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,
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Chapter 1, Problem 1.37P
To determine
To Derive:
The derivation of Lorentz transformation for t' by using the Lorentz equation for x and x'.
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Calculate the interval Δs2 between two events with coordinates (x1 = 55m, y1 = 0m, z1 = 0m, t1 = 1 μs) and (x2 = 125m, y2 = 0m, z2 = 0m, t2 = 1.6 μs) in an inertial frame S. Now transform the coordinates of the events into the S' frame which is travelling at 0.75c along the positive x-axis with respect to frame S, thereby verifying that spacetime interval is invariant.
The positive muon (?+), an unstable particle, lives on average 2.20?10−16 ? (measured in its own frame of reference) before decaying. (a) If such as particle is moving, with respect to the laboratory, with a speed of 0.900?, what average lifetime is measured in the laboratory? (b) What average distance, measured in the laboratory, does the particle move before decaying?
Calculate the interval ∆s^2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1 µs) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S.
i got ∆s^2 = as 1300m^2 but i am stuck on the next part
b) Now transform the coordinates of the events into the S' frame, which is travelling at 0.6c along the x-axis in a positive direction with respect to the frame S. Hence verify that the spacetime interval is invariant.
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
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Length contraction: the real explanation; Author: Fermilab;https://www.youtube.com/watch?v=-Poz_95_0RA;License: Standard YouTube License, CC-BY