Physics, Books a la Carte Plus Mastering Physics with Pearson eText -- Access Card Package (5th Edition)
5th Edition
ISBN: 9780134032610
Author: James S. Walker
Publisher: PEARSON
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Chapter 29, Problem 66PCE
To determine
The radius to which sun must be compressed for it to become a black hole.
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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?
A black hole is an object so massive that not even light can escape, one way to define the size of a black
hole is by the Schwarzschild Radius, which is the radius at which the escape velocity is equal to the speed
of light. If we were to condense the Earth into a black hole, what would be the size of its Schwarzschild Radius?
Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00×10^8 m/s, making all escape impossible. What is the radius of the event horizon for a black hole with a mass 3.5 times the mass of the sun?
Chapter 29 Solutions
Physics, Books a la Carte Plus Mastering Physics with Pearson eText -- Access Card Package (5th Edition)
Ch. 29.1 - Observer 1 shines a beam of light toward observer...Ch. 29.2 - Two identical atomic clocks are manufactured at a...Ch. 29.3 - A horizontal meterstick moving to the right is...Ch. 29.4 - A passenger jogs toward the front of a train with...Ch. 29.5 - Is the relativistic momentum of an object moving...Ch. 29.6 - An object of mass m moves with speed u. Rank the...Ch. 29.7 - If the speed of light were infinite, would the...Ch. 29.8 - Prob. 8EYUCh. 29 - Some distant galaxies are moving away from us at...Ch. 29 - Prob. 2CQ
Ch. 29 - When we view a distant galaxy, we notice that the...Ch. 29 - Prob. 4CQCh. 29 - Give an argument that shows that an object of...Ch. 29 - Section 29-1 The Postulates of Special Relativity ...Ch. 29 - Albert is piloting his spaceship heading east with...Ch. 29 - A street performer tosses a ball straight up into...Ch. 29 - Prob. 4PCECh. 29 - Predict/Explain Suppose you are a traveling...Ch. 29 - A neon sign in front of a cafe flashes on and off...Ch. 29 - A lighthouse sweeps its beam of light around in a...Ch. 29 - As a spaceship flies past with speed u, you...Ch. 29 - How fast should your spacecraft travel so that...Ch. 29 - Usain Bon set a world record for the 100-m dash on...Ch. 29 - (a) Find the average distance (in the Earths frame...Ch. 29 - Referring to Example 29-3, (a) how much does Benny...Ch. 29 - The Pi Meson An elementary particle called a pi...Ch. 29 - Predict/Calculate (a) Is it possible for you to...Ch. 29 - In order to cross the galaxy quickly, a spaceship...Ch. 29 - An observer moving toward Earth with a speed of...Ch. 29 - Predict/Calculate An astronaut moving with a speed...Ch. 29 - BIO Newly sprouted sunflowers can grow at the rate...Ch. 29 - As measured in earths frame of reference, the...Ch. 29 - Captain Jean Luc is piloting the USS Enterprise...Ch. 29 - Prob. 21PCECh. 29 - How fast does a 275-m spaceship move relative to...Ch. 29 - Suppose the speed of light in a vacuum were only...Ch. 29 - A rectangular painting is W = 117 cm wide and H =...Ch. 29 - Prob. 25PCECh. 29 - A cubical box is 0.75 m on a side (a) What are the...Ch. 29 - When parked, your car is 5 8 m long....Ch. 29 - An astronaut travels to a distant star with a...Ch. 29 - Predict/Calculate Laboratory measurements show...Ch. 29 - You and a friend travel through space in identical...Ch. 29 - A ladder 5.0 m long leans against a wall inside a...Ch. 29 - When traveling past an observer with a relative...Ch. 29 - Predict/Calculate The starships Picard and La...Ch. 29 - A spaceship moving toward Earth with a speed of...Ch. 29 - Suppose the probe in Problem 34 is launched in the...Ch. 29 - Suppose the speed of light is 35 mi/h. A paper...Ch. 29 - Two asteroids head straight for Earth from the...Ch. 29 - Two rocket ships approach Earth from opposite...Ch. 29 - A spaceship and an asteroid are moving in the same...Ch. 29 - An electron moves to the right in a laboratory...Ch. 29 - A uranium nucleus is traveling at 0.95c in the...Ch. 29 - Predict/Calculate Two rocket ships are racing...Ch. 29 - A 2.8 106-kg spaceship moves away from Earth with...Ch. 29 - An asteroid with a mass of 8.2 1011-kg is...Ch. 29 - An object has a relativistic momentum that is 8.50...Ch. 29 - A football player with a mass of 88 kg and a speed...Ch. 29 - A space probe with a rest mass of 8 2 107 kg and...Ch. 29 - At what speed does the classical momentum, p = mu,...Ch. 29 - A proton has 1836 times the rest mass of an...Ch. 29 - Star A has a mass of 3 0 1023 kg kg and is...Ch. 29 - Particles A through D have the following rest...Ch. 29 - Find the work that must be done on a proton to...Ch. 29 - A spring with a force constant of 595 N/m is...Ch. 29 - The 15 gallons of gasoline required to refuel your...Ch. 29 - Prob. 55PCECh. 