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Chapter 13: Q4P (page 379)
The Sun and Earth each exert a gravitational force on theMoon. What is the ratioof these two forces? (The average Sun–Moon distance is equal to the Sun–Earth distance.)
The value of the ratio
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A uniform solid sphere of radius R produces a gravitationalacceleration of ag on its surface. At what distance from the sphere’scenter are there points (a) inside and (b) outside the sphere wherethe gravitational acceleration is ?
A satellite orbits a planet of unknown mass in a circle of radius . The magnitude of the gravitational force on the satellite from the planet is .
(a) What is the kinetic energy of the satellite in this orbit?
(b) What would F be if the orbit radius were increased to ?
Question: 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, , where Mis the mass of the black hole and cis the speed of light.
Suppose that you wish to study a black hole near it, at a radial distance of 50Rh. 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) As a multiple of our Sun’s mass Ms , approximately what is the limit to the mass of the black hole you can tolerate at the given radial distance? (You need to estimate your height.) (b) Is the limit an upper limit (you can tolerate smaller masses) or a lower limit (you can tolerate larger masses)?
One dimension.In the figure, two point particles are fixed on anxaxis separated by distanced. ParticleAhas massM and particle Bhas mass. A third particle C, of mass, is to be placed on the xaxis and near particles Aand B. In terms of distance d, at what xcoordinate should Cbe placed so that the net gravitational force on particle Afrom particles Band Cis zero?
In Fig. 13-24, two particles of masses, mand 2m, are fixed in place on an axis. (a) Where on the axis can a third particle of mass 3m be placed (other than at infinity) so that the net gravitational force on it from the first two particles is zero: to the left of the first two particles, to their right, between them but closer to the more massive particle, or between them but closer to the less massive particle? (b) Does the answer change if the third particle has, instead, a mass of 16m ? (c) Is there a point off the axis (other than infinity) at which the net force on the third particle would be zero?
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