Explanation Given information : The force value ( F ) is 200 N. Explanation : Scalar Analysis: Determine the force along the x axis. F x = | F cos θ x | (I) Here, the angle for the force F along the x axis is θ x . Determine the force along the y axis. F y = F cos θ y (II) Here, the angle for the force F along the y axis is θ y . Determine the force along the z axis. F z = F cos θ z (III) Here, the angle for the force F along the z axis is θ z . Determine the moment of force F about the x axis. M x = − F y d z + F z d y (IV) Here, the distance for the force F y about the z axis is d z and the distance for the force F z about the y axis is d y . Vector Analysis: 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 (V) 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 , and 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 moment of force F about x axis. M x = i ⋅ ( r O A × F ) (VI) Conclusion : Substitute 200 N for F and 120 ° for θ x in Equation (I). F x = | 200 cos 120 ° | = 100 N Substitute 200 N for F and 60 ° for θ y in Equation (II). F y = 200 cos 60 ° = 100 N Substitute 200 N for F and 45 ° for θ z in Equation (III)

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

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 4.5, Problem 15FP

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The magnitude of the moment of the force about x axis.

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

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The magnitude of the moment of the force about x axis.

Solution Summary: The author explains how to determine the magnitude of the moment of force about x axis using scalar analysis.

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The magnitude of the moment of the force about x axis.

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