   Chapter 28, Problem 59PE

Chapter
Section
Textbook Problem

(a) Show that ( p c ) 2 / ( m c 2 ) 2 = γ 2 − 1 . This means that at large velocities p c > > m c 2 . (b) Is E ≈ p c when γ = 30.0 , as for the astronaut discussed in the twin paradox?

To determine

(a)

To show:

(pc)2(mc2)2=γ21.

Explanation

Formula used:

The energy momentum relation is,

E2=p2c2+m2c4    ...... (1)

The total energy expression is,

E=γmc2    ...... (2)

From equation (1) and (2).

(γmc2)2=p2c2+m2c4γ2m2c4=p2c2+

To determine

(b)

The given expression pcEis correct or not.

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