Explanation Draw the free body diagram of forces F 1 and F 2 as in Figure (1). Using Figure (1), Establish a position vector from A to B to C to D . The coordinates of the point A ( 3 , 2.5 , 2 ) ft , B ( 0 , 3 , 2.5 ) ft , C ( 0 , 3 , 0 ) ft , and D ( 3 , 2.5 , 0.5 ) ft Express the position vector r in the direction of AB using Figure (1). r A B = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k (I) Here, the coordinates of A and B are x A , x B , y A , y B , z A , and z B , respectively. Express the position vector r in the direction of CD using Figure (1). r A C = ( x C − x A ) i + ( y C − y A ) j + ( z C − z A ) k (II) Here, the coordinates of C and D are x C , x D , y C , y D , z C , and z D , respectively. Express the force F 1 as a Cartesian vector form and position vector r directed from point A to point B . F 1 = F 1 u A B = F 1 ( r A B r A B ) = F 1 ( r A B ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 ) (III) Here, the unit vector in the direction of AB is u A B , position vector in the direction of AB is r A B , and magnitude of the position vector in the direction of AB is r A B . Express the force F 2 as a Cartesian vector form and position vector r directed from point C to point D . F 2 = F 2 u C D = F 2 ( r C D r C D ) = F 2 ( r C D ( x D − x C ) 2 + ( y D − y C ) 2 + ( z D − z C ) 2 ) (IV) Here, the unit vector in the direction of CD is u C D , position vector in the direction of CD is r C D , and magnitude of the position vector in the direction of CD is r C D . Conclusion: Substitute 0 for x B , 3 ft for y B , 2.5 ft for z B , 3 ft for x A , 2.5 ft for y A , and 2 ft for z A in Equation (I). r A B = ( 0 − 3 ) i + ( 3 − 2.5 ) j + ( 2

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2.8, Problem 102P

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The expression of forces F1 and F2 as a Cartesian vector.

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Chapter 2.8, Problem 101P

Chapter 2.8, Problem 103P

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The expression of forces F 1 and F 2 as a Cartesian vector .

Solution Summary: The author explains how to determine the expression of forces F_1 as a Cartesian vector.

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The expression of forces F1 and F2 as a Cartesian vector.

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