Explanation Given: The magnitude of force, F 1 = 400 N . The magnitude of force, F 2 = 400 N . The angle between F 1 and z axes is 35 ° . The angle between F 2 and z -axis is 120 ° . The angle between F 2 and y -axis is 60 ° . The angle between F 2 and z -axis is 45 ° . The angle between F ′ and x -axis is 20 ° . Show the magnitude of component of forces F 1 and F 2 into x , y , and z axes components as in Figure (1). Express the magnitude of component force F 1 along the x- direction using Figure 1. ( F 1 ) x = F 1 ( sin 35 ° cos 20 ° ) i = F 1 ( 0.5735 × 0.9396 ) i = F 1 ( 0.538 ) i Express the magnitude of component force F 1 along the y- direction using Figure 1. ( F 1 ) y = − F 1 ( sin 35 ° sin 20 ° ) j = − F 1 ( 0.5735 × 0.342 ) j = − F 1 ( 0.196 ) j Express the magnitude of component force F 1 along the z- direction using Figure 1. ( F 1 ) z = F 1 ( cos 35 ° ) k = F 1 ( 0.819 ) k Express the magnitude of component force F 2 along the x- direction using Figure 1. ( F 2 ) x = F 2 ( cos 45 ° ) i = F 2 ( 0.7071 ) i Express the magnitude of component force F 2 along the y- direction using Figure 1. ( F 2 ) y = F 2 ( cos 60 ° ) j = F 2 ( 0.5 ) j Express the magnitude of component force F 2 along the z- direction using Figure 1. ( F 2 ) z = F 2 ( cos 120 ° ) k = F 2 ( − 0.5 ) k Determine the unit vector along the line of action of F 1 . u F 1 = ( F 1 ) x + ( F 1 ) y + ( F 1 ) z F 1 (I) Determine the unit vector along the line of action of F 2 . u F 2 = ( F 2 ) x + ( F 2 ) y + ( F 2 ) z F 2 (II) Determine the dot product of u F 1 and u F 2

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 2.9, Problem 133P

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The angle between the two cables attached to the post.

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Chapter 2.9, Problem 132P

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Chapter 2 Solutions

Engineering Mechanics: Statics

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