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 6, Problem 63GP
Show that the rate of change of your weight is
If you are travelling directly away from Earth at constant speed υ. Your mass is m, and r is your distance from the center of the Earth at any moment.
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Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 5.8 ✕ 104 light years from its center.
(a)
What should the orbital period (in y) of that star be?
y
(b)
If its period is 7.0 ✕ 107 y instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
solar masses
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 1011 solar masses. A star orbiting near the galaxy's periphery is 5.6 x 104 light-years from its center.
(a) What should the orbital period (in y) of that star be?
y
(b) If its period is 5.3 x 107 years instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of
the Milky Way.
solar masses
Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway
between them. This statement implies that the masses of the two stars are equal (see figure below). Assume
the orbital speed of each star is v| = 225 km/s and the orbital period of each is 11.6 days. Find the mass M
of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.)
M
XCM
M
Part 1 of 3 - Conceptualize
From the given data, it is difficult to estimate a reasonable answer to this problem without working through
the details and actually solving it. A reasonable guess might be that each star has a mass equal to or slightly
larger than our Sun because fourteen days is short compared to the periods of all the Sun's planets.
Part 2 of 3 - Categorize
The only force acting on each star is the central gravitational force of attraction which results in a centripetal
acceleration. When we solve Newton's second law, we can find the unknown mass in terms of the variables…
Chapter 6 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 6.3 - Suppose you could double the mass of a planet but...Ch. 6.4 - Two satellites orbit the Earth in circular orbits...Ch. 6.4 - Could astronauts in a spacecraft far out in space...Ch. 6.5 - Suppose there were a planet in circular orbit...Ch. 6 - Does an apple exert a gravitational force on the...Ch. 6 - The Suns gravitational pull on the Earth is much...Ch. 6 - Will an object weigh more at the equator or at the...Ch. 6 - Why is more fuel required for a spacecraft to...Ch. 6 - The gravitational force on the Moon due to the...Ch. 6 - How did the scientists of Newton's era determine...
Ch. 6 - If it were possible to drill a hole all the way...Ch. 6 - A satellite in a geosynchronous orbit stays over...Ch. 6 - Which pulls harder gravitationally, the Earth on...Ch. 6 - Would it require less speed to launch a satellite...Ch. 6 - An antenna loosens and becomes detached from a...Ch. 6 - Describe how careful measurements of the variation...Ch. 6 - The Sun is below us at midnight, nearly in line...Ch. 6 - When will your apparent weight be the greatest, as...Ch. 6 - If the Earths mass were double what it actually...Ch. 6 - The source of the Mississippi River is closer to...Ch. 6 - People sometimes ask. What keeps a satellite up in...Ch. 6 - Explain how a runner experiences free fall or...Ch. 6 - If you were in a satellite orbiting the Earth, how...Ch. 6 - Is the centripetal acceleration of Mars in its...Ch. 6 - The mass of the planet Pluto was not known until...Ch. 6 - The Earth moves faster in its orbit around the Sun...Ch. 6 - Keplers laws tell us that a planet moves faster...Ch. 6 - Does your body directly sense a gravitational...Ch. 6 - Discuss the conceptual differences between g as...Ch. 6 - (I) Calculate the force of Earths gravity on a...Ch. 6 - (I) Calculate the acceleration due to gravity on...Ch. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - (II) Calculate the effective value of g, the...Ch. 6 - (II) You are explaining to friends why astronauts...Ch. 6 - Prob. 8PCh. 6 - (II) Four 8.5-kg spheres are located at the...Ch. 6 - (II) Two objects attract each other...Ch. 6 - (II) Four masses are arranged as shown in Fig....Ch. 6 - (II) Estimate the acceleration due to gravity at...Ch. 6 - (II) Suppose the mass of the Earth were doubled,...Ch. 6 - Prob. 14PCh. 6 - (II) At what distance from the Earth will a...Ch. 6 - (II) Determine the mass of the Sun using the known...Ch. 6 - (II) Two identical point masses, each of mass M,...Ch. 6 - Prob. 18PCh. 6 - (III) (a) Use the binomial expansion...Ch. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - (II) You know your mass is 65 kg, but when you...Ch. 6 - (II) A 13.0-kg monkey hangs from a cord suspended...Ch. 6 - (II) Calculate the period of a satellite orbiting...Ch. 6 - Prob. 28PCh. 6 - (II) What will a spring scale read for the weight...Ch. 6 - Prob. 30PCh. 6 - (II) What is the apparent weight of a 75-kg...Ch. 6 - (II) A Ferris wheel 22.0 m in diameter rotates...Ch. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - (III) An inclined plane, fixed to the inside of an...Ch. 6 - (I) Use Keplers laws and the period of the Moon...Ch. 6 - (I) Determine the mass of the Earth from the known...Ch. 6 - (I) Neptune is an average distance of 4.5109 km...Ch. 6 - (II) Planet A and planet B are in circular orbits...Ch. 6 - (II) Our Sun rotates about the center of our...Ch. 6 - (II) Table 63 gives the mean distance, period, and...Ch. 6 - (II) Determine the mean distance from Jupiter for...Ch. 6 - (II) The asteroid belt between Mars and Jupiter...Ch. 6 - (III) The comet Hale-Bopp has a period of 2400...Ch. 6 - Prob. 46PCh. 6 - (III) The orbital periods and mean orbital...Ch. 6 - (II) What is the magnitude and direction of the...Ch. 6 - (II) (a) What is the gravitational field at the...Ch. 6 - Prob. 50PCh. 6 - How far above the Earths surface will the...Ch. 6 - At the surface of a certain planet, the...Ch. 6 - A certain white dwarf star was once an average...Ch. 6 - What is the distance from the Earths center to a...Ch. 6 - The rings of Saturn are composed of chunks of ice...Ch. 6 - During an Apollo lunar landing mission, the...Ch. 6 - Prob. 57GPCh. 6 - Prob. 58GPCh. 6 - Jupiter is about 320 limes as massive as the...Ch. 6 - The Sun rotates about the center of the Milky Way...Ch. 6 - Prob. 61GPCh. 6 - A satellite of mass 5500 kg orbits the Earth and...Ch. 6 - Show that the rate of change of your weight is...Ch. 6 - Astronomers using the Hubble Space Telescope...Ch. 6 - Suppose all the mass of the Earth were compacted...Ch. 6 - A plumb bob (a mass m hanging on a string) is...Ch. 6 - A geologist searching for oil finds that the...Ch. 6 - Prob. 68GPCh. 6 - A science-fiction tale describes an artificial...Ch. 6 - How long would a day be if the Earth were rotating...Ch. 6 - An asteroid of mass m is in a circular orbit of...Ch. 6 - Newton had the data listed in Table 64, plus the...Ch. 6 - A satellite circles a spherical planet of unknown...Ch. 6 - Prob. 74GPCh. 6 - The gravitational force at different places on...Ch. 6 - Prob. 76GPCh. 6 - Estimate the value of the gravitational constant G...Ch. 6 - Between the orbits of Mars and Jupiter, several...
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