FUND. OF PHYSICS (LL)-W/WILEY+NEXTGEN(2)
11th Edition
ISBN: 9781119787235
Author: Halliday
Publisher: WILEY
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Question
Chapter 37, Problem 100P
To determine
To find:
a) Show that the Classical Doppler equation gives a relative velocity of recession greater than
b) Assuming that the relative motion of
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Consider a cosmological spacetime in which the line element is given by
ds? = a²(t)(-dt + dr² + dy² + dz²),
where a(t) > 0 is the scale factor. Two light rays tangent to l = (1,1,0, 0)
and l = (1,0, 1,0) are received at time t =
u" = (a-'(to), 0, 0, 0). Compute the observed angle between the correspond-
ing images.
to by someone with 4-velocity
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Chapter 37 Solutions
FUND. OF PHYSICS (LL)-W/WILEY+NEXTGEN(2)
Ch. 37 - A rod is to move at constant speed v along the x...Ch. 37 - Figure 37-16 shows a ship attached to reference...Ch. 37 - Reference frame S' is to pass reference frame S at...Ch. 37 - Figure 37-17 shows two clocks in stationary frame...Ch. 37 - Figure 37-18 shows two clocks in stationary frame...Ch. 37 - Sam leaves Venus in a spaceship headed to Mars and...Ch. 37 - The plane of clocks and measuring rods in Fig....Ch. 37 - The rest energy and total energy, respectively, of...Ch. 37 - Figure 37-20 shows the triangle of Fig 37-14 for...Ch. 37 - While on board a starship, you intercept signals...
Ch. 37 - Figure 37-21 shows one of four star cruisers that...Ch. 37 - The mean lifetime of stationary muons is measured...Ch. 37 - To eight significant figures, what is speed...Ch. 37 - You wish to make a round trip from Earth in a...Ch. 37 - Come back to the future. Suppose that a father is...Ch. 37 - ILW An unstable high-energy particle enters a...Ch. 37 - GO Reference frame S' is to pass reference frame S...Ch. 37 - The premise of the Planet of the Apes movies and...Ch. 37 - An electron of = 0.999 987 moves along the axis...Ch. 37 - SSM A spaceship of rest length 130 m races past a...Ch. 37 - A meter stick in frame S' makes an angle of 30...Ch. 37 - A rod lies parallel to the x axis of reference...Ch. 37 - The length of a spaceship is measured to be...Ch. 37 - GO A space traveler takes off from Earth and moves...Ch. 37 - A rod is to move at constant speed v along the x...Ch. 37 - GO The center of our Milky Way galaxy is about 23...Ch. 37 - Observer S reports that an event occurred on the x...Ch. 37 - SSM WWW In Fig. 37-9, the origins of the two...Ch. 37 - Inertial frame S' moves at a speed of 0.60c with...Ch. 37 - An experimenter arranges to trigger two flashbulbs...Ch. 37 - GO As in Fig. 37-9, reference frame S' passes...Ch. 37 - Relativistic reversal of events. Figures 37-25a...Ch. 37 - For the passing reference frames in Fig. 37-25,...Ch. 37 - ILW A clock moves along an x axis at a speed of...Ch. 37 - Bullwinkle in reference frame S' passes you in...Ch. 37 - In Fig. 37-9, observer S detects two flashes of...Ch. 37 - In Fig. 37-9, observer 5 detects two flashes of...Ch. 37 - SSM A particle moves along the x' axis of frame S'...Ch. 37 - Prob. 28PCh. 37 - Galaxy A is reported to be receding from us with a...Ch. 37 - Stellar system Q1 moves away from us at a speed of...Ch. 37 - SSM WWW ILW A spaceship whose rest length is 350 m...Ch. 37 - GO In Fig. 37-26a, particle P is to move parallel...Ch. 37 - GO An armada of spaceships that is 1.00 ly long as...Ch. 37 - A sodium light source moves in a horizontal circle...Ch. 37 - SSM A spaceship, moving away from Earth at a speed...Ch. 37 - Prob. 36PCh. 37 - Assuming that Eq. 37-36 holds, find how fast you...Ch. 37 - Figure 37-27 is a graph of intensity versus...Ch. 37 - SSM A spaceship is moving away from Earth at speed...Ch. 37 - How much work must be done to increase the speed...Ch. 37 - SSM WWW The mass of an electron is 9.109 381 88 ...Ch. 37 - Prob. 42PCh. 37 - How much work must be done to increase the speed...Ch. 37 - In the reaction p 19F 16O, the masses are mp =...Ch. 37 - In a high-energy collision between a cosmic-ray...Ch. 37 - Prob. 46PCh. 37 - Prob. 47PCh. 37 - GO The mass of a muon is 207 times the electron...Ch. 37 - GO As you read this page on paper or monitor...Ch. 37 - To four significant figures, find the following...Ch. 37 - ILW What must be the momentum of a particle with...Ch. 37 - Apply the binomial theorem Appendix E to the last...Ch. 37 - Prob. 53PCh. 37 - GO What is for a particle with a K = 2.00E0 and b...Ch. 37 - Prob. 55PCh. 37 - a The energy released in the explosion of 1.00 mol...Ch. 37 - Quasars are thought to be the nuclei of active...Ch. 37 - The mass of an electron is 9.109 381 88 1031 