   Chapter 28, Problem 72PE

Chapter
Section
Textbook Problem

Construct Your Own ProblemConsider an astronaut traveling to another star at a relativistic velocity. Construct a problem in which you calculate the time for the trip as observed on the Earth and as observed by the astronaut. Also calculate the amount of mass that must be converted to energy to get the astronaut and ship to the velocity travelled. Among the things to be considered are the distance to the star, the velocity, and the mass of the astronaut and ship. Unless your instructor directs you otherwise, do not include any energy given to other masses, such as rocket propellants.

To determine

The time for the trip taken by an astronaut traveling to another star at a relativistic velocity as observed on the Earth and as observed by the astronaut. Also, the amount of mass that must be converted to energy to get the astronaut and ship to the velocity travelled is to be calculated.

Explanation

Let the speed of spaceship is v=0.9c and star is l0=5 ly mass of spaceship is 1000kg.

Given info:

m=1000 kg

l0=5 ly

h=6.26×1034 Js1

v=0.9c

c=3×108 ms1

Formula used:

For kinetic energy in of the relativistic particle, the relation between energy and velocity is

K.E(γ1)mc2

Relativistic factor is

γ11 v 2 c 2

Total relativistic particle energy is

EΔmc2

Mass of the particle is

ΔmEc2

Time taken is

tlv

Length of the observer from spaceship is

ll0(1v2c2)

Calculation:

Light year converted into meter first

l0=5 lyl0=5×1016 m

Substituting the length and velocity in relation with time observed from earth, we get

tl0vt5× 10 163× 108t1.67×108 s

Length of the observer from spaceship is

l5×1016(1 (0

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