EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
16th Edition
ISBN: 8220100546716
Author: Katz
Publisher: CENGAGE L
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 39, Problem 10PQ

(a)

To determine

The coordinates (x,y,z,t) as measured in the laboratory frame if the particle is moving along the x and x' axes with relative speed of 400m/s.

(a)

Expert Solution
Check Mark

Answer to Problem 10PQ

The coordinates (12.2m,4.00m,6.00m,4.00×104s) as measured in the laboratory frame if the particle is moving along the x and x' axes with relative speed of 400m/s.

Explanation of Solution

Write the expression to obtain the Lorentz factor.

    γ=11(vrelc)2                                                                                                   (I)

Here, γ is the Lorentz factor, vrel is the relative velocity of the object and c is the speed of light.

Write the expression to obtain the expression of time interval in the laboratory frame.

    t=γ(t'+vrelc2x')                                                                                                 (II)

Here, t is the time interval in the laboratory frame, x' is the position of the object along x axis in primed frame, vrel is the relative velocity of the object and t' is the time interval in primed frame.

Write the expression to obtain the position of the object along x axis in laboratory frame.

    x=γ(x'+vrelt')                                                                                                   (III)

Here, x is the position of the object along x axis in laboratory frame, γ is the Lorentz factor, x' is the position of the object along x axis in primed frame, vrel is the relative velocity of the object and t' is the time interval in primed frame.

As the object is moving with a relative velocity along the x-axis only, thus the coordinate in y-axis and y' axis remain same and similarly the coordinate in z-axis and z' axis remain same

Write the expression to obtain the y coordinate in laboratory frame.

    y=y'                                                                                                                    (IV)

Here, y and y' are coordinates in laboratory frame and primed frame respectively.

Write the expression to obtain the z coordinate in laboratory frame.

    z=z'                                                                                                                    (V)

Here, z and z' are coordinates in laboratory frame and primed frame respectively.

Conclusion:

Substitute 400.0m/s for vrel and 3×108m/s for c in equation (I) to calculate γ.

    γ=11(400.0m/s3×108m/s)2=110=1

Substitute 1 for γ, 3×108m/s for c, 400.0m/s for vrel, (4.00×104s) for t' and 12.0m for x' in equation (II) to calculate t.

    t=1((4.00×104s)+400.0m/s(3×108m/s)2(12.0m))=((4.00×104s)+(5.33×1014s))=4.00×104s

Substitute 1 for γ, 400.0m/s for vrel, (4.00×104s) for t' and 12.0m for x' in equation (III) to calculate x.

    x=1(12.0m+(400.0m/s)(4.00×104s))=12.0+0.16m=12.16m12.2m

Substitute 4.00m for y' in equation (III) to calculate y.

    y=4.00m

Substitute 6.00m for z' in equation (IV) to calculate z.

    z=6.00m

Therefore, the coordinates (12.2m,4.00m,6.00m,4.00×104s) as measured in the laboratory frame if the particle is moving along the x and x' axes with relative speed of 400m/s.

(b)

To determine

The coordinates (x,y,z,t) as measured in the laboratory frame if the particle is moving along the x and x' axes with relative speed of 400m/s.

(b)

Expert Solution
Check Mark

Answer to Problem 10PQ

The coordinates (11.8m,4.00m,6.00m,4.00×104s) as measured in the laboratory frame if the particle is moving along the x and x' axes with relative speed of 400m/s.

Explanation of Solution

Conclusion:

Substitute 400.0m/s for vrel and 3×108m/s for c in equation (I) to calculate γ.

    γ=11(400.0m/s3×108m/s)2=110=1

Substitute 1 for γ, 3×108m/s for c, 400.0m/s for vrel, (4.00×104s) for t' and 12.0m for x' in equation (II) to calculate t.

    t=1((4.00×104s)+400.0m/s(3×108m/s)2(12.0m))=((4.00×104s)(5.33×1014s))=4.00×104s

Substitute 1 for γ, 400.0m/s for vrel, (4.00×104s) for t' and 12.0m for x' in equation (III) to calculate x.

    x=1(12.0m+(400.0m/s)(4.00×104s))=12.0m0.16 m=11.84 m11.8 m

Substitute 4.00m for y' in equation (III) to calculate y.

    y=4.00m

Substitute 6.00m for z' in equation (IV) to calculate z.

    z=6.00m

Therefore, the coordinates (11.8m,4.00m,6.00m,4.00×104s) as measured in the laboratory frame if the particle is moving along the x and x' axes with relative speed of 400m/s.

(c)

To determine

The coordinates (x,y,z,t) as measured in the laboratory frame if the particle is moving along the x and x' axes with relative speed of 2.0×108m/s.

(c)

Expert Solution
Check Mark

Answer to Problem 10PQ

The coordinates (1.1×105m,4.00m,6.00m,5.368×104s) as measured in the laboratory frame if the particle is moving along the x and x' axes with relative speed of 2.0×108m/s.

Explanation of Solution

Conclusion:

Substitute 2.0×108m/s for vrel and 3×108m/s for c in equation (I) to calculate γ.

