Explanation Given information : The force F 1 is ( − 4 i + 2 j − 3 k ) kN . The force F 2 is ( 3 i − 4 j − 2 k ) kN . Determine the resultant force using the formula: F R = F 1 + F 2 (I) Determine the position vector r 1 of force F 1 about point O . r 1 = x i + y j + z k (II) Here, 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 r 2 of force F 2 at point O . r 2 = x i + y j + z k (III). Determine the resultant moment at point O . ( M R ) O = r 1 × F 1 + r 2 × F 2 (IV) Show the calculation of resultant vector and the couple moment as follows: Conclusion : Substitute ( − 4 i + 2 j − 3 k ) kN for F 1 and ( 3 i − 4 j − 2 k ) kN for F 2 in Equation (I). F R = ( − 4 i + 2 j − 3 k ) + ( 3 i − 4 j − 2 k ) = − 4 i + 2 j − 3 k + 3 i − 4 j − 2 k = ( − 1 i − 2 j − 5 k ) kN Thus, the equivalent force F R is ( − 1 i − 2 j − 5 k ) kN _ . Substitute 4.0 m for x , –0.15 m for y , and 0.25 m for z in Equation (II). r 1 = 4.0 i − 0.15 j + 0.25 k Substitute 4.0 m for x , 0.15 m for y , and 0.25 m for z in Equation (III). r 2 = 4.0 i + 0.15 j + 0.25 k Substitute 4.0 i − 0.15 j + 0.25 k for r 1 , ( − 4 i + 2 j − 3 k ) kN for F 1 , 4.0 i + 0.15 j + 0.25 k for r 2 , ( 3 i − 4 j − 2 k ) kN for F 2 in Equation (IV)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 4.7, Problem 106P

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

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Chapter 4.7, Problem 105P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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