29 - When a proton encounters an antiproton, the two...Ch. 29 - If a neutron moves with a speed of 0.99c, what are...Ch. 29 - A rocket with a mass of 2.7 106 kg has a...Ch. 29 - An object has a total energy that is 4.8 times its...Ch. 29 - Prob. 60PCECh. 29 - A nuclear power plant converts fuel energy at an...Ch. 29 - Prob. 62PCECh. 29 - What is the percent difference between the...Ch. 29 - Predict/Calculate Consider a baseball with a rest...Ch. 29 - A lump of putty with a mass of 0.240 kg and a...Ch. 29 - Prob. 66PCECh. 29 - Prob. 67PCECh. 29 - Prob. 68GPCh. 29 - CE You are standing next to a runway as an...Ch. 29 - CE An apple drops from the bough of a tree to the...Ch. 29 - CE Predict/Explain Consider two apple pies that...Ch. 29 - CE Predict/Explain An uncharged capacitor is...Ch. 29 - Cosmic Rays Protons in cosmic rays have been...Ch. 29 - At the CERN particle accelerator in Geneva,...Ch. 29 - A 14C nucleus, initially at rest, emits a beta...Ch. 29 - A clock at rest has a rectangular shape, with a...Ch. 29 - A starship moving toward Earth with a speed of...Ch. 29 - Prob. 78GPCh. 29 - A 2.5-m titanium rod in a moving spacecraft is at...Ch. 29 - Electrons are accelerated from rest through a...Ch. 29 - The rest energy, m0c2, of a particle with a...Ch. 29 - Predict/Calculate Consider a relativistic air...Ch. 29 - Predict/Calculate In Conceptual Example 29-7...Ch. 29 - A pulsar is a collapsed, rotating star that sends...Ch. 29 - Prob. 85GPCh. 29 - Decay of the Particle When at rest, the particle...Ch. 29 - Prob. 87PPCh. 29 - Prob. 88PPCh. 29 - Prob. 89PPCh. 29 - Prob. 90PPCh. 29 - Referring to Example 29-9 The Picard approaches...Ch. 29 - Referring to Example 29-9 Faraway Point starbase...
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- A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. Ii has strayed too close to a black hole having a mass 100 times that of the Sun (Fig. P11.11). The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. (a) Determine the total force on the spacecraft. (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.)arrow_forwardWhat is the Schwarzschild radius for the black hole at the center of our galaxy if it has the mass of 4 million solar masses?arrow_forwardAs an object falls into a black hole, tidal forces increase. Will these tidal forces always tear the object apart as it approaches the Schwarzschild radius? How does the mass of the black hole and size of the object affect your answer?arrow_forward
- If the Sun were to collapse into a black hole, the point of no return for an investigator would be approximately 3 km from the center singularity. Would the investingator be able to survive visiting even 300 km from the center? Answer this by finding the difference in the gravitatoinal attraction the black holes exerts on a 1.0-kg mass at the head and at the feet of the investigator.arrow_forwardA neutron star is a cold, collapsed star with nuclear density. A particular neutron star has a mass twice that of our Sun with a radius of 12.0 km. (a) What would be the weight of a 100-kg astronaut on standing on its surface? (b) What does this tell us about landing on a neutron star?arrow_forwardA black hole is an object with mass, but no spatial extent. It truly is a particle. A black hole may form from a dead star. Such a black hole has a mass several times the mass of the Sun. Imagine a black hole whose mass is ten times the mass of the Sun. a. Would you expect the period of an object orbiting the black hole with a semimajor axis of 1 AU to have a period greater than, less than, or equal to 1 yr? Explain your reasoning. b. Use Equation 7.6 to calculate this period.arrow_forward
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- A black hole has an event horizon radius of 5.00××1033 m. a) What is its mass? b) Determine the gravitational acceleration it produces at a distance of 5.01××1033 m from its center. c) Determine the escape speed at a distance of 5.01××1033 m from its center.arrow_forwardNothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00 × 108^8 m/sm/s, making all escape impossible. What is the radius of the event horizon for a black hole with a mass 7.5 times the mass of the sun? This distance is called the Schwarzschild radius.arrow_forwardA spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 770 kg. It has strayed too close to a black hole having a mass 99 times that of the Sun. The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. Black hole 100 m 10.0 km H (a) Determine the total force on the spacecraft. (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in acceleration grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.) N/kgarrow_forward
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