Explanation Given information : The downward inclined force F 1 is 250 N. The upward inclined force F 2 is 500 N. The horizontal force F 3 is 300 N. Show the free body diagram of the forces acting on the post as in Figure (1). Show the free body diagram of the angle and the location of the resultant force acting on the post as in Figure (2). Assumption : Towards right is positive. Determine the resultant of the horizontal force using the equation of equilibrium. F R x = ∑ F x = F 1 cos θ 1 − F 2 cos θ 2 − F 3 (I) Here, the angle for the force F 1 is θ 1 and the angle for the force F 2 is θ 2 . Assumption : Upward is positive. Determine the resultant of the vertical force using the equation of equilibrium. F R y = ∑ F y = F 2 sin θ 2 − F 1 sin θ 1 (II) Determine the resultant force F R . F R = ( F R x ) 2 + ( F R y ) 2 (III) Determine the direction θ of the resultant force. θ = tan − 1 ( F R y F R x ) (IV) Assumption : Anti-clockwise is positive. Determine the line of action of the resultant by taking the moment about point A . ( M R ) A = ∑ M A F R x d = { F 2 cos θ 2 ( l 1 ) − F 2 sin θ 2 ( l 2 ) − ( F 1 ) cos θ 1 ( l 3 ) − ( F 1 ) sin θ 1 ( l 4 ) + F 3 ( l 5 ) } (V) Here, the vertical distance of F 2 is l 1 , the horizontal distance of F 2 is l 2 , the vertical distance of F 1 is l 3 , the horizontal distance of F 1 is l 4 , and the vertical distance of F 3 is l 5 . Conclusion : Substitute 250 N for F 1 , ( 4 5 ) for cos θ 1 , 500 N for F 2 , 30 ° for θ 2 , and 300 N for F 3 in Equation (I). F R x = 250 ( 4 5 ) − 500 cos 30 ° − 300 = 200 − 433 − 300 = − 533

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 4.8, Problem 122P

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The equivalent resultant force, direction of the resultant force, and the line of action of the resultant that intersects the post AB, which is measured from point A.

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Chapter 4.8, Problem 121P

Chapter 4.8, Problem 123P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The equivalent resultant force, direction of the resultant force, and the line of action of the resultant that intersects the post AB , which is measured from point A .

Solution Summary: The author shows the free body diagram of the forces acting on the post as in Figure (1).

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The equivalent resultant force, direction of the resultant force, and the line of action of the resultant that intersects the post AB, which is measured from point A.

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Chapter 4 Solutions