Explanation Given information : The given force value ( F ) is 30 N. Show the free body diagram of a pipe system as in Figure (1). Using Figure (1), Determine the position vector about the a – a axis. r = ( x a i + y a j + z a k ) (I) Here, the distance of the a – a axis from the origin along the x direction is x a , the distance of the a – a axis from the origin along the y direction is y a , the distance of the a – a axis from the origin along the z direction is z a , 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 modulus of the position vector about the a – a axis. | r | = x a 2 + y a 2 + z a 2 (II) Write the unit vector about the a – a axis. u = j Determine the force vector about the a – a axis. F = F ( cos α i + cos β j + cos γ k ) (III) Here, the angle of force along the x direction is α , the angle of force along the y direction is β , and the angle of force along the z direction is γ . Determine the moment of force about the point a – a axis. M a = u . ( r × F ) (IV) Write the unit vector for the force F. u F = r F | r F | (V) Determine the maximum moment about the a – a axis. M = F | r F | (VI) Conclusion : Substitute − 100 mm for x a , 0 m for y a , and 150 mm for z a in Equation (I). r = { ( − 100 mm × 1 m 1 , 000 mm ) i + 0 j + ( 150 mm × 1 m 1 , 000 mm ) k } = − 0.1 i+ 0 j + 0.15 k Substitute − 100 mm for x a , 0 m for y a , and 150 mm for z a in Equation (II). | r | = ( − 100 mm × 1 m 1 , 000 mm ) 2 + 0 + ( 150 mm × 1 m 1 , 000 mm ) = 0.1803 m Substitute 30 N for F , 60 ° for α , 60 ° for β , and 45 ° for γ in Equation (III). F = 30 ( cos 60 ° i + cos 60 ° j + cos 45 ° k ) = 15 i + 15 j + 21.21 k Substitute j for u, − 0.1 i+ 0 j + 0.15 k for r and 15 i + 15 j + 21.21 k for F in Equation (IV). M a = j . | i j k − 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 4.5, Problem 66P

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The moment of force about an a−a axis.

The coordinate direction angles of the force F.

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Chapter 4.5, Problem 65P

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The moment of force about an a − a axis. The coordinate direction angles of the force F .

Solution Summary: The author explains the moment of force about an a-a axis and the coordinate direction angles of the force F.

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The moment of force about an a−a axis.

The coordinate direction angles of the force F.

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Chapter 4 Solutions

The moment of force about an a − a axis. The coordinate direction angles of the force F .

Solution Summary: The author explains the moment of force about an a-a axis and the coordinate direction angles of the force F.

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The moment of force about an a−a axis. The coordinate direction angles of the force F.

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Chapter 4 Solutions

The moment of force about an a−a axis.

The coordinate direction angles of the force F.