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Chapter 13: Q19P (page 380)
what altitude above Earth’s surface would the gravitational acceleration be?
The altitude above the earth’s surface where g is is
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In deep space, sphere Aof mass is located at the origin of an x-axis and sphere Bof mass is located on the axis at . Sphere Bis released from rest while sphere Ais held at the origin. (a) What is the gravitational potential energy of the two-sphere system just as Bis released? (b) What is the kinetic energy of Bwhen it has moved toward A?
Three identical stars of massMform an equilateral triangle that rotates around the triangle’s center as the stars move in a common circle about that center. The triangle has edge lengthL. What is the speed of the stars?
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?
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?
We watch two identical astronomical bodies Aand B, each of mass m, fall toward each other from rest because of the gravitational force on each from the other. Their initial center-to-center separation isRi. Assume that we are in an inertial reference frame that is stationary with respect to the center of mass of this two body system. Use the principle of conservation of mechanical energy (Kf+ Uf=Ki +Ui ) to find the following when the center-to-center separation is 0.5Ri:
(a) the total kinetic energy of the system,
(b) the kinetic energy of each body,
(c) the speed of each body relative to us, and
(d) the speed of body Brelative to body A. Next assume that we are in a reference frame attached to body A(we ride on the body). Now we see body Bfall from rest toward us. From this reference frame, again useto find the following when the center-to-center separation is:
(e) the kinetic energy of body Band
(f) the speed of body Brelative to body A.
(g) Why are the answers to (d) and (f) different? Which answer is correct?
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