Explanation Given: The vector force F is { 30 i − 45 j + 50 k } lb . Explanation: Establish a position vector from B to A and B to C . Write the coordinates of the points as: A ( 0 , 0 , 0 ) ft B ( 3 , 4 , 0 ) ft C ( 7 , 6 , − 4 ) ft Express 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 (I) Here, the coordinates of B and A in the x , y and z directions are x B , x A , y B , y A , z B , 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 (II) Express 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 (III) Here, the coordinates of C in the x , y and z directions are x C , y C , , 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 (IV) Calculate the dot product of position vectors of B A and B C . r B A ⋅ r B C (V) Calculate the θ between the pipe segments B A and B C . θ = cos − 1 [ r B A ⋅ r B C r B A r B C ] (VI) Conclusion: Substitute 0 ft for x A , 0 ft for y A , 0 ft for z A , 3 ft for x B , 4 ft for y B , and 0 ft for z B in Equation (I). r B A = { ( 0 − 3 ) i + ( 0 − 4 ) j + ( 0 − 0 ) k } ft = { − 3 i − 4 j } ft Substitute 0 ft for x A , 0 ft for y A , 0 ft for z A , 3 ft for x B , 4 ft for y B , and 0 ft for z B in Equation (II)

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works …

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Chapter 2.9, Problem 130P

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The angle θ between the pipe segments.

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Chapter 2.9, Problem 129P

Chapter 2.9, Problem 131P

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Engineering Mechanics: Statics and Study Pack (13th Edition)

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 this force into components acting along...Ch. 2.3 - along the v axis. Prob. F2-6 Ch. 2.3 - Determine the magnitude of the resultant force FR...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...Ch. 2.3 - Determine the magnitude of the resultant force FR...

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The angle θ between the pipe segments.

Solution Summary: The author determines the angle theta between the pipe segments. Establish a position vector from B to A and C.

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The angle θ between the pipe segments.

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Chapter 2 Solutions