Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 1, Problem 1.36P
To determine
To Solve:
The Lorentz transformation equations to give
The Lorentz equation will remain the unchanged while the interchange the primed and unprimed variable and replace
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The reference frame S' moves relative to S with velocity u along the axis. Let va and v. denote the a
component of the velocity vector of a particle in S and S', respectively, with a = x, y, z. Drive the expression
of vy in terms of u, c, vr, vy.
Hint: Start from the Lorentz coordinate transformation.
A particle has a lifetime of 121 nanoseconds, as measured in its own moving reference frame.
It travels at a speed of 0.983c, where c is the speed of light.
What distance will it travel before disintegrating, as measured in the reference frame of a fixed observer? Express your answer in meters and keep three significant digits.
Evaluate the rest energy (in MeV) for the proton (m,= 1.673 x 10-27 kg) and the
deuteron (ma= 3.344 × 102" kg). Next, assume y = 2 for either particle. What is
the particle velocity (m/sec)? What are the "kinetic energies" (the total energy
minus the rest energy) for both particles in MeV. Repeat for y = 10.
Chapter 1 Solutions
Modern Physics For Scientists And Engineers
Ch. 1 - Prob. 1.1PCh. 1 - Prob. 1.2PCh. 1 - Prob. 1.3PCh. 1 - Prob. 1.4PCh. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Prob. 1.7PCh. 1 - Prob. 1.8PCh. 1 - Prob. 1.9PCh. 1 - Prob. 1.10P
Ch. 1 - Prob. 1.11PCh. 1 - Prob. 1.12PCh. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - Prob. 1.16PCh. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Prob. 1.20PCh. 1 - Prob. 1.21PCh. 1 - Prob. 1.22PCh. 1 - Prob. 1.23PCh. 1 - Prob. 1.24PCh. 1 - Prob. 1.25PCh. 1 - Prob. 1.26PCh. 1 - Prob. 1.27PCh. 1 - Prob. 1.28PCh. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Prob. 1.31PCh. 1 - Prob. 1.32PCh. 1 - Prob. 1.33PCh. 1 - Prob. 1.34PCh. 1 - Prob. 1.35PCh. 1 - Prob. 1.36PCh. 1 - Prob. 1.37PCh. 1 - Prob. 1.38PCh. 1 - Prob. 1.39PCh. 1 - Prob. 1.40PCh. 1 - Prob. 1.41PCh. 1 - Prob. 1.42PCh. 1 - Prob. 1.43PCh. 1 - Prob. 1.44PCh. 1 - Prob. 1.45PCh. 1 - Prob. 1.46PCh. 1 - Prob. 1.47PCh. 1 - Prob. 1.48PCh. 1 - Prob. 1.49PCh. 1 - Prob. 1.50PCh. 1 - Prob. 1.51PCh. 1 - Prob. 1.52PCh. 1 - Prob. 1.53P
Knowledge Booster
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
- Derive the Lorentz transformation connecting a frame SS (the lab frame) to a frame S′S′ that moves with respect to SS with a velocity in the xyxy plane. This velocity makes an angle ϕϕ with the xx axis of SS and has speed vv. In order to solve this, take the route of two successive Lorentz transformations, one along the xx axis followed by one along the yy axis.arrow_forwardA particle has a lifetime of 91 nanoseconds (as measured in its own moving reference frame. It travels at a speed of 0.984c, where c is the speed of light. How far does it travel? Express your answer in meters and keep three significant digits.arrow_forwardDerive the Lorentz transformation connecting a frame S (the lab frame) to a frame S′ that moves with respect to S with a velocity in the xy plane. This velocity makes an angle ϕ with the x axis of SS and has speed v. In order to solve this, take the route of two successive Lorentz transformations, one along the x axis followed by one along the y axis.arrow_forward
- Which one of the following matrix is not part of the Lorentz group? Select one: O a. O b. 0 с. O d. cosha sinha 0 0 sinha cosh a 0 0 0 0 1 0 0 01 1 0 0 0 0 0 0 0 sin a 0 sin a cos a 0 0 0 1 cos a cosh a — sinh a 0 0 cosh a sinh a 0 0 −sinha cosh a 0 0 – sinh a cosh a 0 0 3 00 00 10 0 1 3 0 0 00 10 0 1 where a is a real parameter. where a is a real parameter. 3 , where a is a real parameter. where a is a real parameter.arrow_forwardA particle is traveling at 0.98c, where c is the speed of light. According to an observer at rest, the particle is traveling a distance 5.6 meters before disintegrating. What is the lifetime of the particle as measured in the moving frame? Express your answer in nanoseconds and keep three significant digitsarrow_forward2.1 Properties of Lorentz Transformations. By explicit matrix multiplication, show that the matrix A that implements a Lorentz boost along the z-axis with velocity B 0 0 yB 1 (2.158) 1 YB 0 0 leaves the metric invariant: (2.159) Recall that the boost factor y is 1 (2.160) VI - 82arrow_forward
- The work–energy theorem relates the change in kineticenergy of a particle to the work done on it by an externalforce: ΔK = W = ∫ F dx. Writing Newton’s second lawas F = dp/dt, showthatW =∫ v dpand integrate by partsusing the relativistic momentum to obtain Equation 2.34. K = (mc^2)/√((1 − v2)/c^2) − mc^2arrow_forwardAn object is moving with ordinary speed 0.5c in S reference frame along a direction making an angle (tan =) with respect to the positive x - axis. Find the components u, and u.,, of the ordinary velocity. And find the components and ny of the proper velocity.arrow_forwardI am currently working through a physics book (Spacetime Physics by Edwin Taylor) and I have come across this question and I don't know how to solve it: "Take the differential of this equation for g to obtain an approximate algebraic expression for Δg, the change in g, for a small change Δr in height." How do I sovle this question?arrow_forward
- 3.9. A particle is traveling at 3c in the x direction. Determine its proper velocity, n (all four components).arrow_forwardA particle has γ=18,399. a) Calculate c-v in m/s. (I would have asked for 1 - v/c, making the answer dimensionless, but the system doesn't seem to take numbers that small. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 1,739 MeV/c, calculate its energy in MeV. Thank you so much!!arrow_forwardA particle has γ=18,399. a)Calculate c-v in m/s. (I would have asked for 1 - v/c, making the answer dimensionless, but the system doesn't seem to take numbers that small. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In the previous problem, in a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 1,739 MeV/c, calculate its energy in MeV.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
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