Explanation Given: The magnitude of force, F = 100 N . Establish a position vector for points A , B , and C . The coordinates of the points are: point A ( 0 , 0 , 0 ) m and point B ( − 0.5 , 0.2 , 0.2 ) m . Express the position vector r in the direction of AB . r A B = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k (I) Here, the coordinates of A and B are x A , x B , y A , y B , z A , and z B , respectively. From the x yz coordinate system, write the vector force F. F = − F cos 10 ° i + F sin 10 ° k (II) Express the magnitude of the direction of AB . r A B = ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 (III) Determine the unit vector of AB . u A B = ( r A B r A B ) (IV) Here, the position vector in the direction of AB is r A B , and the magnitude of the position vector in the direction of AB is r A B . Apply the dot product to find the angle. θ = cos − 1 ( F ⋅ u A B F ⋅ u A B ) = cos − 1 ( F ⋅ u A B F x 2 + F y 2 + F z 2 ⋅ ( u A B ) x 2 + ( u A B ) y 2 + ( u A B ) z 2 ) (V) Here, the magnitude of the vector force F is F and the magnitude of the unit vector of AB is u A B . Conclusion: Substitute 0 for x A , 0 for y A , 0 for z A , –0.5 m for x B , 0.2 m for y B , and 0.2 m for z B in Equation (I). r A B = ( − 0.5 − 0 ) i + ( 0.2 − 0 ) j + ( 0.2 − 0 ) k = ( − 0.5 i + 0.2 j + 0.2 k ) m Substitute 100 N for F in Equation (II). F = − ( 100 N ) cos 10 ° i + ( 100 N ) sin 10 ° k = ( − 100 × 0

INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2.9, Problem 134P

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The angle θ that F makes with the diagonal AB of the crate.

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Chapter 2.9, Problem 133P

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INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

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The angle θ that F makes with the diagonal AB of the crate.

Solution Summary: The author determines the angle theta that F makes with the diagonal AB of the crate.

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The angle θ that F makes with the diagonal AB of the crate.

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