Explanation Given information : The resultant couple moment is [ 50 i − 45 j − 20 k ] N ⋅ m . Force F 4 is [ 150 k ] kN . 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 0.2 0 F 3 0 0 | + | i j k 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its enviro…

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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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