Explanation Given information : The horizontal force P is 20 N. Show the free body diagram of the socket wrench as in Figure (1). Determine the position vector for point BA . r B A = r A − r B = ( x A i + y A j + z A k ) − ( x B i + y B j + z B k ) = ( x A − x B ) i + ( y A − y B ) j + ( z A − z B ) k (I) Here, the position vector for point A is r A , the position vector for point B is r B , 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 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 vector component along x direction is i, the vector component along y direction is j, and the vector component along z direction is k. Force in handle of the socket wrench BA : F B A = F ( sin θ i − cos θ j ) (II) Here, the angle of force is θ . Write the equation for moment of force F B A about point B . M B = r B A × F B A (III) Determine the magnitude of M B . | M B | = ( M B ) x 2 + ( M B ) y 2 + ( M B ) z 2 (IV) Determine the unit vector for M B M B = M B | M B | = ( M B ) x i + ( M B ) y j + ( M B ) z k | M B | (V) Determine the coordinate direction angle α . cos α = ( ( M B ) x M B ) (VI) Determine the coordinate direction angle β . cos β = ( ( M B ) y M B ) (VII) Determine the coordinate direction angle γ . cos γ = ( ( M B ) z M B ) (VIII) Conclusion : Substitute 0 m for x A , 0.01 m for x B , 0.2 m ft for y A , 0 m for y B ,0 m for z A , and 0 m for z B in Equation (I). r B A = ( 0 − 0.01 ) i + ( 0.2 − 0 ) j + ( 0 − 0 ) k = − 0.01 i − 0.2 j = ( − 0.01 i − 0.2 j ) m Substitute 20 for F and 60 ° for θ in Equation (II). F B A = 20 ( sin 60 i − cos 60 j ) = ( 17.32 i − 10 j ) N Substitute − 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

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 4.4, Problem 13P

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The moment due to force about point B and the coordinate direction angles α,β, and γ of the moment axis.

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Chapter 4.4, Problem 12P

Chapter 4.4, Problem 14P

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motor supplies 200 kW at 6 Hz to flange A of the shaft shown in Figure. Gear B transfers 125 W of power to operating machinery in the factory, and the remaining power in the shaft is mansferred by gear D. Shafts (1) and (2) are solid aluminum (G = 28 GPa) shafts that have the same diameter and an allowable shear stress of t= 40 MPa. Shaft (3) is a solid steel (G = 80 GPa) shaft with an allowable shear stress of t = 55 MPa. Determine: a) the minimum permissible diameter for aluminum shafts (1) and (2) b) the minimum permissible diameter for steel shaft (3). c) the rotation angle of gear D with respect to flange A if the shafts have the minimum permissible diameters as determined in (a) and (b).

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The moment due to force about point B and the coordinate direction angles α , β , a n d γ of the moment axis.

Solution Summary: The author shows the free body diagram of the socket wrench as in Figure (1).

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The moment due to force about point B and the coordinate direction angles α,β, and γ of the moment axis.

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