Explanation Given information : Force ( F ) is 80 N. Force (– F ) is –80 N. Calculation : Show the free body diagram of the assembly as in Figure 1. Use figure 1. 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 (1) 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 for point BA . r B A = r A − r B = ( x A i + y A j + z A k ) − ( x B i + y B j + z B k ) = ( x A − x B ) i + ( y A − y B ) j + ( z A − z B ) k (2) Express force ( F ) as follows: F = [ 80 k ] N (3) Express force (– F ) as follows: − F = [ − 80 k ] N (4) Determine the couple moment due to force F. M C = r A B × F (5) Determine the couple moment due to force –F. M C = r B A × ( − F ) (6) Determine the magnitude of M C using the formula: M = M x 2 + M y 2 + M z 2 (7) Determine the coordinate direction angle α : α = cos − 1 ( M x M ) (8) Determine the coordinate direction angle β : β = cos − 1 ( M y M ) (9) Determine the coordinate direction angle γ : γ = cos − 1 ( M z M ) (10) Show the calculation of couple moment and the coordinate direction angle as follows: Conclusion : Substitute 0.3 m for x B , 0.2 m for x A , 0.8 m for y B , 0.3 m for y A , 0 m for z B , and 0 m for z A in Equation (1). r A B = ( 0.3 − 0.2 ) i + ( 0.8 − 0.3 ) j + ( 0 − 0 ) k = 0.1 i + 0.5 j + 0 k = ( 0.1 i + 0.5 j ) m Substitute 0.2 m for x A , 0.3 m for x B , 0.3 m for y A , 0.8 m for y B , 0 m for z A , and 0 m for z B , and in Equation (2). r B A = ( 0.2 − 0.3 ) i + ( 0.3 − 0.8 ) j + ( 0 − 0 ) k = − 0.1 i − 0.5 j + 0 k = ( − 0.1 i − 0.5 j ) m Substitute ( 0.1 i + 0

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 3.6, Problem 66P

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Find the magnitude and coordinate direction angles of the couple moment.

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Chapter 3.6, Problem 65P

Chapter 3.6, Problem 67P

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