kg....Ch. 37 - GO An alpha particle with kinetic energy 7.70 MeV...Ch. 37 - Temporal separation between two events. Events A...Ch. 37 - Spatial separation between two events. For the...Ch. 37 - GO In Fig. 37-28a, particle P is to move parallel...Ch. 37 - Superluminal jets. Figure 37-29a shows the path...Ch. 37 - GO Reference frame S' passes reference frame S...Ch. 37 - Another approach to velocity transformations. In...Ch. 37 - Continuation of Problem 65. Use the result of part...Ch. 37 - Continuation of Problem 65. Let reference frame C...Ch. 37 - Figure 37-16 shows a ship attached to reference...Ch. 37 - Prob. 69PCh. 37 - An airplane has rest length 40.0 m and speed 630...Ch. 37 - SSM To circle Earth in low orbit, a satellite must...Ch. 37 - Prob. 72PCh. 37 - SSM How much work is needed to accelerate a proton...Ch. 37 - A pion is created in the higher reaches of Earths...Ch. 37 - SSM If we intercept an electron having total...Ch. 37 - Prob. 76PCh. 37 - A spaceship at rest in a certain reference frame S...Ch. 37 - Prob. 78PCh. 37 - SSM What is the momentum in MeV/c of an electron...Ch. 37 - The radius of Earth is 6370 km, and its orbital...Ch. 37 - A particle with mass m has speed c/2 relative to...Ch. 37 - An elementary particle produced in a laboratory...Ch. 37 - What are a K, b E, and c p in GeV/c for a proton...Ch. 37 - Prob. 84PCh. 37 - One cosmic-ray particle approaches northsouth axis...Ch. 37 - How much energy is released in the explosion of a...Ch. 37 - What potential difference would accelerate an...Ch. 37 - A Foron cruiser moving directly toward a Reptulian...Ch. 37 - In Fig. 37-35, three spaceships are in a chase....Ch. 37 - Space cruisers A and B are moving parallel to the...Ch. 37 - In Fig. 37-36, two cruisers fly toward a space...Ch. 37 - A relativistic train of proper length 200 m...Ch. 37 - Particle A with rest energy 200 MeV is at rest in...Ch. 37 - Figure 37-37 shows three situations in which a...Ch. 37 - Ionization measurements show that a particular...Ch. 37 - Prob. 96PCh. 37 - Prob. 97PCh. 37 - An astronaut exercising on a treadmill maintains a...Ch. 37 - A spaceship approaches Earth at a speed of 0.42c....Ch. 37 - Prob. 100PCh. 37 - In one year the United States consumption of...Ch. 37 - Quite apart from effects due to Earths rotational...Ch. 37 - Prob. 103P
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- Figure P9.21 shows a jet of material (at the upper right) being ejected by galaxy M87 (at the lower left). Such jets are believed to be evidence of supermassive black holes at the center of a galaxy. Suppose two jets of material from the center of a galaxy are ejected in opposite directions. Both jets move at 0.750c relative to the galaxy center. Determine the speed of one jet relative to the other. Figure P9.21arrow_forward(a) Let L be the diameter of our galaxy.Suppose that a person in a spaceship of massm wants to travel across the galaxy at constantspeed, taking proper time τ. Find the kineticenergy of the spaceship. (b) Your friend is impa-tient, and wants to make the voyage in an hour.For L = 105 light years, estimate the energy inunits of megatons of TNT (1 megaton=4×109 J).arrow_forwardConsider a cosmological spacetime in which the line element is given by ds? = a°(t)(-dt + da² + dy° + dz?), where a(t) > 0 is the scale factor. Two light rays tangent to l4 = (1, 1, 0,0) and = (1,0, 1,0) are received at time t = to by someone with 4-velocity u" = (a-'(to), 0, 0, 0). Compute the observed angle between the correspond- ing images.arrow_forward
- (a) If a KS0 meson at rest decays in 7.80 ✕ 10−11 s, how far (in cm) does a KS0 meson travel if it is moving at 0.900c? cm (b) What If? At what speed will the KS0 meson travel twice the distance found in part (a) before decaying? (Give your answer in terms of c.) carrow_forwardSay that the mean lifetime of a π+ meson in its own rest frame is τ = 2.6 x 10-8 s. A pion of this lifetime is created at an altitude 100 km in the atmosphere by the collision of an incoming cosmic·ray proton with an atmospheric nucleus, and it has lifetime τ. Use the binomial approximation (see attached image) to determine how fast would this π+ meson need to move in order to reach the ground before decaying. Express the velocity in the form v/c = 1 - ϵ, where ϵ << 1.arrow_forwardConsider the energy-momentum tensor Tμv = (p+p) uu+P9μ applied to the matter/energy distribution in the universe on large scales, and assume an equation of state of the form p = wp, with w a constant. Determine the type of matter/energy dominating the universe if the energy-momentum tensor is traceless, that is, T"μ = 0.arrow_forward
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