Explanation Given information : The horizontal force F is 30 N. Determine the position vector for point OA . r O A = r A − r O = ( x A i + y A j + z A k ) − ( x O i + y O j + z O k ) = ( x A − x O ) i + ( y A − y O ) j + ( z A − z O ) k (I) Here, the position vector for point A is r A , the position vector for point O is r O , 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 O from the origin along x direction is x O , the distance of point O from the origin along y direction is y O , the distance of point O from the origin along z direction is z O , 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 as follows: F = F u F = F ( sin θ i − cos θ j ) N (II) Write the equation for moment of force about point O . M O = r O A × F (III) Determine the magnitude of M O using the formula; ( M C ) R = M x 2 + M y 2 + M z 2 (IV) Determine the coordinate direction angle α : α = cos − 1 ( M x M ) (V) Determine the coordinate direction angle β : β = cos − 1 ( M y M ) (VI) Determine the coordinate direction angle γ : γ = cos − 1 ( M z M ) (VII) Show the calculation of moment and the coordinate direction angle as follows: Conclusion : Substitute –0.01 m for x A , 0 m for x O , 0.2 m for y A , 0 m for y O , 0.05 m for z A , and 0 m for z O in Equation (I). r O A = ( − 0.01 − 0 ) i + ( 0.2 − 0 ) j + ( 0.05 − 0 ) k = − 0.01 i + 0.2 j + 0.05 k = ( − 0.01 i + 0.2 j + 0.05 k ) m Substitute 30 N for F and 45 ° for θ in Equation (II). F = 30 ( sin 45 ° i − cos 45 ° j ) N = ( 21 .213i − 21.213 j ) N Substitute ( − 0.01 i + 0.2 j + 0.05 k ) m for r O A and ( 21 .213i − 21

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 4.9, Problem 165RP

To determine

The moment of the force about point O and the coordinate direction angles of the resultant couple moment.

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Chapter 4.9, Problem 164RP

Chapter 4.9, Problem 166RP

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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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