the muons clock registered only 0.7 msecondsof elapsed time.
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