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 2, Problem 2.39P
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Calculate the interval ∆s2 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.
b) Now transform the coordinates of the events into the S'frame, which is travelling at 0.6calong the x-axis in a positive direction with respect to the frame S. Hence verify that thespacetime 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?
In the experiment to verify time dilation by flying the cesium clocks around the Earth, what is the order of the speed of the four clocks in a system fi xed at the center of the Earth, but not rotating?
Chapter 2 Solutions
Modern Physics For Scientists And Engineers
Ch. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - Prob. 2.3PCh. 2 - Prob. 2.4PCh. 2 - Prob. 2.5PCh. 2 - Prob. 2.6PCh. 2 - Prob. 2.7PCh. 2 - Prob. 2.8PCh. 2 - Prob. 2.9PCh. 2 - Prob. 2.10P
Ch. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - Prob. 2.14PCh. 2 - Prob. 2.15PCh. 2 - Prob. 2.16PCh. 2 - Prob. 2.17PCh. 2 - Prob. 2.18PCh. 2 - Prob. 2.19PCh. 2 - Prob. 2.20PCh. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - Prob. 2.23PCh. 2 - Prob. 2.24PCh. 2 - Prob. 2.25PCh. 2 - Prob. 2.26PCh. 2 - Prob. 2.27PCh. 2 - Prob. 2.28PCh. 2 - Prob. 2.29PCh. 2 - Prob. 2.30PCh. 2 - Prob. 2.31PCh. 2 - Prob. 2.32PCh. 2 - Prob. 2.33PCh. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - Prob. 2.38PCh. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - Prob. 2.43PCh. 2 - Prob. 2.44PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - Prob. 2.52P
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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.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_forwardIf relativistic effects are to be less than 1%, then the dimensionless parameter γ must be less than 1.01. At what velocity, in terms of c, is γ = 1.01?arrow_forward
- Please answer fast For a rocket traveling at 11010 m/s, by what factor does its relativistic momentum differ from its ordinary momentum?arrow_forwardThis problem deals quantitatively with the experiment of problem 1.1. Let 5denote the ground frame of reference and 5' the train's rest frame. Let the speedof the train, as measured by ground observers, be 30 m/sec in the x direction, andsuppose the stone is released at t' = a at the point x' = y' = 0, z' = 7.2 m.(a) Write the equations that describe the stone's motion in frame 5'. That is,give x', y', and z' as functions of t'. (Note: A body starting from rest and movingwith constant acceleration g travels a distance 1/2 gt2 in time t. Gravity produces aconstant acceleration whose lnagnitude is approximately 10 m/sec/sec.)(b) Use the Galilean transform,ation to write the equations that describe theposition of the stone in frame S. Plot the stone's position at intervals of 0.2 sec,and sketch the curve that describes its trajectory in frame 5. What curve is this?(c) The velocity acquired by a body starting from rest with acceleration g is gt.Write the equations that describe the three…arrow_forwardRecall, from this chapter, that the factor gamma (γ) governs both time dilation and length contraction, where When you multiply the time in a moving frame by γ, you get the longer (dilated) time in your fixed fame. When you divide the length in a moving frame by γ, you get the shorter (contracted) length in your fixed frame. If the bus driver in Problem 1 decided to drive at 99.99% of the speed of light in order to gain some time, show that you’d measure the length of the bus, to be a little less than 1 foot. problem1 Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length contraction, where When you multiply the time in a moving frame by γ, you get the longer (dilated) time in your fixed fame. When you divide the length in a moving frame by γ, you get the shorter (contracted) length in your fixed frame. A passenger on an interplanetary express bus traveling at v = 0.99c takes a 5-minute catnap, according to her watch. Show that her catnap from the…arrow_forward
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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