Explanation Given information : Forces ( F 1 ) and ( F 2 ) is 40 N. Angle ( θ ) is 45 ° . Assumption : Anticlockwise is positive. Show the free body diagram of the pulley as in Figure (1). Use Figure (1). Express the force vector F 1 as follows: F 1 = { − 40 k } N Express the force vector F 2 as follows: F 2 = { − 40 cos 45 ° j − 40 sin 45 ° k } = { − 28.28 j − 28.28 k } N Determine the equivalent resultant force using the formula. F R = F 1 + F 2 F R = ( F 1 cos θ ) j + ( F 2 − F 2 sin θ ) k (I) Here, the resolving angle of forces F 1 and F 2 is θ , the vector component along the y direction is j, the vector component along the z direction is k. Express the position vector r A F 1 of force 1 about point A as follows: r A F 1 = { − 0.3 i + 0.08 j } m (II) Here, the vector component along the x direction is i. Express the position vector r A F 2 of force 2 about point A as follows: r A F 2 = { − 0.3 i − 0.0566 j + 0.08 cos 45 ° k } = { − 0.3 i − 0.0566 j + 0.0566 k } m (III) Determine the resultant moment at point A using the formula. M R A = r A F 1 × F 1 + r A F 2 × F 2 (IV) Conclusion : Substitute 40 N for F 1 , 45 ° for θ , and 40 N for F 1 in Equation (I). F R = ( 40 cos 45 ° ) j + ( − 40 − 40 sin 45 ° ) k = 28.28 j − 68.28 k ≈ 28.3 j − 68.3 k Thus, the equivalent resultant force is { − 28.3 j − 68.3 k } N _ . Substitute { − 0.3 i + 0.08 j } m for r A F 1 , { − 40 k } N for F 1 , { − 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 112P

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The equivalent resultant force and couple moment at point A in the Cartesian vector form.

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