chapter 37 solutions - R ELATIVITY 37.1. I DENTIFY and S ET...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: R ELATIVITY 37.1. I DENTIFY and S ET U P : Consider the distance A to OO and B to OO as observed by an observer on the ground (Figure 37.1). Figure 37.1 E XECUTE : Simultaneous to observer on train means light pulses from and A B O arrive at OO at the same time. To observer at O light from AO has a longer distance to travel than light from BO so O will conclude that the pulse from ( ) A AO started before the pulse at ( ). B BO To observer at O bolt A appeared to strike first. E VALUATE : 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 BO struck first. 37.2. (a) 2 1 γ 2.29. 1 (0.9) = =- 6 6 γ (2.29) (2.20 10 s) 5.05 10 s. t τ-- = = x = (b) 8 6 3 (0.900) (3.00 10 m s) (5.05 10 s) 1.36 10 m 1.36 km. d vt- = = = ; = 37.3. I DENTIFY and S ET U P : The problem asks for u such that 1 / . 2 t t ∆ ∆ = E XECUTE : 2 2 1 / t t u c ∆ ∆ =- gives ( 29 2 2 8 8 1 1 / (3.00 10 m/s) 1 2.60 10 m/s 2 u c t t =- ∆ ∆ =- = ; 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. I DENTIFY : Time dilation occurs because the rocket is moving relative to Mars. S ET U P : The time dilation equation is t t γ ∆ = ∆ , where t is the proper time. E XECUTE : (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) 2 1 (75.0 s) 435 s 1 (0.985) t t γ μ μ ∆ = ∆ = =- E VALUATE : The pulse lasts for a shorter time relative to the rocket than it does relative to the Mars observer. 37.5. (a) I DENTIFY and S ET U P : 8 7 2.60 10 s; 4.20 10 s. t t-- ∆ = x ∆ = ; In the lab frame the pion is created and decays at different points, so this time is not the proper time. E XECUTE : 2 2 2 2 2 says 1 1 / t u t t c t u c ∆ ∆ ∆ =- = ∆- 2 2 8 7 2.60 10 s 1 1 0.998; 0.998 4.20 10 s u t u c c t-- ∆ =- =- = = ∆ E VALUATE : , u c < as it must be, but u / c is close to unity and the time dilation effects are large. (b) I DENTIFY and S ET U P : The speed in the laboratory frame is 0.998 ; u c = the time measured in this frame is , t ∆ so the distance as measured in this frame is d u t = ∆ E XECUTE : 8 7 (0.998)(2.998 10 m/s)(4.20 10 s) 126 m d- = = E VALUATE : The distance measured in the pion’s frame will be different because the time measured in the pion’s frame is different (shorter). 37-1 37 37-2 Chapter 37 37.6. γ 1.667 = (a) 8 1.20 10 m 0.300 s. γ γ(0.800 ) t t c ∆ ∆ = = = (b) 7 (0.300 s) (0.800 ) 7.20 10 m. c = (c) 0.300 sγ 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....
View Full Document

This note was uploaded on 04/14/2008 for the course PHYS 2303 taught by Professor Hoffman during the Fall '07 term at University of Texas at Dallas, Richardson.

Page1 / 20

chapter 37 solutions - R ELATIVITY 37.1. I DENTIFY and S ET...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online