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Chapter37 - 1 From the time dilation equation t = t0(where...

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1. From the time dilation equation t = γ t 0 (where t 0 is the proper time interval, γ β = 1 1 2 / , and β = v / c ), we obtain β = F H G I K J 1 0 2 t t . The proper time interval is measured by a clock at rest relative to the muon. Specifically, t 0 = 2.2000 µ s. We are also told that Earth observers (measuring the decays of moving muons) find t = 16.000 µ s. Therefore, 2 2.2000 s 1 0.99050. 16.000 s µ β µ = =
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2. (a) We find β from γ β = 1 1 2 / : ( ) 2 2 1 1 1 1 0.14037076. 1.0100000 β γ = = = (b) Similarly, ( ) 2 1 10.000000 0.99498744. β = = (c) In this case, ( ) 2 1 100.00000 0.99995000. β = = (d) The result is ( ) 2 1 1000.0000 0.99999950. β = =
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