YF_ISM_37

YF_ISM_37 - RELATIVITY 37 Figure 37.1 37.1. IDENTIFY and...

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37-1 R ELATIVITY 37.1. IDENTIFY and SET UP: Consider the distance A to O and B to O as observed by an observer on the ground (Figure 37.1). Figure 37.1 EXECUTE: Simultaneous to observer on train means light pulses from and AB ′′ arrive at O at the same time. To observer at O light from A has a longer distance to travel than light from B so O will conclude that the pulse from () AA started before the pulse at () . BB To observer at O bolt A appeared to strike first. EVALUATE: Section 37.2 shows that if they are simultaneous to the observer on the ground then an observer on the train measures that the bolt at B struck first. 37.2. (a) 2 1 γ 2.29. 1 (0.9) == 66 γ (2.29) (2.20 10 s) 5.05 10 s. t τ −− × = × (b) 86 3 (0.900) (3.00 10 m s) (5.05 10 s) 1.36 10 m 1.36 km. dv t × × = × = 37.3. IDENTIFY and SET UP: The problem asks for u such that 0 1 / . 2 tt ΔΔ = EXECUTE: 0 22 1/ t t uc Δ Δ= gives () 2 2 88 0 1 1 / (3.00 10 m/s) 1 2.60 10 m/s 2 t t ⎛⎞ =− Δ Δ = × = × ⎜⎟ ⎝⎠ ; 0.867 u c = Jet planes fly at less than ten times the speed of sound, less than about 3000 m/s. Jet planes fly at much lower speeds than we calculated for u . 37.4. IDENTIFY: Time dilation occurs because the rocket is moving relative to Mars. SET UP: The time dilation equation is 0 γ Δ=Δ , where t 0 is the proper time. EXECUTE: (a) The two time measurements are made at the same place on Mars by an observer at rest there, so the observer on Mars measures the proper time. (b) 0 2 1 (75.0 s) 435 s 1 (0.985) γμ μ Δ=Δ = = EVALUATE: The pulse lasts for a shorter time relative to the rocket than it does relative to the Mars observer. 37.5. (a) IDENTIFY and SET UP: 87 0 2.60 10 s; 4.20 10 s. × × In the lab frame the pion is created and decays at different points, so this time is not the proper time. EXECUTE: 2 2 00 2 says 1 tu t t ct = Δ 2 2 8 0 7 2.60 10 s 1 1 0.998; 0.998 4.20 10 s ut Δ× = = EVALUATE: , < as it must be, but u / c is close to unity and the time dilation effects are large. (b) IDENTIFY and SET UP: The speed in the laboratory frame is 0.998 ; = the time measured in this frame is , t Δ so the distance as measured in this frame is du t EXECUTE: (0.998)(2.998 10 m/s)(4.20 10 s) 126 m d =×× = EVALUATE: The distance measured in the pion’s frame will be different because the time measured in the pion’s frame is different (shorter). 37
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37-2 Chapter 37 37.6. γ 1.667 = (a) 8 0 1.20 10 m 0.300 s. γγ (0.800 ) t t c Δ× Δ= = = (b) 7 (0.300 s) (0.800 ) 7.20 10 m. c (c) 0 0.300 s γ 0.180 s. t = (This is what the racer measures your clock to read at that instant.) At your origin you read the original 8 8 1.20 10 m 0.5 s. (0.800) (3 10 m s) × = × Clearly the observers (you and the racer) will not agree on the order of events! 37.7. IDENTIFY and SET UP: A clock moving with respect to an observer appears to run more slowly than a clock at rest in the observer’s frame. The clock in the spacecraft measurers the proper time 0 . t Δ 365 days 8760 hours. t = EXECUTE: The clock on the moving spacecraft runs slow and shows the smaller elapsed time.
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This note was uploaded on 03/14/2012 for the course MAE 162D taught by Professor Shaefer during the Spring '11 term at UCLA.

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YF_ISM_37 - RELATIVITY 37 Figure 37.1 37.1. IDENTIFY and...

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