Gravitational potential The gravitational force between two point masses M and m is (x, y, z) F = GMm- |r|3 GMm (x² + y² + z?}3/2° where G is the gravitational constant. a. Verify that this force field is conservative on any region ex- cluding the origin. b. Find a potential function o for this force field such that F = -Vọ. c. Suppose the object with mass m is moved from a point A to a point B, where A is a distance r, from M, and B is a distance r, from M. Show that the work done in moving the object is GMm d. Does the work depend on the path between A and B? Explain.

Gravitational potential The gravitational force between two point masses M and m is (x, y, z) F = GMm- |r|3 GMm (x² + y² + z?}3/2° where G is the gravitational constant. a. Verify that this force field is conservative on any region ex- cluding the origin. b. Find a potential function o for this force field such that F = -Vọ. c. Suppose the object with mass m is moved from a point A to a point B, where A is a distance r, from M, and B is a distance r, from M. Show that the work done in moving the object is GMm d. Does the work depend on the path between A and B? Explain.

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Description: Gravitational potential The gravitational force between twopoint masses M and m is(x, y, z)F = GMm-|r|3GMm(x² + y² + z?}3/2°where G is the gravitational constant.a. Verify that this force field is conservative on any region ex-cluding the origin.b.

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Question

Gravitational potential The gravitational force between two
point masses M and m is
(x, y, z)
F = GMm-
|r|3
GMm
(x² + y² + z?}3/2°
where G is the gravitational constant.
a. Verify that this force field is conservative on any region ex-
cluding the origin.
b. Find a potential function o for this force field such that
F = -Vọ.
c. Suppose the object with mass m is moved from a point A to a
point B, where A is a distance r, from M, and B is a distance
r, from M. Show that the work done in moving the object is
GMm
d. Does the work depend on the path between A and B?
Explain.

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