Explanation Given information : The magnitude of the force ( F ) is 120 lb. 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 (I) 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 OC . r O C = r C − r O = ( x C i + y C j + z C k ) − ( x O i + y O j + z O k ) = ( x C − x O ) i + ( y C − y O ) j + ( z C − z O ) k (II) Here, the position vector for point C is r C , the distance of point C from the origin along x direction is x C , the distance of point C from the origin along y direction is y C , and the distance of point C from the origin along z direction is z C . Determine the position vector for point BC . r B C = r C − r B = ( x C i + y C j + z C k ) − ( x B i + y B j + z B k ) = ( x C − x B ) i + ( y C − y B ) j + ( z C − z B ) k (III) Determine the modulus of the position vector for point BC . | r B C | = ( x B − x C ) 2 + ( y B − y C ) 2 + ( z B − z C ) 2 (IV) Force vector: F = F u B C = F ( r B C | r B C | ) (V) Determine the moment of force F about point O . M O = r O B × F (VI) Conclusion : Substitute 1 ft for x B , 0 ft for x O , 4 ft for y B , 0 ft for y O , 2 ft for z B , and 0 ft for z O in Equation (I). r O B = { ( 1 − 0 ) i + ( 4 − 0 ) j + ( 2 − 0 ) k } = ( 1 i + 4 j + 2 k ) ft Substitute 5 ft for x C , 0 ft for x O , 0 ft for y C , 0 ft for y O , 0 ft for z C , and 0 ft for z O in Equation (II)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

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 4.4, Problem 11FP

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The moment of the force F about point O.

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The moment of the force F about point O .

Solution Summary: The author explains how to determine the moment of the force F about point O. The position vector for point B is cr_OB

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