Lifetime of a moving muon Example l: The mean lifetime of a muon at rest is 2.2X10-6S and it is traveling at v=0.6c relative to the lab. a) What is the mean lifetime measured in the lab? b)How far does it travel before decaying? Solution: a) ean lifetime at rest proper time △ △t=275×106s b) Distance travel before decaying d=△t=(.:8×103)(2,75×106=495m
Lifetime of a moving muon 11 Example1: The mean lifetime of a muon at rest is 2.2×10-6 s, and it is traveling at v=0.6c relative to the lab. a) What is the mean lifetime measured in the lab? b) How far does it travel before decaying? Solution: a) Mean lifetime at rest: proper time 0 2 2 1 / t t v c = − 6 0 5 2.75 10 s 4 t − = = b) Distance travel before decaying: ( )( ) 8 6 d v t 1.8 10 2.75 10 495m − = = =
Time dilation of space station Example2: a space station moves around the earth with v=7700m/s. a spaceman stays in the station for 100 days, how much younger will he become? Solution: Time dilation: At V/C △t Mtn×(1+3.3×10 5、2 (2.57×103) →At-4b=3.3×10×△6=0.029s Ignorable for human Correction of GPS time 12
Time dilation of space station 12 Example2: A space station moves around the Earth with v=7700m/s. A spaceman stays in the station for 100 days, how much younger will he become? Solution: Time dilation: 0 2 2 1 / t t v c = − 0 5 2 1 1 (2.57 10 ) t − = − ( ) 9 0 t 1 3.3 10− = + 9 0 0 t t t 3.3 10 0.029s − = = − Ignorable for human Correction of GPS time
Length contraction(1) Earth L △t=L0 △t =△t 1/C Earth Mars 13
Length contraction (1) 13 Earth Mars v L0 0 =t L v/ , Earth Mars v L v 2 2 0 1 / L t t v c v = = −
Length contraction(2) L 2 0 The length of an object is measured to be shorter when it is moving relative to the observer than when it is at rest 1)Proper length(measured at rest) 2) Not noticeable in everyday life 3)Relativistic effect universality 4) Occurs only along the direction of motion 14
Length contraction (2) 14 2 2 L L v c L = − = 0 0 1 / / The length of an object is measured to be shorter when it is moving relative to the observer than when it is at rest. 2) Not noticeable in everyday life 3) Relativistic effect & universality 1) Proper length (measured at rest) 4) Occurs only along the direction of motion