Explanation Given information : The force F 1 is ( − 300 i + 150 j + 200 k ) N . The force F 2 is ( − 450 k ) N . Determine the resultant force using the equation of equilibrium. F R = ∑ F = F 1 + F 2 (I) 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 (II) Here, the position vector for point A is r A , the position vector for point O is r O , the distance of point A from the origin along the x direction is x A , the distance of point A from the origin along the y direction is y A , the distance of point A from the origin along the z direction is z A , the distance of point O from the origin along the x direction is x O , the distance of point O from the origin along the y direction is y O , the distance of point O from the origin along the z direction is z O , the vector component along the x direction is i, the vector component along the y direction is j, and the vector component along the z direction is k. 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 (III) Here, the position vector for point B is r B , the distance of point B from the origin along the x direction is x B , the distance of point B from the origin along the y direction is y B , and the distance of point B from the origin along the z direction is z B . Express the force 1 as follows: F 1 = ( − 300 i + 150 j + 200 k ) N (IV) Express the force 1 as follows: F 2 = ( − 450 k ) N (V) Write the equation for moment of force about point O . ( M R ) o = ∑ M ( M R ) o = r O B × F 1 + r O A × F 2 (VI) Conclusion : Substitute ( − 300 i + 150 j + 200 k ) N for F 1 and ( − 450 k ) N for F 2 in Equation (I). F R = ( − 300 i + 150 j + 200 k ) + ( − 450 k ) = ( − 300 i + 150 j − 250 k ) N Substitute 0 m for x B , 0 m for x O , 2.0 m for y B , 0 m for y O , 0 m for z B , and 0 m 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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Chapter 4.7, Problem 29FP

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The equivalent resultant force and couple moment acting at point O.

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