Solved: Gravitational potential The gravitational force

Chapter 14, Problem 53

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Gravitational potential The gravitational force between two point masses M and m is F = GMm r _ r _3 = GMm 8x, y, z9 1x2 + y2 + z223>2 , where G is the gravitational constant. a. Verify that this force field is conservative on any region excluding the origin. b. Find a potential function w for this force field such that F = -_w. c. Suppose the object with mass m is moved from a point A to a point B, where A is a distance r1 from M and B is a distance r2 from M. Show that the work done in moving the object is GMm a 1 r2 - 1 r1 b. d. Does the work depend on the path between A and B? Explain.