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Chapter 36: Q. 46 (page 1060)

Two events in reference frame S occur 10 ms apart at the same point in space. The distance between the two events is 2400 m in reference frame S鈥�.

a. What is the time interval between the events in reference frame S鈥�?

b. What is the velocity of S鈥� relative to S?

Short Answer

Expert verified

The time interval between the events in reference frame S鈥� is 12.8渭s.

The velocity of S鈥� relative to S is 0.625 c.

Step by step solution

01

Given information

We have given that, two events in reference frame S occur 10 ms apart at the same point in space. The distance between the two events is 2400 m in reference frame S鈥�.

02

Part(a) Step 1.

The spacetime interval between two events is invariant in all frames.

03

Step 2.

Equating the two spacetime intervals :

c2(螖t)2-(螖x)2=c2(螖t')2-(螖x')2

(300m渭s)2(10渭s)2-(0m)2=(300m渭s)2(螖t')2-(2400m)2

螖t'=12.8渭s

04

Part(b) Step 1

The event occurs at the same point in space, so 螖t'=螖味.

05

Step 2.

Hence :

螖t'=螖味1-v2c2

12.8渭s=10渭s1-v2c2

v=0.625c

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You are standing at x=9.0kmand your assistant is standing a x=3.0kmLightning bolt 1strikes atx=0kmand a lightning bolt 2strikes atx=12.0km. You see the flash from bolt 2att=10msand the flash from bolt1att=50ms According to your assistant, were the lightning strikes simultaneous? If not, which occurred first, and what was the time difference between the two?

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