Explanation Given: The component force F 1 is 70 N . The component force F 2 is 40 N . Show the cable along with coordinates of the point at A , B and C as in Figure (1). From Figure (1), Establish a position vector from A to B to A to C . The coordinates of the point A ( 2 , − 3 , 3 ) m , B ( 0 , 3 , 0 ) m , and C ( − 2 , 3 , 4 ) m . Express the unit vector u in the direction of AB . u A B = r A B r A B = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 (I) Here, the position vector r in the direction of AB is r A B , the length of the cable A B is r A B , and the coordinates of B and A in x , y and z directions are x B , x A , y B , y A , z B , and z A , respectively. Calculate the vector force F 1 . F 1 = F 1 u A B (II) Express the unit vector u in the direction of AC . u A C = r A C r A C = ( x C − x A ) i + ( y C − y A ) j + ( z C − z A ) k ( x C − x A ) 2 + ( y C − y A ) 2 + ( z C − z A ) 2 (III) Here, the position vector r in the direction of AC is r A C , the length of the cable Tagged-Solutions is r A C , and the coordinates of C in x , y and z directions are x C , y C , and z C , respectively. Calculate the magnitude of the projection of the vector force F 1 along cable A C . ( F 1 ) A C = F 1 ⋅ u A C (IV) Conclusion: Substitute 0 m for x B , 3 m for y B , 0 m for z B , 2 m for x A , − 3 m for y A and 3 m for z A in Equation (I). u A B = ( 0 − 2 ) i + [ 3 − ( − 3 ) ] j + ( 0 − 3 ) k ( 0 − 2 ) 2 + [ 3 − ( − 3 ) ] 2 + ( 0 − 3 ) 2 = − 2 i + 6 j − 3 k 4 + 36 + 9 = − 2 i + 6 j − 3 k 7 = − 2 7 i + 6 7 j − 3 7 k Substitute 70 N for F 1 and − 2 7 i + 6 7 j − 3 7 k for u A B in Equation (II)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2.9, Problem 115P

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The magnitude of the projection of the vector force F1 along cable AC.

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Chapter 2.9, Problem 114P

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The magnitude of the projection of the vector force F 1 along cable AC .

Solution Summary: The author shows the cable along with coordinates of the point at A,B, and C as in Figure (1).

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The magnitude of the projection of the vector force F1 along cable AC.

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