Explanation Draw the free body diagram of force F B and F C from point A as in Figure 1. Establish a position vector from A to B to A to C . The coordinates of the point A ( 0 , 0 , 6 ) m , B ( 3 , − 2 , 0 ) m and point C ( 2 , 3 , 0 ) m . 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 Here, the coordinates of A and B are x A , x B , y A , y B , z A , and z B , respectively. Substitute 3 m for x B , 2 m for y B , 0 m for z B , 0 for x A , 0 for y A , and 6 m for z A . r A B = ( 3 − 0 ) i + ( − 2 − 0 ) j + ( 0 − 6 ) k = { 3 i − 2 j − 6 k } m Express the position vector r in the direction of AC using Figure 1. r A C = ( x C − x A ) i + ( y C − y A ) j + ( z C − z A ) k Here, the coordinates of A and C are x C , x A , y C , y A , z C , and z A respectively. Substitute 2 m for x C , 3 m for y C , 0 m for z C , 0 for x A , 0 for y A , and 6 m for z A . r A C = ( 2 − 0 ) i + ( 3 − 0 ) j + ( 0 − 6 ) k = { 2 i + 3 j − 6 k } m Express the force F B as a Cartesian vector form and position vector r directed from point A to point B . F B = F B u A B = F B ( r A B r A B ) = F B ( r A B ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 ) 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 . Substitute 3 m for x B , 2 m for y B , 0 m for z B , 0 for x A , 0 for y A , 6 m for z A , 840 N for F B , and { 3 i − 2 j − 6 k } m for r A B . F B = 840 N ( { 3 i − 2 j − 6 k } m ( 3 − 0 ) 2 + ( − 2 − 0 ) 2 + ( 0 − 6 ) 2 ) = 840 ( { 3 i − 2 j − 6 k } 7 ) = { 360 i − 240 j − 720 k } N Express the force F C as a Cartesian vector form and position vector r directed from point A to point C

Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (5th Edition)

5th Edition

ISBN: 9780134301006

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2.8, Problem 23FP

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Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (5th Edition)

Ch. 2.3 - In each case, construct the parallelogram law to...Ch. 2.3 - In each case, show how to resolve the force F into...Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - Resolve the force into components acting along...Ch. 2.3 - Prob. 6FP Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...

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Solution Summary: The author explains how to find the magnitude of the resultant force at A. Establish a position vector from A to B to C.

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