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Chapter 13: 101P (page 385)
A spaceship is on a straight-line path between Earth and the Moon. At whatdistance from Earth is the net gravitational force on the spaceship zero?
Net gravitational force on the spaceship is zero at a distance of from the earth.
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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)?
A thin rod with mass M=is bent in a semicircle of radius. (Fig. 13-56). (a) What is its gravitational force (both magnitude and direction on a particle with massat P, the center of curvature? (b) What would be the force on the particle the rod were a complete circle?
To alleviate the traffic congestion between two cities such as Boston and Washington, D.C, engineers have proposed building a rail tunnel along a chord line connecting the cities (Fig. 13-55). A train, unpropelled by any engine and starting from rest, would fall through the first half of the tunnel and then move up the second half. Assuming Earth is a uniform sphere and ignoring air drag and friction, find the city-to-city travel time.
In the figure, a square of edge length20.0 cmis formed by four spheres of masses In unit-vector notation, what is the net gravitational force from them on a central sphere with mass?
Question: The orbit of Earth around the Sun is almost circular. The closest and farthest distances are and respectively. Determine the corresponding variations in (a) total energy, (b) gravitational potential energy, (c) kinetic energy, and (d) orbital speed. (Hint:Use conservation of energy and conservation of angular momentum.)
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