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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′.

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

b. What is the velocity of S′ relative to S?

Short Answer

Expert verified

The time interval between the events in reference frame S′ is 12.8μs.

The velocity of S′ 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′.

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(Δt)2-(Δx)2=c2(Δt')2-(Δx')2

(300mμs)2(10μs)2-(0m)2=(300mμs)2(Δt')2-(2400m)2

Δt'=12.8μs

04

Part(b) Step 1

The event occurs at the same point in space, so Δt'=Δζ.

05

Step 2.

Hence :

Δt'=Δζ1-v2c2

12.8μs=10μs1-v2c2

v=0.625c

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