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 2.16P
To determine
To Verify:
The Pythagorean relation,
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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.
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^2
A particle has γ=15,687. 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.
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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- Estimate the age of the universe (in Gyrs) at the time when radiation was emitted from an object with redshift z. For 1 < z < 3200, you can assume the Universe is matter dominated, in which case a ∝ t^2/3 and equation 5.102 should hold. Values: Assume H0 = 70 km/s/Mpc Ωm,0 = 0.3 z=3.6 Equation 5.102 is : a(t) = (3/2 (sqrtΩm,0 ) H0 t)^2/3arrow_forward3.15 A pion traveling at speed v decays into a muon and a neutrino, ´¯` −→ µ¯ + ¯µ. If the neutrino emerges at 90° to the original pion direction, at what angle does the come off? [Answer: tane = (1 - m²/m²)/(2By2²).]arrow_forwardThe answer is already shown, I am just confused about the steps. On part a, how does the 3.1447 go to 4.94Re? and then h=3.94Re and then 25097800m? On part b, where does the 2.5 come from? please solve in simpler steps, thank you.arrow_forward
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- Mass of a proton: 1.007825 u; Mass of a neutron: 1.008665 u 1 The lifetime of a free neutron is 887 s. If a neutron moves with a speed 2.9 × 108 m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? What is this an example of? 2. (a) What is the rest energy (in joules) of a subatomic particle whose (rest) mass is 6.7 x 10-3¹ kg? (b) How many MeV's of energy is this? 3. The rest energy of a particular subatomic particle is 1200 MeV. If this particle is traveling at 90% the speed of light, what is its total relativistic energy?arrow_forward6.10 Assuming the orbits of earth and Mars are circular and coplanar, calculate (a) The time required for a Hohmann transfer from earth orbit to Mars orbit. (b) The initial position of Mars (a) in its orbit relative to earth for interception to occur. Radius of earth orbit 1.496(10*) km. %D Radius of Mars orbit = 2.279(10*) km. HSun = 1.327(10)km³/s?. {Ans.: (a) 259 days; (b) a = 44.3°} PROBLEMS 337 Hohmann transfer orbit Mars at launch Mars at encounter Sun Earth at launcharrow_forward(1.30) If ø = x²yzo + 2z²y² find (a) Vo at the point (1,-1, 1) (b) the magnitude of Vo at (1,-1, 1) (c) the direction cosines of Vo at (1, –1, 1)arrow_forward
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