Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 6, Problem 77GP
Estimate the value of the gravitational constant G in Newton’s law of universal gravitation using the following data: the acceleration due to gravity at the Earth’s surface is about 10 m/s2; the Earth has a circumference of about 40 × 106 m; rocks found on the Earth’s surface typically have densities of about 3000 kg/m3 and assume this density is constant throughout (even though you suspect it is not true).
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So let's consider a person with a mass of 51.0 kg standing on the Earth. To find the gravitational force on the person, we'll again use Newton's law of universal gravitation with the Earth as
m2
and the radius of the Earth for the distance
F =
GmME
RE2
.
Now all we need to do is substitute values and calculate. We already said
m = 51.0 kg,
and we know
G = 6.67 ✕ 10−11 N · m2/kg2.
The Earth is not a perfect sphere, but, its average radius is
RE = 6.37 ✕ 106 m.
The mass of the Earth is
ME = 5.97 ✕ 10−24 kg.
We can then substitute these values in the following formula. (Enter your answer in N.)
F =
(6.67 ✕ 10−11 N · m2/kg2)(51.0 kg)(5.97 ✕ 1024 kg)
(6.37 ✕ 106 m)2
(A) = _______ N
Now let's compare this result to the person's weight (in N) found by multiplying the person's mass by g (or, that is,
w = mg)
where
g = 9.80 m/s2.
w = (51.0 kg)(9.80 m/s2) =(b) __________________ N
You should have found that these two methods give about the same result!…
The density of Planet Y in the previous problem is Show the entire calculation. Calculation: The universal gravitational
-11 3 -1 -2
constant is 6.67430*10 m kg s . Planet Y has a radius of 5360km or 5.360*10 m and a mass of 4.56*10²3 kg. On
this planet, a rock falls vertically down from a cliff overhang to the ground. The height of the cliff is 86m. The time it
M
takes the rock to fall from the overhang to the ground is Show the entire calculation. Calculation: g = G*- The density
O
R
of Planet Y in the previous problem is Show the entire calculation. Calculation:
A research team has discovered that a moon is circling a planet of our solar system: The moonorbits the planet once every 7 hours on a nearly circular orbit in a distance R of 48000 km fromthe centre of the planet. Unfortunately, the mass m of the moon is not known. Use Newton’s lawof gravitation with G = 6.67 · 10−11 m3/(kg·s2) to approach the following questions:F = G ·mMR2(1)(a) Based on the observations, determine the total mass M of the planet.(b) Which moon and planet of our solar system is the team observing? (Use literature.)
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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