Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
bartleby

Videos

Question
Book Icon
Chapter 26, Problem 67P

(a)

To determine

The speed of the ship travelling according to an Earth observer.

(a)

Expert Solution
Check Mark

Answer to Problem 67P

The speed of the ship travelling according to an Earth observer is 0.625c_.

Explanation of Solution

The time elapse between the two events is 50.0ns, the length of the ship is 12.0m.

Let us use the symbols with primes for the astronaut’s frame and symbols without primes for the Earth’s frame. Earth measures the proper time between the events since they occur at the same location in that frame so that Δt0=Δt which is 50.0ns. The astronaut’s measures the proper length of the ship since it is at rest in that frame so that L=L0 which is 12.0m.

Write the expression for the contracted length in the Earth’s frame.

    L=L0γ                                                                                                                       (I)

Here, L is the contracted length in the Earth frame, L0 is the proper length of the ship, γ is the Lorentz factor.

Write the expression for the speed of the ship measured in the Earth’s frame.

    v=LΔt                                                                                                                        (II)

Here, v is the speed of the ship measured in the Earth’s frame, Δt is the change in time.

Use equation (I) in equation (II).

    v=L0γΔt                                                                                                                   (III)

Rearrange the above equation,

    vγ=L0Δt                                                                                                                  (IV)

Write the expression for the Lorentz factor.

    γ=11v2/c2                                                                                                        (V)

Here, v is the speed of the spaceship, c is the speed of light.

Conclusion:

Substitute 12.0m for L0, and 50.0ns for Δt in equation (IV).

    vγ=12.0m/s50.0ns=12.0m/s50.0ns×1s1×109ns=2.40×108m/s×1c3×108m/s=0.800c                                                                            (VI)

Use equation (V) and (VI) in equation (IV)and solve for to v.

    v(11v2/c2)=0.800cv2=(0.800c)2(1v2/c2)v=0.6401.640c=0.625c

Therefore, the speed of the ship travelling according to an Earth observer is 0.625c_.

(b)

To determine

The elapsed time between light flashes in the astronaut’s frame of reference.

(b)

Expert Solution
Check Mark

Answer to Problem 67P

The elapsed time between light flashes in the astronaut’s frame of reference is 64.0ns_.

Explanation of Solution

The clock measures the proper time interval Δt0 in the reference frame in which the clock is at rest. In any other frame, the time interval is longer.

Write the expression for the time dilation.

    Δt=γΔt0                                                                                                              (VII)

Here, Δt is the time elapsed in the astronauts frame.

Use equation (V) in equation (VII),

    Δt=Δt1v2c2                                                                                                       (VIII)

Conclusion:

Substitute 50.0ns for Δt and 0.625c for v in equation (VIII) to find Δt.

    Δt=50.0ns1(0.625c)2c2=64.0ns

Therefore, the elapsed time between light flashes in the astronaut’s frame of reference is 64.0ns_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 26 Solutions

Physics

Ch. 26 - Prob. 1CQCh. 26 - Prob. 2CQCh. 26 - Prob. 3CQCh. 26 - Prob. 4CQCh. 26 - Prob. 5CQCh. 26 - Prob. 6CQCh. 26 - Prob. 7CQCh. 26 - Prob. 8CQCh. 26 - Prob. 9CQCh. 26 - Prob. 10CQCh. 26 - Prob. 11CQCh. 26 - Prob. 12CQCh. 26 - Prob. 1MCQCh. 26 - Prob. 2MCQCh. 26 - Prob. 3MCQCh. 26 - Prob. 4MCQCh. 26 - 5. Which best describes the proper time interval...Ch. 26 - Prob. 6MCQCh. 26 - Prob. 7MCQCh. 26 - Prob. 8MCQCh. 26 - Prob. 9MCQCh. 26 - Prob. 1PCh. 26 - Prob. 2PCh. 26 - Prob. 3PCh. 26 - Prob. 4PCh. 26 - Prob. 5PCh. 26 - Prob. 6PCh. 26 - Prob. 7PCh. 26 - Prob. 8PCh. 26 - Prob. 9PCh. 26 - Prob. 10PCh. 26 - Prob. 11PCh. 26 - Prob. 12PCh. 26 - Prob. 13PCh. 26 - Prob. 14PCh. 26 - Prob. 15PCh. 26 - Prob. 16PCh. 26 - Prob. 17PCh. 26 - Prob. 18PCh. 26 - Prob. 19PCh. 26 - Prob. 20PCh. 26 - Prob. 21PCh. 26 - Prob. 22PCh. 26 - Prob. 23PCh. 26 - Prob. 24PCh. 26 - Prob. 25PCh. 26 - Prob. 26PCh. 26 - Prob. 27PCh. 26 - Prob. 28PCh. 26 - Prob. 29PCh. 26 - Prob. 30PCh. 26 - Prob. 31PCh. 26 - Prob. 32PCh. 26 - Prob. 33PCh. 26 - Prob. 34PCh. 26 - Prob. 35PCh. 26 - Prob. 36PCh. 26 - Prob. 37PCh. 26 - Prob. 38PCh. 26 - Prob. 39PCh. 26 - 40. A white dwarf is a star that has exhausted its...Ch. 26 - Prob. 41PCh. 26 - Prob. 42PCh. 26 - Prob. 43PCh. 26 - Prob. 44PCh. 26 - Prob. 45PCh. 26 - Prob. 46PCh. 26 - Prob. 47PCh. 26 - Prob. 48PCh. 26 - Prob. 49PCh. 26 - Prob. 50PCh. 26 - Prob. 51PCh. 26 - Prob. 52PCh. 26 - Prob. 53PCh. 26 - Prob. 54PCh. 26 - Prob. 55PCh. 26 - Prob. 56PCh. 26 - Prob. 57PCh. 26 - Prob. 58PCh. 26 - Prob. 59PCh. 26 - Prob. 60PCh. 26 - Prob. 61PCh. 26 - Prob. 62PCh. 26 - Prob. 63PCh. 26 - Prob. 64PCh. 26 - Prob. 65PCh. 26 - Prob. 66PCh. 26 - Prob. 67PCh. 26 - Prob. 68PCh. 26 - Prob. 69PCh. 26 - 70. At the 10.0 km long Stanford Linear...Ch. 26 - Prob. 71PCh. 26 - Prob. 72PCh. 26 - Prob. 73PCh. 26 - Prob. 74PCh. 26 - Prob. 75PCh. 26 - Prob. 76PCh. 26 - Prob. 77PCh. 26 - Prob. 78PCh. 26 - Prob. 79PCh. 26 - Prob. 80PCh. 26 - Prob. 81PCh. 26 - Prob. 82PCh. 26 - Prob. 83PCh. 26 - Prob. 84PCh. 26 - Prob. 85PCh. 26 - Prob. 87PCh. 26 - Prob. 86PCh. 26 - Prob. 89PCh. 26 - Prob. 88PCh. 26 - Prob. 90PCh. 26 - Prob. 92PCh. 26 - Prob. 91PCh. 26 - Prob. 94PCh. 26 - Prob. 93PCh. 26 - 96. The solar energy arriving at the outer edge of...Ch. 26 - Prob. 96PCh. 26 - Prob. 97PCh. 26 - Prob. 98P
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Text book image
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
Text book image
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
Time Dilation - Einstein's Theory Of Relativity Explained!; Author: Science ABC;https://www.youtube.com/watch?v=yuD34tEpRFw;License: Standard YouTube License, CC-BY