Chapter 37 - 37.1 If O ′ sees simultaneous flashes then O...

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Unformatted text preview: 37.1: If O ′ sees simultaneous flashes then O will see the ) A A( ′ flash first since O would believe that the A ′ flash must have traveled longer to reach O ′ , and hence started first. 37.2: a) . 29 . 2 ) 9 . ( 1 1 γ 2 =- = s. 10 5.05 s) 10 20 . 2 ( ) 29 . 2 ( γ 6 6-- × = × = = τ t b) km. 1.36 m 10 1.36 s) 10 05 . 5 ( ) s m 10 00 . 3 ( ) 900 . ( 3 6 8 = × = × × = =- vt d 37.3: +- ≈- =- 2 2 2 1 2 2 2 2 2 1 ) 1 ( 1 c u c u c u s. 10 00 . 5 ) ( ) s m 10 2(3.00 (3600) hrs) 4 ( ) s m 250 ( 2 ) )( 1 1 ( ) ( 9 2 8 2 2 2 2 2- × = ∆- ∆ ⇒ × ⋅ = ∆ = ∆-- = ∆- ∆ ⇒ t t t c u t c u t t The clock on the plane shows the shorter elapsed time. 37.4: . 79 . 4 ) 978 . ( 1 1 γ 2 =- = ms. 0.395 s 10 3.95 s) 10 4 . 82 ( ) 79 . 4 ( γ-4 6 = × = × = ∆- t 37.5: a) 2 2 2 2 2 1 1 ∆ ∆ =- ⇒- ∆ = ∆ t t c u c u t t 2 2 42 6 . 2 1 1 - = ∆ ∆- = ⇒ c t t c u . 998 . c u = ∴ b) m. 126 s) 10 (4.2 ) s m 10 00 . 3 ( ) 998 . ( 7 8 = × × = ∆ = ∆- t u x 37.6: 667 . 1 γ = a) s. 300 . ) 800 . ( γ m 10 20 . 1 γ 8 = × = ∆ = ∆ c t t b) m. 10 7.20 ) (0.800 s) 300 . ( 7 × = c c) s. 180 . γ s 300 . = = ∆ t (This is what the racer measures your clock to read at that instant.) At your origin you read the original s. 5 . ) s m 10 (3 (0.800) m 10 20 . 1 8 8 = × × Clearly the observes (you and the racer) will not agree on the order of events! 37.7: yr) (1 s m 10 3.00 s m 10 4.80 1 1 2 8 6 2 2 × ×- = ∆- = ∆ t c u t hrs. 1.12 yr ) 10 28 . 1 ( ) ( 4 = × = ∆- ∆ ⇒- t t The least time elapses on the rocket’s clock because it had to be in two inertial frames whereas the earth was only in one. 37.8: a) The frame in which the source (the searchlight) is stationary is the spacecraft’s frame, so 12.0 ms is the proper time. b) To three figures, . c u = Solving Eq. (37.7) for c u in terms of , γ . γ 2 1 1 ) γ 1 ( 1 2 2- ≈- = c u Using . 998 . gives ms 190 ms . 12 γ 1 = = ∆ ∆ = c u t t 37.9: 00 . 6 ) 9860 . ( 1 1 ) ( 1 1 γ 2 2 =- =- = c u a) km. 17 . 9 6.00 km 55 γ = = = l l b) In muon’s frame: %. 1 . 7 071 . 17 . 9 651 . % km. 0.651 s) 10 20 . 2 )( 9860 . ( 6 = = = = ⇒ = × = ∆ =- h d c t u d c) In earth’s frame: %. 1 . 7 km 55.0 km 90 . 3 % km 3.90 s) 10 )(1.32 (0.9860 s 10 1.32 s)(6.00) 10 2 . 2 ( γ 5 5 6 = = ′ ′ = ⇒ = × = ∆ = ′ ⇒ × = × = ∆ = ∆--- h d c t u d t t 37.10: a) s. 10 1.51 0.99540 m 10 4.50 4 4- × = × = c t km. 4.31 10.44 km 45 γ 10.44 (0.9954) 1 1 γ ) 2 = = = ′ =- = h h b c) s; 10 1.44 γ and s, 10 1.44 0.99540 5 5-- × = × = ′ t c h so the results agree but the particle’s lifetime is dilated in the frame of the earth. 37.11: a) m 3600 = l m. 3568 m)(0.991) (3600 ) s m 10 00 . 3 ( ) s m 10 00 . 4 ( 1 ) m 3600 ( 1 2 8 2 7 2 2 = = × ×- =- = ⇒ l c u l l ) b . s 10 9.00 s m 10 4.00 m 3600 5 7- × = × = = ∆ u l t c) . s 10 8.92 s m 10 4.00 m 3568...
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This homework help was uploaded on 02/26/2008 for the course PHYS 11 and 21 taught by Professor Hickman during the Spring '08 term at Lehigh University .

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Chapter 37 - 37.1 If O ′ sees simultaneous flashes then O...

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