    γ=11(2.0×108m/s3×108m/s)2=1.342

Substitute 1.342 for γ, 3×108m/s for c, 2.0×108m/s for vrel, (4.00×104s) for t' and 12.0m for x' in equation (II) to calculate t.

    t=1.342((4.00×104s)+2.0×108m/s(3×108m/s)2(12.0m))=1.342[(4.00×104s)(2.667×108s)]=5.368×104s

Substitute 1.342 for γ, 2.0×108m/s for vrel, (4.00×104s) for t' and 12.0m for x' in equation (III) to calculate x.

    x=1.342(12.0m+(2.0×108m/s)(4.00×104s))=1.342(12.0m+8×104m)=1.072×105m1.1×105m

Substitute 4.00m for y' in equation (III) to calculate y.

    y=4.00m

Substitute 6.00m for z' in equation (IV) to calculate z.

    z=6.00m

Therefore, the coordinates (1.1×105m,4.00m,6.00m,5.368×104s) as measured in the laboratory frame if the particle is moving along the x and x' axes with relative speed of 2.0×108m/s.

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!
Students have asked these similar questions
What is the critical angle fir the light travelling from the crown glass(n=1.52) into the air(n=1.00)?
No chatgpt pls will upvote
You are working with a team that is designing a new roller coaster-type amusement park ride for a major theme park. You are present for the testing of the ride, in which an empty 150 kg car is sent along the entire ride. Near the end of the ride, the car is at near rest at the top of a 100 m tall track. It then enters a final section, rolling down an undulating hill to ground level. The total length of track for this final section from the top to the ground is 250 m. For the first 230 m, a constant friction force of 370 N acts from computer-controlled brakes. For the last 20 m, which is horizontal at ground level, the computer increases the friction force to a value required for the speed to be reduced to zero just as the car arrives at the point on the track at which the passengers exit. (a) Determine the required constant friction force (in N) for the last 20 m for the empty test car. Write AK + AU + AE int = W+Q + TMW + TMT + TET + TER for the car-track-Earth system and solve for…

Chapter 39 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

Ch. 39 - Prob. 6PQCh. 39 - Prob. 7PQCh. 39 - Prob. 8PQCh. 39 - Prob. 9PQCh. 39 - Prob. 10PQCh. 39 - Prob. 11PQCh. 39 - Prob. 12PQCh. 39 - Prob. 13PQCh. 39 - Prob. 14PQCh. 39 - Prob. 15PQCh. 39 - Prob. 16PQCh. 39 - Prob. 17PQCh. 39 - Prob. 18PQCh. 39 - Prob. 19PQCh. 39 - Prob. 20PQCh. 39 - Prob. 21PQCh. 39 - Prob. 22PQCh. 39 - Prob. 23PQCh. 39 - A starship is 1025 ly from the Earth when measured...Ch. 39 - A starship is 1025 ly from the Earth when measured...Ch. 39 - Prob. 26PQCh. 39 - Prob. 27PQCh. 39 - Prob. 28PQCh. 39 - Prob. 29PQCh. 39 - Prob. 30PQCh. 39 - Prob. 31PQCh. 39 - Prob. 32PQCh. 39 - Prob. 33PQCh. 39 - Prob. 34PQCh. 39 - Prob. 35PQCh. 39 - Prob. 36PQCh. 39 - Prob. 37PQCh. 39 - Prob. 38PQCh. 39 - As measured in a laboratory reference frame, a...Ch. 39 - Prob. 40PQCh. 39 - Prob. 41PQCh. 39 - Prob. 42PQCh. 39 - Prob. 43PQCh. 39 - Prob. 44PQCh. 39 - Prob. 45PQCh. 39 - Prob. 46PQCh. 39 - Prob. 47PQCh. 39 - Prob. 48PQCh. 39 - Prob. 49PQCh. 39 - Prob. 50PQCh. 39 - Prob. 51PQCh. 39 - Prob. 52PQCh. 39 - Prob. 53PQCh. 39 - Prob. 54PQCh. 39 - Prob. 55PQCh. 39 - Prob. 56PQCh. 39 - Consider an electron moving with speed 0.980c. a....Ch. 39 - Prob. 58PQCh. 39 - Prob. 59PQCh. 39 - Prob. 60PQCh. 39 - Prob. 61PQCh. 39 - Prob. 62PQCh. 39 - Prob. 63PQCh. 39 - Prob. 64PQCh. 39 - Prob. 65PQCh. 39 - Prob. 66PQCh. 39 - Prob. 67PQCh. 39 - Prob. 68PQCh. 39 - Prob. 69PQCh. 39 - Prob. 70PQCh. 39 - Joe and Moe are twins. In the laboratory frame at...Ch. 39 - Prob. 72PQCh. 39 - Prob. 73PQCh. 39 - Prob. 74PQCh. 39 - Prob. 75PQCh. 39 - Prob. 76PQCh. 39 - Prob. 77PQCh. 39 - In December 2012, researchers announced the...Ch. 39 - Prob. 79PQCh. 39 - Prob. 80PQCh. 39 - How much work is required to increase the speed of...Ch. 39 - Prob. 82PQCh. 39 - Prob. 83PQCh. 39 - Prob. 84PQCh. 39 - Prob. 85PQ
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.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Length contraction: the real explanation; Author: Fermilab;https://www.youtube.com/watch?v=-Poz_95_0RA;License: Standard YouTube License, CC-BY