a) Explanation Given information : The given forces F 1 , F 2 , and F 3 and values are 60 N, 85 N, and 45 N. Show the free body diagram of the forces acting on the plane as in Figure (1). Using Figure (1), Vector Analysis: Determine the position vector 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 , and 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) Determine the unit vector about AB axis. u A B = r A B | r A B | (III) Determine the moment of force F 1 about AB axis. ( M A B ) 1 = u A B ⋅ ( r 1 × F 1 ) (IV) Determine the moment of force F 2 about AB axis. ( M A B ) 2 = u A B ⋅ ( r 2 × F 2 ) (V) Determine the moment of force F 3 about AB axis. ( M A B ) 3 = u A B ⋅ ( r 3 × F 3 ) (VI) Conclusion : Substitute 2 m for x B , 0 m for x A , 0 m for y B , 1.5 m for y A , 0 m for z B , and 0 m for z A in Equation (I). r A B = { ( 2 − 0 ) i + ( 0 − 1.5 ) j + ( 0 − 1.5 ) k } = ( 2 i + 0 j − 1.5 j ) m Substitute 2 m for x B , 0 m for x A , 0 m for y B , 0 m for y A , 0 m for z B , and 1.5 m for z A in Equation (II). | r A B | = ( 2 − 0 ) 2 + ( 0 − 1.5 ) 2 + ( 0 − 0 ) 2 = 2.5 m Substitute ( 2 i − 1.5 j + 0 k ) m for r A B and 2 b) To determine The magnitude of the moments of each of the forces about axis AB using scalar analysis.

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 4.5, Problem 47P

To determine

The magnitude of the moments of each of the forces about axis AB using the vector analysis.

To determine

The magnitude of the moments of each of the forces about axis AB using scalar analysis.

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Chapter 4.5, Problem 18FP

Chapter 4.5, Problem 48P

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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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