PHYSIC FOR SCI & ENGINEERS W/MASTERING
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ISBN: 9781269651639
Author: GIANCOLI
Publisher: Pearson Custom Publishing
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Textbook Question
Chapter 44.4, Problem 1DE
A black hole has radius R. Its mass is proportional to (a) R, (b) R2, (c) R3, Justify your answer.
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The Schwarzschild radius RBH for an object of mass M is defined as
(See image.)
where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole.
1. The mass of the Sun is about 1.99 × 1030 kg. What would be the radius of a black hole with this mass?
2. The mass of Mars is about 6.42 × 1023 kg. What would be the radius of a black hole with this mass?
3. Suppose you want to make a black hole that is roughly the size of an atom (take RBH = 1.10 x 10-10 m). What would be the mass M of such a black hole?
Cosmologists have speculated that black holes the size of a proton could have formed
during the early days of the Big Bang when the universe began. If we take the diameter
of a proton to be 1.0 × 10-¹5 m, what would be the mass of a mini black hole?
The radius Rh of a black hole is the radius of a mathematicalsphere, called the event horizon, that is centered on the blackhole. Information from events inside the event horizon cannotreach the outside world. According to Einstein’s general theory ofrelativity, Rh = 2GM/c2, where M is the mass of the black hole andc is the speed of light.Suppose that you wish to study a black hole near it, at a radialdistance of 50Rh. However, you do not want the difference in gravitationalacceleration between your feet and your head to exceed10 m/s2 when you are feet down (or head down) toward the blackhole. (a) As a multiple of our Sun’s mass MS, approximately what isthe limit to the mass of the black hole you can tolerate at the givenradial distance? (You need to estimate your height.) (b) Is the limitan upper limit (you can tolerate smaller masses) or a lower limit(you can tolerate larger masses)?
Chapter 44 Solutions
PHYSIC FOR SCI & ENGINEERS W/MASTERING
Ch. 44.1 - Suppose we could place a huge mirror 1 light-year...Ch. 44.2 - Prob. 1BECh. 44.4 - What is the Schwarzschild radius for an object...Ch. 44.4 - A black hole has radius R. Its mass is...Ch. 44.9 - Prob. 1EECh. 44 - The Milky Way was once thought to be murky or...Ch. 44 - Prob. 2QCh. 44 - Prob. 3QCh. 44 - Prob. 4QCh. 44 - Prob. 5Q
Ch. 44 - Prob. 6QCh. 44 - Prob. 7QCh. 44 - Prob. 8QCh. 44 - Prob. 9QCh. 44 - Prob. 10QCh. 44 - Prob. 11QCh. 44 - Prob. 12QCh. 44 - Prob. 13QCh. 44 - Compare an explosion on Earth to the Big Bang....Ch. 44 - If nothing, not even light, escapes from a black...Ch. 44 - Prob. 16QCh. 44 - Prob. 17QCh. 44 - Explain what the 2.7-K cosmic microwave background...Ch. 44 - Prob. 19QCh. 44 - Prob. 20QCh. 44 - Prob. 21QCh. 44 - Under what circumstances would the universe...Ch. 44 - Prob. 23QCh. 44 - Prob. 24QCh. 44 - Prob. 1PCh. 44 - Prob. 2PCh. 44 - Prob. 3PCh. 44 - Prob. 4PCh. 44 - Prob. 5PCh. 44 - Prob. 6PCh. 44 - (II) What is the relative brightness of the Sun as...Ch. 44 - Prob. 8PCh. 44 - Prob. 9PCh. 44 - Prob. 10PCh. 44 - Prob. 11PCh. 44 - Prob. 12PCh. 44 - Prob. 13PCh. 44 - Prob. 14PCh. 44 - Prob. 15PCh. 44 - Prob. 16PCh. 44 - Prob. 17PCh. 44 - Prob. 18PCh. 44 - Prob. 19PCh. 44 - Prob. 20PCh. 44 - Prob. 21PCh. 44 - Prob. 22PCh. 44 - Prob. 23PCh. 44 - Prob. 24PCh. 44 - Prob. 25PCh. 44 - Prob. 26PCh. 44 - Prob. 27PCh. 44 - Prob. 28PCh. 44 - Prob. 29PCh. 44 - Prob. 30PCh. 44 - Prob. 31PCh. 44 - (II) Calculate the peak wavelength of the CMB at...Ch. 44 - Prob. 33PCh. 44 - (II) The scale factor or the universe (average...Ch. 44 - Prob. 35PCh. 44 - Prob. 36PCh. 44 - Prob. 37GPCh. 44 - Prob. 38GPCh. 44 - Prob. 39GPCh. 44 - Prob. 40GPCh. 44 - Prob. 41GPCh. 44 - Prob. 42GPCh. 44 - Prob. 43GPCh. 44 - Prob. 44GPCh. 44 - Prob. 45GPCh. 44 - Prob. 46GPCh. 44 - Prob. 47GPCh. 44 - Prob. 48GPCh. 44 - Prob. 49GPCh. 44 - Prob. 50GPCh. 44 - Calculate the Schwarzschild radius using a...Ch. 44 - How large would the Sun be if its density equaled...Ch. 44 - Prob. 53GPCh. 44 - (a) Use special relativity and Newtons law of...Ch. 44 - Prob. 55GPCh. 44 - Prob. 56GPCh. 44 - Prob. 57GPCh. 44 - Prob. 58GP
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