Physics for Scientists and Engineers
9th Edition
ISBN: 9781133947271
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 39, Problem 39.24P
The identical twins Speedo and Goslo join a migration from the Earth to Planet X, 20.0 ly away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same moment on different spacecraft. Speedo’s spacecraft travels steadily at 0.950c and Goslo’s at 0.750c. (a) Calculate the age difference between the twins after Goslo’s spacecraft lands on Planet X. (b) Which twin is older?
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter 39 Solutions
Physics for Scientists and Engineers
Ch. 39 - Which observer in Figure 38.1 sees the balls...Ch. 39 - A baseball pitcher with a 90-mi/h fastball throws...Ch. 39 - Suppose the observer O on the train in Figure 38.6...Ch. 39 - A crew on a spacecraft watches a movie that is two...Ch. 39 - Suppose astronauts are paid according to the...Ch. 39 - You are packing for a trip to another star. During...Ch. 39 - You are observing a spacecraft moving away from...Ch. 39 - You are driving on a freeway at a relativistic...Ch. 39 - The following pairs of energiesparticle 1: E, 2E;...Ch. 39 - (i) Does the speed of an electron have an upper...
Ch. 39 - A spacecraft zooms past the Earth with a constant...Ch. 39 - As a car heads down a highway traveling at a speed...Ch. 39 - A spacecraft built in the shape of a sphere moves...Ch. 39 - An astronaut is traveling in a spacecraft in outer...Ch. 39 - You measure the volume of a cube at rest to be V0....Ch. 39 - Two identical clocks are set side by side and...Ch. 39 - Prob. 39.8OQCh. 39 - Which of the following statements are fundamental...Ch. 39 - A distant astronomical object (a quasar) is moving...Ch. 39 - In several cases, a nearby star has been found to...Ch. 39 - Prob. 39.2CQCh. 39 - A train is approaching yon at very high speed as...Ch. 39 - List three ways our day-to-day lives would change...Ch. 39 - Prob. 39.5CQCh. 39 - Prob. 39.6CQCh. 39 - Prob. 39.7CQCh. 39 - Prob. 39.8CQCh. 39 - Give a physical argument that shows it is...Ch. 39 - Prob. 39.10CQCh. 39 - Prob. 39.11CQCh. 39 - (i) An object is plated at a position p f from a...Ch. 39 - With regard to reference frames, how does general...Ch. 39 - Two identical clocks are in the same house, one...Ch. 39 - The truck in Figure P39.1 is moving at a speed of...Ch. 39 - In a laboratory frame of reference, an observer...Ch. 39 - The speed of the Earth in its orbit is 29.8 km/s....Ch. 39 - Prob. 39.4PCh. 39 - Prob. 39.5PCh. 39 - A meterstick moving at 0.900c relative to the...Ch. 39 - Prob. 39.7PCh. 39 - A muon formed high in the Earths atmosphere is...Ch. 39 - How fast must a meterstick be moving if its length...Ch. 39 - An astronaut is traveling in a space vehicle...Ch. 39 - A physicist drives through a stop light. When he...Ch. 39 - A fellow astronaut passes by you in a spacecraft...Ch. 39 - A deep-space vehicle moves away from the Earth...Ch. 39 - For what value of does = 1.010 0? Observe that...Ch. 39 - A supertrain with a proper length of 100 m travels...Ch. 39 - The average lifetime of a pi meson in its own...Ch. 39 - An astronomer on the Earth observes a meteoroid in...Ch. 39 - A cube of steel has a volume of 1.00 cm3 and mass...Ch. 39 - A spacecraft with a proper length of 300 m passes...Ch. 39 - A spacecraft with a proper length of Lp passes by...Ch. 39 - A light source recedes from an observer with a...Ch. 39 - Review. In 1963, astronaut Gordon Cooper orbited...Ch. 39 - Police radar detects the speed of a car (Fig....Ch. 39 - The identical twins Speedo and Goslo join a...Ch. 39 - An atomic clock moves at 1 000 km/h for 1.00 h as...Ch. 39 - Prob. 39.26PCh. 39 - A red light flashes at position xR = 3.00 m and...Ch. 39 - Shannon observes two light pulses to be emitted...Ch. 39 - A moving rod is observed to have a length of =...Ch. 39 - A rod moving with a speed v along the horizontal...Ch. 39 - Keilah, in reference frame S, measures two events...Ch. 39 - Figure P38.21 shows a jet of material (at the...Ch. 39 - An enemy spacecraft moves away from the Earth at a...Ch. 39 - A spacecraft is launched from the surface of the...Ch. 39 - Prob. 39.35PCh. 39 - Calculate the momentum of an electron moving with...Ch. 39 - Prob. 39.37PCh. 39 - Prob. 39.38PCh. 39 - Prob. 39.39PCh. 39 - Prob. 39.40PCh. 39 - Prob. 39.41PCh. 39 - Prob. 39.42PCh. 39 - An unstable particle at rest spontaneously breaks...Ch. 39 - Prob. 39.44PCh. 39 - Prob. 39.45PCh. 39 - Protons in an accelerator at the Fermi National...Ch. 39 - A proton moves at 0.950c. Calculate its (a) rest...Ch. 39 - (a) Find the kinetic energy of a 78.0-kg...Ch. 39 - A proton in a high-energy accelerator moves with a...Ch. 39 - Prob. 39.50PCh. 39 - The total energy of a proton is twice its rest...Ch. 39 - Prob. 39.52PCh. 39 - When 1.00 g of hydrogen combines with 8.00 g of...Ch. 39 - In a nuclear power plain, the fuel rods last 3 yr...Ch. 39 - The power output of the Sun is 3.85 1026 W. By...Ch. 39 - Prob. 39.56PCh. 39 - Prob. 39.57PCh. 39 - Prob. 39.58PCh. 39 - The rest energy of an electron is 0.511 MeV. The...Ch. 39 - Prob. 39.60PCh. 39 - A pion at rest (m = 273me) decays to a muon (m =...Ch. 39 - An unstable particle with mass m = 3.34 1027 kg...Ch. 39 - Prob. 39.63PCh. 39 - Prob. 39.64PCh. 39 - Review. A global positioning system (GPS)...Ch. 39 - Prob. 39.66APCh. 39 - The net nuclear fusion reaction inside the Sun can...Ch. 39 - Prob. 39.68APCh. 39 - A Doppler weather radar station broadcasts a pulse...Ch. 39 - An object having mass 900 kg and traveling at...Ch. 39 - An astronaut wishes to visit the Andromeda galaxy,...Ch. 39 - A physics professor on the Earth gives an exam to...Ch. 39 - An interstellar space probe is launched from...Ch. 39 - Prob. 39.74APCh. 39 - Prob. 39.75APCh. 39 - An object disintegrates into two fragments. One...Ch. 39 - The cosmic rays of highest energy are protons that...Ch. 39 - Spacecraft I. containing students taking a physics...Ch. 39 - Review. Around the core of a nuclear reactor...Ch. 39 - The motion of a transparent medium influences the...Ch. 39 - Prob. 39.81APCh. 39 - Prob. 39.82APCh. 39 - An alien spaceship traveling at 0.600c toward the...Ch. 39 - Prob. 39.84APCh. 39 - Prob. 39.85APCh. 39 - An observer in a coasting spacecraft moves toward...Ch. 39 - Prob. 39.87APCh. 39 - A particle with electric charge q moves along a...Ch. 39 - Prob. 39.89CPCh. 39 - Suppose our Sun is about to explode. In an effort...Ch. 39 - Owen and Dina are at rest in frame S. which is...
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