Explanation Given information: The force F is 100 lb . Calculation: Establish a position vector from B to C and B to A . The coordinates are: A ( − 3 , 0 , 0 ) ft , B ( 0 , 0 , 0 ) ft , and C ( 6 , 4 , − 2 ) ft . Calculate the position vector r in the direction of BC is r B C . r B C = ( x C − x B ) i + ( y C − y B ) j + ( z C − z B ) k (1) Here, the coordinates of B and C in the x , y and z directions are x B , x C , y B , y C , z B , and z C , respectively. Calculate the length of the cable B C is r B C . r B C = ( x C − x B ) 2 + ( y C − y B ) 2 + ( z C − z B ) 2 (2) Calculate the position vector r in the direction of BA is r B A . r B A = ( x A − x B ) i + ( y A − y B ) j + ( z A − z B ) k (3) Here, the coordinates of A in the x , y and z directions are x A , y A , , and z A , respectively. Calculate the length of the cable B A is r B A . r B A = ( x A − x B ) 2 + ( y A − y B ) 2 + ( z A − z B ) 2 (4) Express the angle θ between the pipe segments B A and B C . θ = 180 ° − { cos − 1 [ r B C ⋅ r B A | r B C | | r B A | ] } (5) Conclusion: Substitute 6 ft for x C , 4 ft for y C , − 2 ft for z C , 0 ft for x B , 0 ft for y B , and 0 ft for z B in Equation (1). r B C = ( 6 − 0 ) i + ( 4 − 0 ) j + ( − 2 − 0 ) k = { 6 i + 4 j − 2 k } ft Substitute 6 ft for x C , 4 ft for y C , − 2 ft for z C , 0 ft for x B , 0 ft for y B , and 0 ft for z B in Equation (2)

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2.9, Problem 80P

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Find the angle θ between the pipe segments BA and BC.

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Chapter 2.9, Problem 79P

Chapter 2.9, Problem 81P

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Statics and Mechanics of Materials (5th Edition)

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Find the angle θ between the pipe segments B A and B C .

Solution Summary: The author calculates the angle theta between the pipe segments and the length of the cable BC.

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Find the angle θ between the pipe segments BA and BC.

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