(a) Explanation Given: F = ( 2 x y − 3 ) i + x 2 j Formula used: Work done by F W = ∫ A B F d r The following graph depicting the paths A B ¯ = x 1 + y 1 = 1 ; x + y = 1 ; y = 1 − x Work done by F W = ∫ A B F d r W = ∫ A B ( 2 x y − 3 ) d x + x 2 d x W = ∫ x = 1 0 [ 2 x ( 1 − x (b) To determine To find: The work done W by F along the circular arc are A B ¯ is conservative vector field (c) To determine To find: The work done W by F along the straight line are A C ¯ is conservative vector field

Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Question

Chapter 6.8, Problem 6P

(a)

To determine

To find:

The work done W by F along the straight line are AB¯ is conservative vector field

(b)

To determine

To find:

The work done W by F along the circular arc are AB¯ is conservative vector field

(c)

To determine

To find:

The work done W by F along the straight line are AC¯ is conservative vector field

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Chapter 6.8, Problem 5P

Chapter 6.8, Problem 7P

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Chapter 6 Solutions

Mathematical Methods in the Physical Sciences

Ch. 6.3 - If A=2ijk,B=2i3j+k,C=j+k, find (AB)C,A(BC),(AB)C,...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - A force F=2i3j+k acts at the point (1,5,2). Find...Ch. 6.3 - Prob. 8P Ch. 6.3 - Prob. 9P Ch. 6.3 - In Figure 3.5, let r be another vector from O to...

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The work done W by F along the straight line are A B ¯ is conservative vector field

Concept explainers

To find: The work done W by F along the straight line are AB¯ is conservative vector field

To find: The work done W by F along the circular arc are AB¯ is conservative vector field

To find: The work done W by F along the straight line are AC¯ is conservative vector field

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Chapter 6 Solutions

To find:

The work done W by F along the straight line are AB¯ is conservative vector field

To find:

The work done W by F along the circular arc are AB¯ is conservative vector field

To find:

The work done W by F along the straight line are AC¯ is conservative vector field