Explanation Given information : The chain AB exerts a force ( F ) on the door at B is 20 lb. The given angle θ is 20 ° . Determine the position vector for point OB . r O B = r B − r O = ( x B i + y B j + z B k ) − ( x O i + y O j + z O k ) = ( x B − x O ) i + ( y B − y O ) j + ( z B − z O ) k (I) Here, the position vector for point B is r B , the position vector for point O is r O , 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 , the distance of point B from the origin along z direction is z B , the distance of point O from the origin along x direction is x O , the distance of point O from the origin along y direction is y O , the distance of point O from the origin along z direction is z O , 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 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 (II) Here, the position vector for point A is r A , 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 , and the distance of point A from the origin along z direction is z A . 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 (III) Determine the modulus of position vector for point AB | r A B | = ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 (IV) Force vector: F = F ( r A B | r A B | ) (V) Write the equation for moment of force F about x axis. M x = i ⋅ ( r O B × F ) (VI) Conclusion : Substitute 3 ft for x B , 0 ft for x O , 0 ft for y B , 0 ft for y O , 4 ft for z B , and 0 ft for z O , in Equation (I). r O B = { ( 3 − 0 ) i + ( 0 − 0 ) j + ( 4 − 0 ) k } = ( 3 i + 0 j + 4 k ) ft Substitute 0 ft for x A , 0 ft for x O , ( 3 cos 20 ° ) ft for y A , 0 ft for y O , ( 3 sin 20 ° ) ft for z A , and 0 ft for z O , in Equation (II)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 4.5, Problem 50P

To determine

The magnitude of the moment of the force along the hinged axis x of the door.

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Chapter 4.5, Problem 49P

Chapter 4.5, Problem 51P

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Chapter 4 Solutions

Engineering Mechanics: Statics

Ch. 4.4 - F41. Determine the moment of the force about point...Ch. 4.4 - F42. Determine the moment of the force about point...Ch. 4.4 - F43. Determine the moment of the force about point...Ch. 4.4 - Neglect the thickness of the member.Ch. 4.4 - F45. Determine the moment of the force about point...Ch. 4.4 - F46. Determine the moment of the force about point...Ch. 4.4 - F47. Determine the resultant moment produced by...Ch. 4.4 - F48. Determine the resultant moment produced by...Ch. 4.4 - F49. Determine the resultant moment produced by...Ch. 4.4 - Express the result as a Cartesian vector.

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