Explanation Given information : The force F 1 is 400 N. The force F 2 is 1500 N. 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 (I) Here, the position vector for point A is r A , the position vector for point B is r B , 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 , the distance of point A from the origin along z direction is z A , 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 vector component along x direction is i, the vector component along y direction is j, and the vector component along z direction is k. Express the force F 1 in the vector form as follows: F 1 = ( 400 i ) N (II) Write the equation for moment couple acting on the pipe as follows: M C 1 = r A B × F 1 (III) 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 (IV) Here, 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 , and the distance of point B from the origin along z direction is z B . Express the force F 2 in the vector form as follows: F 1 = ( 150j ) N (V) Write the equation for moment couple acting on the pipe as follows: M C 2 = r O B × F 2 (VI) Determine the resultant couple moment of the two couples that act on the assembly using the formula. ( M C ) R = M C 1 + M C 2 (VII) Conclusion : Substitute ( 0.6 cos 45 ° ) m for x B , 0 m for x A , –0.5 m for y B , 0 m for y A , ( − 0.6 sin 45 ° ) m for z B , and 0 m for z A in Equation (I). r A B = ( 0.6 cos 45 ° − 0 ) i + ( − 0.5 − 0 ) j + ( − 0.6 sin 45 ° − 0 ) k = 0.424 i − 0.5 j − 0.424 k = ( 0.424 i − 0.5 j − 0.424 k ) m Substitute ( 0.424 i − 0.5 j − 0.424 k ) m for r A B and ( 400 i ) N for F 1 in Equation (III). M C 1 = | i j k 0

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ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 4.9, Problem 163RP

To determine

The resultant couple moment of the two couples that act on the assembly.

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Chapter 4.9, Problem 162P

Chapter 4.9, Problem 164RP

Chapter 4 Solutions

Engineering Mechanics: Statics

Ch. 4.4 - F41. Determine the moment of the force about point...Ch. 4.4 - F42. Determine the moment of the force about point...Ch. 4.4 - F43. Determine the moment of the force about point...Ch. 4.4 - Neglect the thickness of the member.Ch. 4.4 - F45. Determine the moment of the force about point...Ch. 4.4 - F46. Determine the moment of the force about point...Ch. 4.4 - F47. Determine the resultant moment produced by...Ch. 4.4 - F48. Determine the resultant moment produced by...Ch. 4.4 - F49. Determine the resultant moment produced by...Ch. 4.4 - Express the result as a Cartesian vector.

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