Explanation Given information : The force F 1 is ( 300i + 400 j − 100 k ) N . The force F 2 is ( 100i − 100 j − 50 k ) N . The force F 3 is ( − 500 k ) N . Determine the resultant force F R using the formula. F R = F 1 + F 2 + F 3 (I) Express the position vector r A B of point AB as follows: r A B = { 12 k } m (II) Express the position vector r A E of point AE as follows: r A E = { − 1 j } m (III) 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 (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 , 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 position vector r A E for point AE . r A E = r E − r A = ( x E i + y E j + z E k ) − ( x A i + y A j + z A k ) = ( x E − x A ) i + ( y E − y A ) j + ( z E − z A ) k (V) Here, the position vector for point E is r E , the distance of point E from the origin along x direction is x E , the distance of point E from the origin along y direction is y E , and the distance of point E from the origin along z direction is z E . Determine the resultant couple moment ( M R ) A at point A using the formula. ( M R ) A = r A B × F 1 + r A B × F 2 + r A E × F 3 (VI) Conclusion : Substitute ( 300i + 400 j − 100 k ) N for F 1 , ( 100i − 100 j − 50 k ) N for F 2 , and ( − 500 k ) N for F 3 in Equation (I). F R = ( 300i + 400 j − 100 k ) + ( 100i − 100 j − 50 k ) + ( − 500 k ) = ( 400i + 300 j − 650 k ) N Substitute 0 m for x A , 0 m for x B , 0 m for y A , 0 m for y B , 12 m for z A , and 0 m for z B in Equation (IV). r A B = ( 0 − 0 ) i + ( 0 − 0 ) j + ( 12 − 0 ) k = ( 0i + 0 j + 12 k ) m Substitute 0 m for x E , 0 m for x A , –1

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 109P

To determine

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

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Chapter 4.7, Problem 108P

Chapter 4.7, Problem 110P

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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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