Explanation Given information : Force F is 80 N. Determine the resultant force by resolving the force along the x , y , and z direction. F R = ∑ F = ( F cos θ sin θ 1 ) i + ( F cos θ cos θ 1 ) j − ( F sin θ ) k (I) Here, the vector component along x direction is i, the vector component along y direction is j, the vector component along z direction is k, and the angle of forces in x, y, and z direction is θ and θ 1 . Determine the position vector r 1 as follows: r 1 = x i + y j + z k (II) Determine the couple moment due to the force as follows: ( M R ) A = r 1 × ( F R ) (III) Show the calculation of the resultant force, force vector, and couple moment as follows: Conclusion : Substitute 80 N for F , 30 ° for θ , and 40 ° for θ 1 in Equation (I). F R = ( 80 cos 30 ° sin 40 ° ) i + ( 80 cos 30 ° cos 40 ° ) j − ( 80 sin 30 ° ) k = 44.53 i + 53.07 j − 40 k ≈ ( 44.5 i + 53.1 j − 40 k ) N Thus, the equivalent resultant force is [ 44.5 i + 53.1 j − 40 k ] N _ . Substitute 0.55 m for x , 0.4 m for y , and –0

Engineering Mechanics: Statics & Dynamics, Student Value Edition Plus Modified Mastering Engineering Revision with Pearson eText -- Access Card Package

14th Edition

ISBN: 9780135841532

Author: HIBBELER, Russell , HIBBLER

Publisher: PEARSON

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Chapter 4.7, Problem 110P

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The equivalent resultant force and couple moment at point A.

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Chapter 4.7, Problem 109P

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The equivalent resultant force and couple moment at point A .

Solution Summary: The author determines the equivalent resultant force and couple moment at point A by resolving the force along x, y, and z directions.

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