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Muon

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Exercise

https://texercises.com/exercise/muon/

Question

Solution

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The following quantities appear in the problem: Zeit \(t\) / Geschwindigkeit \(v\) / Strecke \(s\) /

The following formulas must be used to solve the exercise: \(s = vt \quad \) \(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \quad \) \(t = \gamma t_0 \quad \)

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Exercise:
A muon half-life taO created hO above the surface of the Earth reaches the surface at the of its half-life. Calculate the distance to the Earth in the muon’s rest frame.

Solution:
The proper distance i.e. the distance in the rest frame of the Earth can be expressed as lambda v t v gamma tau beta c gamma tau sqrt-fracgamma^ gamma ctau sqrtgamma^- ctau It follows for the Lorentz factor gamma sqrt+leftfraclambdactauright^ The contracted length i.e. in the rest frame of the muon is thus ell fraclambdagamma fraclambdasqrt+leftfraclambdactauright^ hmF leftsqrtfrach^+fracncctimesta^right^- resulthmP This is only slightly less than the distance the muon could travel within its half-life if it was moving at the speed of light: sscellmax lmaxF ncctimesta lmaxP

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Contained in these collections:

Zeitdilatation Lorentz-Faktor gleichförmige Bewegung by TeXercises

5 | 6
Relativistic Kinematics by by

10 | 15
Relativistic Kinematics (BC) by by

9 | 9

Attributes & Decorations

Branches	special relativity
Tags	length contraction, lorentz factor, muon
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Difficulty	(3, default)
Points	0 (default)
Language	(English)
Type	Calculative / Quantity
Creator	by
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