Explanation Given information : The force vector ( F ) is { 50 i − 20 j − 80 k } N . Calculation: Determine the position vector for point AD . r A D = r D − r A = ( x D i + y D j + z D k ) − ( x A i + y A j + z A k ) = ( x D − x A ) i + ( y D − y A ) j + ( z D − z A ) k (1) Here, the position vector for point D is r D , the position vector for point A is r A , the distance of point D from the origin along x direction is x D , the distance of point D from the origin along y direction is y D , the distance of point D from the origin along z direction is z D , the distance of point A from the origin along x direction is x A , the distance of point A from the origin along y direction is y A , the distance of point A from the origin along z direction is z A , the vector component along x direction is i , the vector component along y direction is j, and the vector component along z direction is k. Determine the position vector for point AB . r A B = r B − r A = ( x B i + y B j + z B k ) − ( x A i + y A j + z A k ) = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k (2) Here, the position vector for point B is r B , the distance of point B from the origin along x direction is x B , the distance of point B from the origin along y direction is y B , and the distance of point B from the origin along z direction is z B . Determine the modulus of the position vector for point AB . | r A B | = ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 (3) Unit vector: u A B = r A B | r A B | (4) Determine the resultant moment of force F about the baseline AB . M A B = u A B ⋅ ( r A B × F ) (5) Conclusion : Substitute 2.5 m for x D , 0 m for x A , 0 m for y D , 0 m for y A , 4 m for z D , and 0 m for z A in Equation (1). r A D = { ( 2.5 − 0 ) i + ( 0 − 0 ) j + ( 4 − 0 ) k } = ( 2 .5i + 0 j + 4 k ) m Substitute 3.5 m for x B , 0 m for x A , 0

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its enviro…

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Chapter 3.5, Problem 48P

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Find the magnitude of the moment of the force F about the baseline AB of the tripod.

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Chapter 3.5, Problem 47P

Chapter 3.5, Problem 49P

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Statics and Mechanics of Materials (5th Edition)

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Find the magnitude of the moment of the force F about the baseline AB of the tripod.

Solution Summary: The author calculates the magnitude of the moment of force F about the baseline AB of a tripod. The position vector for point AD is cr_AD

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Find the magnitude of the moment of the force F about the baseline AB of the tripod.

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