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Chapter 37: Q3P (page 1145)

You wish to make a round trip from Earth in a spaceship, traveling at constant speed in a straight line for exactly 6 months (as you measure the time interval) and then returning at the same constant speed. You wish further, on your return, to find Earth as it will be exactly 1000 years in the future. (a) To eight significant figures, at what speed parameter βmust you travel? (b) Does it matter whether you travel in a straight line on your journey?

Short Answer

Expert verified

(a) The speed parameter is 0.99999950.

(b) It does not matter whether the journey is in straight line or not.

Step by step solution

01

Identification of given data

The duration of traveling in spaceship is t0=6months=0.5y

The duration passed on Earth for future is t=1000y

The Lorentz factor is used to find the speed parameter which is the ratio of the speed of particle with speed of light.

02

Determination of speed parameter  (a) 

The speed parameter for travel is given as:

β=1-2t0t2

Substitute all the values in equation.

β=1-20.5y0.999999502β=0.99999950

Therefore, the speed parameter is 0.99999950 .

03

Effect of straight-line journey in travel  (b) 

The speed parameter is independent from the acceleration of spaceship so speed parameter does not change with change in path other than straight line. It does not matter that journey is in straight line or in any other path.

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Most popular questions from this chapter

Question: Apply the binomial theorem (Appendix E) to the last part of Eq. 37-52 for the kinetic energy of a particle. (a) Retain the first two terms of the expansion to show the kinetic energy in the form

K=(firstterm)+(secondterm)

The first term is the classical expression for kinetic energy. The second term is the first-order correction to the classical expression. Assume the particle is an electron. If its speed vis c/20, what is the value of (b) the classical expression and (c) the first-order correction? If the electron’s speed is 0.80s, what is the value of (d) the classical expression and (e) the first-order correction? (f) At what speed parameter βdoes the first-order correction become 10%or greater of the classical expression?

Question: A certain particle of mass m has momentum of magnitude mc .What are (a) β, (b)γ, and (c) the ratioK/E0?

Observer Sreports that an even occurred on thexaxis of his reference frame at x=3.00×108mat time t=2.50s. ObserverS'and her frame are moving in the positive direction of the xaxis at a speed of0.400c. Furtherx=x'=0att=t'=0. What are the (a) spatial and (b) temporal coordinate of the event according to S'? If S'were, instead, moving in the negative direction of thexaxis, what would be that (c) spatial and (d) temporal coordinate of the event according toS'?

Figure 37-27 is a graph of intensity versus wavelength for light reaching Earth from galaxy NGC 7319, which is about 3×108light-years away. The most intense light is emitted by the oxygen in NGC 7319. In a laboratory that emission is at wavelength λ=513nm, but in the light from NGC 7319 it has been shifted to 525 nm due to the Doppler effect (all the emissions from NGC 7319 have been shifted). (a) What is the radial speed of NGC 7319 relative to Earth? (b) Is the relative motion toward or away from our planet?

Question: What isβ for a particle with (a) K=2.00Eoand (b)E=2.00Eo ?
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