Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Chapter 13, Problem 22P
To determine
To find:
a) The gravitational acceleration in terms of
b) Effect of
c) The value of gravitational acceleration at given mass.
d) Differential gravitational acceleration between head and feet.
e) Effect of that differential gravitational acceleration.
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The radius Rhand mass Mh of a black hole are related by R₁ = 2GM₁/c², where c is the speed of light. Assume that the gravitational
acceleration as of an object at a distance r= 1.001Rh from the center of a black hole is given by ag = GM/r² (it is, for large black holes).
(a) In terms of Mh, find ag at ro.
(b) Does
sag
at ro increase or decrease as M₁ increases?
(c) What is ag at ro for a very large black hole whose mass is 1.54 × 10¹3 times the solar mass of 1.99 × 10³⁰ kg?
(d) If an astronaut with a height of 1.66 m is at råwith her feet toward this black hole, what is the difference in gravitational acceleration
between her head and her feet ahead-afeet?
(e) Is the tendency to stretch the astronaut severe?
The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light.
Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole.
(a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun.
The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light.
Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun. (b) Is the ratio an upper limit estimate or a lower limit estimate?
Chapter 13 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 13 - In Fig. 13-21, a central particle of mass M is...Ch. 13 - Prob. 2QCh. 13 - In Fig. 13-23, a central particle is surrounded by...Ch. 13 - In Fig. 13-24, two particles, of masses m and 2m,...Ch. 13 - Prob. 5QCh. 13 - In Fig. 13-26, three particles are fixed in place....Ch. 13 - Rank the four systems of equal- mass particles...Ch. 13 - Figure 13-27 gives the gravitational acceleration...Ch. 13 - Figure 13-28 shows three particles initially fixed...Ch. 13 - Figure 13-29 shows six paths by which a rocket...
Ch. 13 - Figure 13-30 shows three uniform spherical planets...Ch. 13 - In Fig. 13-31, a particle of mass m which is not...Ch. 13 - ILW A mass M is split into two parts, m and M m,...Ch. 13 - Moon effect. Some people believe that the Moon...Ch. 13 - Prob. 3PCh. 13 - The Sun and Earth each exert a gravitational force...Ch. 13 - Miniature black holes. Left over from the big-bang...Ch. 13 - GO In Fig. 13-32, a square of edge length 20.0 cm...Ch. 13 - One dimension. In Fig. 13-33, two point particles...Ch. 13 - In Fig. 13-34, three 5.00 kg spheres are located...Ch. 13 - SSM WWW We want to position a space probe along a...Ch. 13 - Prob. 10PCh. 13 - As seen in Fig. 13-36, two spheres of mass m and a...Ch. 13 - GO In Fig. 13-37a, particle A is fixed in place at...Ch. 13 - Figure 13-38 shows a spherical hollow inside a...Ch. 13 - Prob. 14PCh. 13 - GO Three dimensions. Three point particles are...Ch. 13 - GO In Fig. 13-40, a particle of mass m1 = 0.67 kg...Ch. 13 - a What will an object weigh on the Moons surface...Ch. 13 - Mountain pull. A large mountain can slightly...Ch. 13 - SSM At what altitude above Earths surface would...Ch. 13 - Mile-high building. In 1956, Frank Lloyd Wright...Ch. 13 - ILW Certain neutron stars extremely dense stars...Ch. 13 - Prob. 22PCh. 13 - Prob. 23PCh. 13 - Two concentric spherical shells with uniformly...Ch. 13 - A solid sphere has a uniformly distributed mass of...Ch. 13 - Prob. 26PCh. 13 - Figure 13-42 shows, not to scale, a cross section...Ch. 13 - Prob. 28PCh. 13 - Prob. 29PCh. 13 - In Problem 1, what ratio m/M gives the least...Ch. 13 - SSM The mean diameters of Mars and Earth are 6.9 ...Ch. 13 - a What is the gravitational potential energy of...Ch. 13 - Prob. 33PCh. 13 - Prob. 34PCh. 13 - GO Figure 13-44 shows four particles, each of mass...Ch. 13 - Zero, a hypothetical planet, has a mass of 5.0 ...Ch. 13 - GO The three spheres in Fig, 13-45, with masses mA...Ch. 13 - In deep space, sphere A of mass 20 kg is located...Ch. 13 - Prob. 39PCh. 13 - A projectile is shot directly away from Earths...Ch. 13 - SSM Two neutron stars arc separated by a distance...Ch. 13 - GO Figure 13-46a shows a particle A that can he...Ch. 13 - a What linear speed must an Earth satellite have...Ch. 13 - Prob. 44PCh. 13 - The Martian satellite Photos travels in an...Ch. 13 - The first known collision between space debris and...Ch. 13 - Prob. 47PCh. 13 - The mean distance of Mars from the Sun is 1.52...Ch. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Prob. 51PCh. 13 - The Suns center is at one focus of Earths orbit....Ch. 13 - A 20 kg satellite has a circular orbit with a...Ch. 13 - Prob. 54PCh. 13 - In 1610, Galileo used his telescope to discover...Ch. 13 - In 1993 the spacecraft Galileo sent an image Fig....Ch. 13 - Prob. 57PCh. 13 - Prob. 58PCh. 13 - Three identical stars of mass M form an...Ch. 13 - In Fig. 13-50, two satellites, A and B, both of...Ch. 13 - Prob. 61PCh. 13 - Prob. 62PCh. 13 - SSM WWW An asteroid, whose mass is 2.0 10-4 times...Ch. 13 - A satellite orbits a planet of unknown mass in a...Ch. 13 - A Satellite is in a circular Earth orbit of radius...Ch. 13 - One way to attack a satellite in Earth orbit is to...Ch. 13 - Prob. 67PCh. 13 - GO Two small spaceships, each with mass m = 2000...Ch. 13 - Prob. 69PCh. 13 - Prob. 70PCh. 13 - Several planets Jupiter. Saturn, Uranus are...Ch. 13 - Prob. 72PCh. 13 - Figure 13-53 is a graph of the kinetic energy K of...Ch. 13 - The mysterious visitor that appears in the...Ch. 13 - ILW The masses and coordinates of three spheres...Ch. 13 - SSM A very early, simple satellite consisted of an...Ch. 13 - GO Four uniform spheres, with masses mA = 40 kg,...Ch. 13 - a In Problem 77, remove sphere A and calculate the...Ch. 13 - Prob. 79PCh. 13 - Prob. 80PCh. 13 - Prob. 81PCh. 13 - Prob. 82PCh. 13 - Prob. 83PCh. 13 - Prob. 84PCh. 13 - Prob. 85PCh. 13 - Prob. 86PCh. 13 - Prob. 87PCh. 13 - Prob. 88PCh. 13 - Prob. 89PCh. 13 - A 50 kg satellite circles planet Cruton every 6.0...Ch. 13 - Prob. 91PCh. 13 - A 150.0 kg rocket moving radially outward from...Ch. 13 - Prob. 93PCh. 13 - Two 20 kg spheres are fixed in place on a y axis,...Ch. 13 - Sphere A with mass 80 kg is located at the origin...Ch. 13 - In his 1865 science fiction novel From the Earth...Ch. 13 - Prob. 97PCh. 13 - Prob. 98PCh. 13 - A thin rod with mass M = 5.00 kg is bent in a...Ch. 13 - In Fig. 13-57, identical blocks with identical...Ch. 13 - A spaceship is on a straight-line path between...
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