Modern Physics For Scientists And Engineers
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
To determine

To Prove:

cosθB=β, where β is the dimensionless velocity of A .

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This 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…
Problem 3: A mass m is thrown from the origin att = 0 with initial three-momentum po in the y direction. If it is subject to a constant force F, in the x direction, find its velocity v as a function of t, and by integrating v find its trajectory. Check that in the non-relativistic limit the trajectory is the expected parabola. Hint: The relationship F = P is still true in relativistic mechanics, but now p = ymv instead of p = mv. To find the non-relativistic limit, treat c as a very large quantity and use the Taylor approximation (1+ x)" = 1 + nx when a is small.
2.9. (a) Solve the integral ...| (dx .dx3N) 3N and use it to determine the "volume" the relevant region of the phase space of an extreme relativistic gas ( = pc) of 3N particles moving in one dimension. Determine, as well, the number of ways of distributing a given energy E among this system of particles and show that, asymptotically, w0 = h³N. (b) Compare the thermodynamics of this system with that of the system considered in Problem 2.8.
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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