Explanation Given: The gravitational attraction F is F = m g R 2 r 2 Approach: To find f x ( x , y ) differentiate the f ( x , y ) with respect to x by holding y . f x ( x , y ) = ∂ ∂ x f ( x , y ) To find f y ( x , y ) differentiate the f ( x , y ) with respect to y by holding x . f y ( x , y ) = ∂ ∂ y f ( x , y ) Calculation: Consider the gravitational attraction F on a body a distance r from the center of Earth, F ( m , r ) = m g R 2 r 2 To find F m ( m , r ) differentiate the F ( m , r ) with respect to m by holding r . F m ( m , r ) = ∂ ∂ m ( m g R 2 r 2 ) = g R 2 r 2 ∂ < To determine (b) To prove: That F m > 0 and F r < 0 , also explain why is it reasonable.

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 9.2, Problem 68E

To determine

(a)

To find:

The and interpret Fm and Fr

To determine

(b)

To prove:

That Fm>0 and Fr<0, also explain why is it reasonable.

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Chapter 9.2, Problem 67E

Chapter 9.2, Problem 69E

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