Explanation Given: The magnitude of resultant force, F R = 600 N The angle between the x axes and magnitude of component force ( F 1 ) 300 lb is 30 ° . The angle between the x axes and vector force F is θ . The magnitude of component force ( F 2 ) is 200 lb . Apply the parallelogram law of addition and triangular rule. Follow the steps to draw the parallelogram law of addition. 1. First join the tails of the given components at a point to make them concurrent. 2. From the head of magnitude of vector force F 1 , draw a line parallel to the x axes. 3. From the head of magnitude of force F 2 , draw a line parallel to the y axes. 4. Join the above two lines at an intersection point to form the adjacent sides of a parallelogram. 5. Draw the resultant force F R as F R 1 at the intersection point. Show the parallelogram law of addition of vectors using above steps as in Figure (1). Show the triangular rule using Figure (1) as in Figure (2). Show the free body diagram for the condition when magnitude of vector force is minimum as in Figure (3). Conclusion: From Figure (1), Apply cosine law and calculate the resultant force F R 1 . F R 1 = ( F 1 ) 2 + ( F 2 ) 2 − 2 F 1 F 2 cos θ (I) Substitute 300 lb for F 1 , 200 lb for F 2 , and 60 ° for θ in Equation (I). F R 1 = ( 300 ) 2 + ( 200 ) 2 − 2 ( 300 ) ( 200 ) ( cos 60 ° ) = 90 , 000 + 40 , 000 − 60 , 000 = 70 , 000 = 264.6 lb From Figure (2), Apply the sine law using Figure (2) to calculate the angle θ of the third chain measured clockwise from the positive x axis

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 2.3, Problem 31P

To determine

The angle θ of the third chain measured clockwise from the positive x axis and the minimum magnitude of vector force Fmin.

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Chapter 2.3, Problem 30P

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Chapter 2 Solutions

Engineering Mechanics: Statics

Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - Resolve this force into components acting along...Ch. 2.3 - along the v axis. Prob. F2-6 Ch. 2.3 - Determine the magnitude of the resultant force FR...Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...Ch. 2.3 - Determine the magnitude of the resultant force FR...

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The angle θ of the third chain measured clockwise from the positive x axis and the minimum magnitude of vector force F min .

The angle θ of the third chain measured clockwise from the positive x axis and the minimum magnitude of vector force Fmin.

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Chapter 2 Solutions