Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Textbook Question
Chapter 36, Problem 13Q
Explain how the length contraction and time dilation formulas might be used to indicate that c is the limiting speed in the universe.
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Explain the fact the special theory of relativity defines the limits for the validity of Newtonian mechanics.
Two distant galaxies are observed to have redshifts z1 = 0.05 and z2 = 0.15, and distances d1 = 220.60 Mpc and d2 = 661.75 Mpc, respectively. Assuming the motion of the galaxies is due to the Hubble flow, determine the value of the Hubble constant, H0. Show how the value of H0 can be used to estimate the age of the Universe, describing any assumptions that you make. Use the value of H0 you have obtained to estimate the age of the Universe, expressing your answer in Gyr.
Name:
Hubble Distances
Redshift z parameter
The relativistic redshift is parametrized by z and given by
Δ
In terms of the scale factor,
2=
X
do - de
de
1+z=
ao
a
(2)
Problem 01. Find the redshift z for a Hydrogen spectral line originally at 656 nm which
has been observed at a wavelength of 1.64 μm.
Astro 001 Fall 2022
Problem 02. How much smaller was the universe when this light was emitted?
U₁ = DHO
Using the redshift to measure the velocity, we find
D~
(1)
0.1 Hubble's Law
Hubble's Law states that the recession velocity of a redshifted galaxy is given by the product
of the distance and the Hubble constant.
(3)
ZC
Ho
where c = 3 x 108 m/s and Ho = 2.3 x 10-18 s in standard units. The standard measurement
of the Hubble constant is Ho = 71 (km/s)/Mpc.
Problem 03. What is the distance in Mpc and ly to the galaxy measured in problem 01?
1 pc = 3.26 ly.
Chapter 36 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 36.4 - Examine the experiment of Fig. 366 from O1s...Ch. 36.5 - What is the muons mean lifetime (Example 361) if...Ch. 36.5 - A certain atomic clock keeps perfect time on...Ch. 36.6 - Prob. 1DECh. 36.8 - Use Eqs. 367 to calculate the speed of rocket 2 in...Ch. 36.8 - A rocket is headed away from Earth at a speed of...Ch. 36.11 - A proton is traveling in an accelerator with a...Ch. 36.11 - For 1% accuracy, does an electron with K = 100 eV...Ch. 36 - You are in a windowless car in an exceptionally...Ch. 36 - You might have had the experience of being at a...
Ch. 36 - Prob. 3QCh. 36 - Does the Earth really go around the Sun? Or is it...Ch. 36 - If you were on a spaceship traveling at 0.5c away...Ch. 36 - The time dilation effect is sometimes expressed as...Ch. 36 - Does time dilation mean that time actually passes...Ch. 36 - Prob. 8QCh. 36 - If you were traveling away from Earth at speed...Ch. 36 - Do time dilation and length contraction occur at...Ch. 36 - Suppose the speed of light were infinite. What...Ch. 36 - Discuss how our everyday lives would be different...Ch. 36 - Explain how the length contraction and time...Ch. 36 - The drawing at the start of this Chapter shows the...Ch. 36 - Prob. 15QCh. 36 - Can a particle of nonzero mass attain the speed of...Ch. 36 - Prob. 17QCh. 36 - If mass is a form of energy, does this mean that a...Ch. 36 - Prob. 19QCh. 36 - Is our intuitive notion that velocities simply...Ch. 36 - (I) A spaceship passes you at a speed of 0.850c....Ch. 36 - Prob. 2PCh. 36 - (II) According to the special theory of...Ch. 36 - (II) If you were to travel to a star 135...Ch. 36 - (II) What is the speed of a pion if its average...Ch. 36 - (II) In an Earth reference frame, a star is 56...Ch. 36 - (II) Suppose you decide to travel to a star 65...Ch. 36 - (II) At what speed v will the length of a 1.00-m...Ch. 36 - (II) Escape velocity from the Earth is 11.2 km/s....Ch. 36 - (II) A friend speeds by you in her spacecraft at a...Ch. 36 - (II) At what speed do the relativistic formulas...Ch. 36 - (II) A certain star is 18.6 light-years away. How...Ch. 36 - (II) Suppose a news report stated that starship...Ch. 36 - (II) An unstable particle produced in an...Ch. 36 - (II) When