(a) Explanation Given information : The force vector ( F ) is { 6 i + 2j + 3 k } kN . Determine the position vector for point Oa . r O a = r a − r O = ( x a i + y a j + z a k ) − ( x O i + y O j + z O k ) = ( x a − x O ) i + ( y a − y O ) j + ( z a − z O ) k (I) Here, the position vector for point a–a is r a , the position vector for point O is r O , the distance of point a–a from the origin along the x direction is x a , the distance of point a–a from the origin along the y direction is y a , and the distance of point a–a from the origin along the z direction is z a , the distance of point O from the origin along the x direction is x O , the distance of point O from the origin along the y direction is y O , the distance of point O from the origin along the z direction is z O , the vector component along the x direction is i, the vector component along the y direction is j, and the vector component along the z direction is k. Determine the modulus of position vector for point Oa . | r O a | = ( x a − x O ) 2 + ( y a − y O ) 2 + ( z a − z O ) 2 (II) Unit vector: u O a = r O a | r O a | (III) Determine the moment of force about a – a axis. M a = u O a ⋅ ( r × F ) = u O a ⋅ | i j k r x r y r z F x F y F z | (IV) Here, the x component of the position vector is r x , the y component of the position vector is r y , the z component of the position vector is r z , the x component of the force vector is F x , the y component of the force vector is F y , and the z component of the force vector is F z . Conclusion : Substitute –4 m for x a , 0 m for x O , –3 m for y a , 0 m for y O , 0 m for z a , and 0 m for z O in Equation (I). r O a = ( − 4 − 0 ) i + ( − 3 − 0 ) j + ( 0 − 0 ) k = ( − 4 i − 3 j + 0 k ) m Substitute –4 m for x a , 0 m for x O , –3 m for y a , 0 m for y O , 0 m for z a , and 0 m for z O in Equation (II) (b) To determine The determinant of the moment of force about a − a axis. (c) To determine The determinant of the moment of force about a − a axis.

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 4.5, Problem 4PP

(a)

To determine

The determinant of the moment of force about a−a axis.

(b)

To determine

The determinant of the moment of force about a−a axis.

(c)

To determine

The determinant of the moment of force about a−a axis.

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Chapter 4.5, Problem 3PP

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The determinant of the moment of force about a − a axis.

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The determinant of the moment of force about a−a axis.

The determinant of the moment of force about a−a axis.

The determinant of the moment of force about a−a axis.

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