Explanation Given information : The moment M 1 is 50 N ⋅ m . The moment M 2 is 20 N ⋅ m . Express the moment M 1 in vector form as follows: M 1 = ( 50 k ) N ⋅ m (I) Here, the vector component along the z -direction is k. Express the moment M 2 in vector form as follows: M 2 = M 2 ( − cos θ 1 sin θ ) i ( − cos θ 1 cos θ ) j + ( sin θ 1 k ) (II) Here, the vector component along the x -direction is i, the vector component along the z -direction is k, the horizontal and vertical resolving angle of moment M 2 in the x -direction is θ and θ 1 , the horizontal and vertical resolving angle of moment M 2 in the y -direction is θ and θ 1 , and the vertical resolving angle of M 2 in the z -direction is θ 1 . Determine the resultant moment using the following formula: ( M C ) R = ∑ M = M 1 + M 2 (III) Determine the magnitude of M R using the following formula: M R = M x 2 + M y 2 + M z 2 (IV) Determine the coordinate direction angle α : α = cos − 1 ( M x M R ) (V) Determine the coordinate direction angle β : β = cos − 1 ( M y M R ) (VI) Determine the coordinate direction angle γ : γ = cos − 1 ( M z M R ) (VII) Show the calculation of moment and the coordinate direction angle as follows: Conclusion : Substitute 20 N ⋅ m for M 2 , 20 ° for θ 1 , and 30 ° for θ in Equation (II). M 2 = 20 ( − cos 20 ° sin 30 ° ) i ( − cos 20 ° cos 30 ° ) j + ( sin 20 ° k ) = ( − 9.397 i − 16.276 j + 6.804 k ) N ⋅ m Substitute ( 50 k ) N ⋅ m for M 1 and ( − 9.397 i − 16.276 j + 6.804 k ) N ⋅ m for M 2 in Equation (III)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 4.6, Problem 86P

To determine

The magnitude and coordinate direction angles of the resultant couple moment.

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Chapter 4.6, Problem 85P

Chapter 4.6, Problem 87P

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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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