Explanation Given information : The magnitude of the force ( F ) is 500 N. Calculation: Determine the position vector for point OB . r O B = r B − r O = ( x B i + y B j + z B k ) − ( x O i + y O j + z O k ) = ( x B − x O ) i + ( y B − y O ) j + ( z B − z O ) k (1) Here, the position vector for point B is r B , the position vector for point O is r O , the distance of point B from the origin along x direction is x B , the distance of point B from the origin along y direction is y B , the distance of point B from the origin along z direction is z B , the distance of point O from the origin along x direction is x O , the distance of point O from the origin along y direction is y O , the distance of point O from the origin along z direction is z O , the vector component along x direction is i , the vector component along y direction is j, and the vector component along z direction is k. Determine the position vector for point OA . r O A = r A − r O = ( x A i + y A j + z A k ) − ( x O i + y O j + z O k ) = ( x A − x O ) i + ( y A − y O ) j + ( z A − z O ) k (2) Here, the position vector for point A is r A , the distance of point A from the origin along x direction is x A , the distance of point A from the origin along y direction is y A , and the distance of point A from the origin along z direction is z A . Determine the position vector for point AB . r A B = r B − r A = ( x B i + y B j + z B k ) − ( x A i + y A j + z A k ) = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k (3) Determine the modulus of the position vector for point BC . | r A B | = ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 (4) Force vector: F = F u A B = F ( r A B | r A B | ) (5) Write the equation for the moment of force F about point O . M O = r O B × F (6) Conclusion : Substitute 4 m for x B , 0 m for x O , 0 m for y B , 0 m for y O , 0 m for z B , and 0 m for z O in Equation (1). r O B = { ( 4 − 0 ) i + ( 0 − 0 ) j + ( 0 − 0 ) k } = ( 4 i + 0 j + 0 k ) m Substitute 0 m for x A , 0 m for x O , 3 m for y A , 0 m for y O , 0 m for z A , and 0 m for z O in Equation (2)

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its enviro…

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Chapter 3.4, Problem 10FP

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Find the moment of the force F about point O.

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Statics and Mechanics of Materials (5th Edition)

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Find the moment of the force F about point O .

Solution Summary: The author calculates the magnitude of the force F about point O. The position vector for point B is cr_OB

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