Explanation Given information : The resultant couple moment is [ 50 i − 45 j − 20 k ] N ⋅ m . Force F 4 is [ 150 k ] kN . Explanation : Show the free body diagram of the pipe assembly as in Figure (1). Use Figure (1). Determine the position vector r 1 of force F 1 . r 1 = x i + y j + z k (I) 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 . r 2 = x i + y j + z k (II). Determine the position vector r 3 of force F 3 . r 3 = x i + y j + z k (III) Show the geometry as in Figure (2). Use Figure (2). Determine the position vector r 4 of force F 4 . r 4 = 0.3 cos θ cos θ 1 i + 0.3 cos θ sin θ 1 j − 0.3 sin θ k (IV) Here, the horizontal and vertical resolving angle is θ & θ 1 . Express the force vector F 1 as follows: F 1 = ( F 1 k ) N (V) Express the force vector F 2 as follows: F 2 = ( F 2 k ) N (VI) Express the force vector F 3 as follows: F 3 = ( F 3 i ) N (VII) Express the force vector F 4 as follows: F 4 = [ 150 k ] kN (VIII) Determine the couple moment at point O . ( M C ) R = r 1 × F 1 + r 2 × F 2 + r 3 × F 3 + r 4 × F 4 (IX) Show the calculation of couple moment and the coordinate direction angle as follows: Conclusion : Substitute 0.2 m for x , 0 m for y , and 0 m for z in Equation (II). r 1 = 0.2 i + 0 j + 0 k = ( 0 .2i ) m Substitute 0 m for x , 0.20 m for y , and 0 m for z in Equation (II). r 2 = 0 i + 0.2 j + 0 k = ( 0.2 j ) m Substitute 0 m for x , 0.2 m for y , and 0 m for z in Equation (III). r 3 = 0 i + 0.2 j + 0 k = ( 0.2 j ) m Substitute 30 ° for θ and 45 ° for θ 1 in Equation (IV). r 4 = ( 0.3 cos 30 ° cos 45 ° ) i + ( 0.3 cos 30 ° sin 45 ° ) j − ( 0.3 sin 30 ° ) k = ( 0.1837 i + 0.1837 j − 0.15 k ) m Substitute [ 50 i − 45 j − 20 k ] N ⋅ m for ( M C ) R , ( 0 .2i ) m for r 1 , ( F 1 k ) N for F 1 , ( 0.2 j ) m for r 2 , ( F 2 k ) N for F 2 , ( 0.2 j ) m for r 3 , ( F 3 i ) N for F 3 , ( 0.1837 i + 0.1837 j − 0.15 k ) m for r 4 , and ( 150 k ) kN for F 4 in Equation (IX). 50 i − 45 j − 20 k = { | i j k 0.2 0 0 0 0 F 1 | + | i j k 0 0.2 0 0 0 F 2 | + | i j k 0 0

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

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 4.6, Problem 96P

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The magnitudes of F1, F2, and F3.

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

Ch. 4.4 - P41. In each case, determine the moment of the...Ch. 4.4 - P42. In each case, set up the determinant to find...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...

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The magnitudes of F 1 , F 2 , and F 3 .

Solution Summary: The author shows the free body diagram of the pipe assembly as in Figure (1).

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