it is stationary, the half-life of a...Ch. 36 - (II) In its own reference frame, a box has the...Ch. 36 - (II) When at rest, a spaceship has the form of an...Ch. 36 - (II) How fast must a pion be moving on average to...Ch. 36 - (I) An observer on Earth sees an alien vessel...Ch. 36 - (I) Suppose in Fig. 3611 that the origins of S and...Ch. 36 - (I) Repeat Problem 20 using the Lorentz...Ch. 36 - (II) In Problem 21, suppose that the person moves...Ch. 36 - (II) Two spaceships leave Earth in opposite...Ch. 36 - (II) Reference frame S moves at speed v = 0.92c in...Ch. 36 - (II) A spaceship leaves Earth traveling at 0.61c....Ch. 36 - (II) Your spaceship, traveling at 0.90c, needs to...Ch. 36 - (II) A spaceship traveling at 0.76c away from...Ch. 36 - Prob. 28PCh. 36 - (II) A stick of length 0, at rest in reference...Ch. 36 - (III) In the old West, a marshal riding on a train...Ch. 36 - (III) Two lightbulbs, A and B, are placed at rest...Ch. 36 - (III) An observer in reference frame S notes that...Ch. 36 - (III) A farm boy studying physics believes that he...Ch. 36 - (I) What is the momentum of a proton traveling at...Ch. 36 - Prob. 35PCh. 36 - (II) A particle of mass m travels at a speed v =...Ch. 36 - (II) An unstable particle is at rest and suddenly...Ch. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - (I) The total annual energy consumption in the...Ch. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - (II) How much energy can be obtained front...Ch. 36 - (II) To accelerate a particle of mass m from rest...Ch. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - (II) What is the speed of a proton accelerated by...Ch. 36 - (II) Two identical particles of mass m approach...Ch. 36 - (II) What is the speed of an electron just before...Ch. 36 - Prob. 55PCh. 36 - Prob. 56PCh. 36 - (II) Suppose a spacecraft of mass 17,000 kg is...Ch. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - (III) (a) In reference frame S, a particle has...Ch. 36 - Prob. 64PCh. 36 - (II) A spaceship moving toward Earth at 0.70c...Ch. 36 - Prob. 66PCh. 36 - (III) A radar speed gun emits microwaves of...Ch. 36 - (III) A certain atom emits light of frequency f0...Ch. 36 - An atomic clock is taken to the North Pole, while...Ch. 36 - A spaceship in distress sends out two escape pods...Ch. 36 - An airplane travels 1300 km/h around the Earth in...Ch. 36 - The nearest star to Earth is Proxima Centauri, 4.3...Ch. 36 - Prob. 73GPCh. 36 - A healthy astronauts heart rate is 60 beats/min....Ch. 36 - A spacecraft (reference frame S) moves past Earth...Ch. 36 - Rocket A passes Earth at a speed of 0.65c. At the...Ch. 36 - (a) What is the speed v of an electron whose...Ch. 36 - As a rough rule, anything traveling faster than...Ch. 36 - Prob. 79GPCh. 36 - Prob. 80GPCh. 36 - Prob. 81GPCh. 36 - A free neutron can decay into a proton, an...Ch. 36 - The Sun radiates energy at a rate of about 4 1026...Ch. 36 - An unknown particle is measured to have a negative...Ch. 36 - How much energy would be required to break a...Ch. 36 - Prob. 86GPCh. 36 - Two protons, each having a speed of 0.985c in the...Ch. 36 - When two moles of hydrogen molecules (H2) and one...Ch. 36 - The fictional starship Enterprise obtains its...Ch. 36 - A spaceship and its occupants have a total mass of...Ch. 36 - In a nuclear reaction two identical particles are...Ch. 36 - A 32,000-kg spaceship is to travel to the vicinity...Ch. 36 - Suppose a 14,500-kg spaceship left Earth at a...Ch. 36 - A pi meson of mass m decays at rest into a muon...Ch. 36 - Astronomers measure the distance to a particular...Ch. 36 - A 1.88-kg mass oscillates on the end of a spring...Ch. 36 - Show that the spacetime interval, (c t)2 (x)2, is...Ch. 36 - Prob. 98GPCh. 36 - (II) For a 1.0-kg mass, make a plot of the kinetic...
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Time Dilation - Einstein's Theory Of Relativity Explained!; Author: Science ABC;https://www.youtube.com/watch?v=yuD34tEpRFw;License: Standard YouTube License, CC-BY