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 1.52P
To determine
To Show:
The way, the given three expressions for Doppler shift are equal.
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6.10 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 launch
1.16. Establish thermodynamically the formulae
(F).
V
= S and
v (3) ₁²
V
T
= N.
Express the pressure P of an ideal classical gas in terms of the variables μ and T, and verify the
above formulae.
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.
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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- 3. Let's imagine that the earth is shrinking and we want to escape before it is too late. Let's set up some notation: R: the radius of Earth MẸ : the mass of Earth m: your mass G : the universal gravitational constant c: the speed of light Note that, since Earth is shrinking, R is not constant, but MẸ is constant (the values of ME, G and c are available on Wikipedia). In this question, we will compute the velocity needed to escape Earth and the radius of (shrunken) Earth for which even light cannot escape (when Earth becomes a black hole). In fact, all of the related formulae are well known and the purpose of this question is to justify our work using what we have learned in this course so far. (a) The work (energy) W needed to free yourself from Earth when its radius is R metres is w = G ME m dh. h2 R Show that this improper integral is equal to GME m Rarrow_forward(3.8) This question introduces a rather efficient method for calculating the mean and variance of probability distributions. We define the moment generating function M(t) for a random variable x by M(t) = (etx). Show that this definition implies that (x) = M(n) (0), (3.51) (3.52) where M(n) (t) mean (x) = d" M/dt" and further that the M (¹) (0) and the variance σ = = M(2)(0) [M(¹) (0)] 2. Hence show that: - (a) for a single Bernoulli trial, = M(t) pe 1-p; (3.53) (b) for the binomial distribution, M(t) = (pe +1 - p)"; (3.54) (c) for the Poisson distribution, M(t) = em(et-1); (3.55) (d) for the exponential distribution, λ M(t) (3.56) Hence derive the mean and variance in each case and show that they agree with the results derived earlier.arrow_forward6.2.4 In the presence of a headwind of nor- malized intensity W, your speed on your bike is V = g(W) = 2010W ¹/3 mi/hr. The wind intensity W is the continuous uni- form (-1,1) random variable. (Note: If W is negative, then the headwind is actually a tailwind.) Find the PDF fv(v).arrow_forward
- Figure 2.72 For Prob. 2.8. 2.5 For the network graph in Fig. 2.69, find the number of nodes, branches, and loops.arrow_forwardLet's say you have a plot for Pendulum experiment. Let's assume g for this experiment was measured (from the slope of the plot) to be 9.78 [ms-2.The vertical intercept, however, is 0.021 [s2].What might this translate to for a measurement of the length offset systematic in all the length measurements?Length Offset =arrow_forwardI am confused with part (e). I don't understand the steps. How is 1.427 obtained? How is the 20t moved to the left side of the equation, since it is inside the COS() function? I am just not understanding the math. Can you step it through with an explanation at each individual step?arrow_forward
- Problem 1.24. Calculate the total thermal energy in a gram of lead at room temperature, assuming that none of the degrees of freedom are "frozen out" (this happens to be a good assumption in this case).arrow_forwardProblem 1.33. An ideal gas is made to undergo the cyclic process shown in Figure 1.10(a). For each of the steps A, B, and C, determine whether each of the following is positive, nogative, or zero: (a) the work done on the gas; (b) the change in the energy content of the gas: (c) the heat added to the gas. Then determine the sign of each of these three quantities for the whole cycle. What does this process accomplish? (a) A (b) B Pa B A A D Volume V1 V Volume Figure 1.10. PV diagrams for Problems 1.33 and 1.34. steps; for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed. (c) Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as you expected? Explain briefly. Show that knowing the initial condition of a compressed system consisting of a gas you can derive its final temperature. Pressure Pressurearrow_forward1.4 Show that the distance of closest approach d, in Rutherford scattering leading to an angle of deflection 0, is given by d=(1+ cosec 0,2). where p is detined in Fig. 1.6. (Use the conservation of energy and angular momentum.]arrow_forward
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