Explanation Given information : The force F B is 5.0 kN. The force F D is 7.0 kN. Show the free body diagram of the flag post as in Figure (1). Use Figure (1). Determine the position vector r A B for point AB . r A B = r B − r A = ( x B i + y B j + z B k ) − ( x A i + y A j + z A k ) = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k (I) Here, the position vector for point B is r B , the position vector for point A is r A , the distance of point B from the origin along x direction is x B , the distance of point B from the origin along y direction is y B , the distance of point B from the origin along z direction is z B , 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 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 modulus of position vector for point AB . | r A B | = ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 (II) Express the force F B as follows: F B = F B [ r A B | r A B | ] (III) Determine the position vector r C D for point CD . r C D = r C − r D = ( x C i + y C j + z C k ) − ( x D i + y D j + z D k ) = ( x C − x D ) i + ( y C − y D ) j + ( z C − z D ) k (IV) Here, the position vector for point B is r B , the position vector for point A is r A , the distance of point B from the origin along x direction is x B , the distance of point B from the origin along y direction is y B , the distance of point B from the origin along z direction is z B , 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 , and the distance of point A from the origin along z direction is z A . Determine the modulus of position vector for point CD . | r C D | = ( x D − x C ) 2 + ( y D − y C ) 2 + ( z D − z C ) 2 (V) Express the force F D as follows: F D = F D [ r C D | r C D | ] (VI) Determine the resultant force using the formula. F R = F B + F D (VII) Express the position vector r O B of point OB as follows: r O B = { 6 j } m (VIII) Express the position vector r O C of point OC as follows: r O C = { 6 k } m (IX) Determine the resultant couple moment ( M R ) O at point O using the formula. ( M R ) O = r O B × F B + r O C × F D (X) Conclusion : Substitute 0 m for x A , 0 m for x B , 6.0 m for y A , 0 m for y B , 0 m for z A , and 8.0 m for z B in Equation (I). r A B = ( 0 − 0 ) i + ( 6 − 0 ) j + ( 0 − 8 ) k = ( 0i + 6 j − 8 k ) m Substitute 0 m for x A , 0 m for x B , 6.0 m for y A , 0 m for y B , 0 m for z A , and 8.0 m for z B in Equation (II). | r A B | = ( 0 − 0 ) 2 + ( 6 − 0 ) 2 + ( 0 − 8 ) 2 = 10 m Substitute 5.0 kN for F B , ( 0i + 6 j − 8 k ) m for r A B , and 10 m for | r A B | in Equation (III)

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 4.7, Problem 108P

To determine

The resultant force and resultant couple moment at point O as a Cartesian vector form.

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Chapter 4.7, Problem 107P

Chapter 4.7, Problem 109P

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Chapter 4 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

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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