University Physics (14th Edition)
14th Edition
ISBN: 9780133969290
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Chapter 13, Problem 13.38E
Mini Black Holes. 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?
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Students have asked these similar questions
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 following quotation is taken from the article “Quantum Black Holes”, by Bernard J. Carr and Steven B. Giddings, in the
May 2005 issue of Scientific American. "The total time for a black hole to evaporate away is proportional to the cube of its
initial mass. For a solar-mass hole, the lifetime is an unobservably long 1064 years."
a. Recall that the solar mass is 2 × 10³0 kilograms. Write a formula for the lifetime, L, of a black hole as a function of its
mass, m. Start by finding the value of the constant k, then write your function using the letter k (rather than its value in
scientific notation). For example, for a direct variation you would write “L(m) = km”.
k = a × 10¹ where a =
L(m) =
b. The present age
mass = c × 10ª kg, where c =
A
and b =
=
of the universe is about 10¹0 years. What would be the mass of a black hole as old as the universe?
ID
and d
=
J
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?
Chapter 13 Solutions
University Physics (14th Edition)
Ch. 13 - A student wrote: The only reason an apple falls...Ch. 13 - If all planets had the same average density, how...Ch. 13 - Is a pound of butler on the earth the same amount...Ch. 13 - Example 13.2 (Section 13.1) shows that the...Ch. 13 - When will you attract the sun more: today at noon,...Ch. 13 - Since the moon is constantly attracted toward the...Ch. 13 - Prob. Q13.7DQCh. 13 - A planet makes a circular orbit with period T...Ch. 13 - The sun pulls on the moon with a force that is...Ch. 13 - Which takes more fuel: a voyage from the earth to...
Ch. 13 - Prob. Q13.11DQCh. 13 - Does the escape speed for an object at the earths...Ch. 13 - If a projectile is fired straight up from the...Ch. 13 - Discuss whether this statement is correct: In the...Ch. 13 - The earth is closer to the sun in November than in...Ch. 13 - A communications firm wants to place a satellite...Ch. 13 - Prob. Q13.17DQCh. 13 - What would Keplers third law be for circular...Ch. 13 - In the elliptical orbit of Comet Hailey shown in...Ch. 13 - Many people believe that orbiting astronauts feel...Ch. 13 - As part of their training before going into orbit,...Ch. 13 - What is the ratio of the gravitational pull of the...Ch. 13 - CP Cavendish Experiment. In the Cavendish balance...Ch. 13 - Rendezvous in Space! A couple of astronauts agree...Ch. 13 - Two uniform spheres, each with mass M and radius...Ch. 13 - Two uniform spheres, each of mass 0.260 kg, are...Ch. 13 - Find the magnitude and direction of the net...Ch. 13 - A typical adult human has a mass of about 70 kg....Ch. 13 - An 8.00-kg point mass and a 12.0-kg point mass are...Ch. 13 - Prob. 13.9ECh. 13 - The point masses m and 2m lie along the x-axis,...Ch. 13 - At what distance above the surface of the earth is...Ch. 13 - The mass of Venus is 81.5% that of the earth, and...Ch. 13 - Prob. 13.13ECh. 13 - Rhea, one of Saturns moons, has a radius of 764 km...Ch. 13 - Calculate the earths gravity force on a 75-kg...Ch. 13 - Prob. 13.16ECh. 13 - Use the results of Example 13.5 (Section 13.3) to...Ch. 13 - Ten days after it was launched toward Mars in...Ch. 13 - A planet orbiting a distant star has radius 3.24 ...Ch. 13 - Prob. 13.20ECh. 13 - Prob. 13.21ECh. 13 - Aura Mission. On July 15, 2004, NASA launched the...Ch. 13 - Two satellites are in circular orbits around a...Ch. 13 - International Space Station. In its orbit each...Ch. 13 - Prob. 13.25ECh. 13 - Prob. 13.26ECh. 13 - The star Rho1 Cancri is 57 light-years from the...Ch. 13 - In March 2006. two small satellites were...Ch. 13 - The dwarf planet Pluto has an elliptical orbit...Ch. 13 - Hot Jupiters. In 2004 astronomers reported the...Ch. 13 - Planets Beyond the Solar System. On October 15,...Ch. 13 - A uniform, spherical, 1000.0-kg shell has a radius...Ch. 13 - A uniform, solid, 1000.0-kg sphere has a radius of...Ch. 13 - CALC A thin, uniform rod has length L and mass M....Ch. 13 - Prob. 13.35ECh. 13 - A Visit to Santa. You decide to visit Santa Claus...Ch. 13 - The acceleration due to gravity at the north pole...Ch. 13 - Mini Black Holes. Cosmologists have speculated...Ch. 13 - Prob. 13.39ECh. 13 - In 2005 astronomers announced the discovery of a...Ch. 13 - Neutron stars, such as the one at the center of...Ch. 13 - Four identical masses of 8.00 kg each are placed...Ch. 13 - Three uniform spheres are fixed at the positions...Ch. 13 - CP Exploring Europa. There is strong evidence that...Ch. 13 - A uniform sphere with mass 50.0 kg is held with...Ch. 13 - Mission to Titan. On December 25, 2004, the...Ch. 13 - Prob. 13.47PCh. 13 - At a certain instant, the earth, the moon, and a...Ch. 13 - Prob. 13.49PCh. 13 - CP Submarines on Europa. Some scientists are eager...Ch. 13 - What is the escape speed from a 300-km-diameter...Ch. 13 - A landing craft with mass 12,500 kg is in a...Ch. 13 - Planet X rotates in the same manner as the earth,...Ch. 13 - (a) Suppose you are at the earths equator and...Ch. 13 - CP An astronaut, whose mission is to go where no...Ch. 13 - CP Your starship, the Aimless Wanderer, lands on...Ch. 13 - CP You are exploring a distant planet. When your...Ch. 13 - The 0.100-kg sphere in Fig. P13.58 is released...Ch. 13 - An unmanned spacecraft is in a circular orbit...Ch. 13 - Mass of a Comet. On July 4, 2005, the NASA...Ch. 13 - Falling Hammer. A hammer with mass m is dropped...Ch. 13 - Prob. 13.62PCh. 13 - Prob. 13.63PCh. 13 - Prob. 13.64PCh. 13 - Prob. 13.65PCh. 13 - The planet Uranus has a radius of 25,360 km and a...Ch. 13 - Prob. 13.67PCh. 13 - A rocket with mass 5.00 103 kg is in a circular...Ch. 13 - A 5000-kg spacecraft is in a circular orbit 2000...Ch. 13 - Prob. 13.70PCh. 13 - CALC Planets are not uniform inside. Normally,...Ch. 13 - One of the brightest comets of the 20th century...Ch. 13 - CALC An object in the shape of a thin ring has...Ch. 13 - CALC A uniform wire with mass M and length L is...Ch. 13 - Prob. 13.75PCh. 13 - DATA For each of the eight planets Mercury to...Ch. 13 - DATA For a spherical planet with mass M, volume V,...Ch. 13 - DATA For a planet in our solar system, assume that...Ch. 13 - CHALLENGE PROBLEMS 13.79Interplanetary Navigation....Ch. 13 - CP Tidal Forces near a Black Hole. An astronaut...Ch. 13 - CALC Mass M is distributed uniformly over a disk...Ch. 13 - EXOPLANETS. As planets with a wide variety of...Ch. 13 - EXOPLANETS. As planets with a wide variety of...Ch. 13 - EXOPLANETS. As planets with a wide variety of...
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