Chapter 20 - Relativity - Davidson Physics

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Announcements Review The Twin Paradox Length Contraction Final QuestionsMuons and time dilationMuons are created in the Earth’s atmosphere at an altitude of 10-15 kilometers and approach the Earthwith a speed near that of light (about v = 0.998c).Muons are unstable, and quickly decay into other particles (average lifetime of a muon at rest is about∆t 0 = 2.20 × 10 −6 seconds)In this time, a muon would travel a distance d = v∆t 0 = 659 metersSince this distance is small we would expect very few of them to reach the Earth’s surface (but anappreciable number of muons do reach the surface!)We haven’t taken into account time dilationMuons decay by their own internal clockTherefore, in a time interval ∆t 0 = 2.20 × 10 −6 seconds, an Earth clock reads a time interval∆t =t√1 − v 2 /c 2 = 2.20 × 10−6 s√1 − (0.998) 2 = 3.48 × 10 −5 sTherefore, on average, the muons travel a distance(d = v∆t = (0.998c) 3.48 × 10 −5 )s = 1.04 × 10 4 m = 10.4 kmRelativity
Announcements Review The Twin Paradox Length Contraction Final QuestionsMuons: continuedHowever, a hypothetical observer on the muon would not invoke time dilation, because in their frame ofreference they are not moving!Relativity
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Chapter 20 - Relativity - Davidson Physics

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