Explanation Given: The magnitude of component force, F 1 = 60 lb . The magnitude of component force, F 2 = 70 lb . The magnitude of component force, F 3 = 50 lb . The angle between the magnitude of component forces F 2 and F 3 is 60 ° . Show the magnitude of component force F 1 , F 2 and F 3 into x and y axis components as in Figure (1). Show the magnitude of resultant force F R into x and y axis components as in Figure (2). Use Figure (1) and find out the cos θ and sin θ . cos θ = 1 2 sin θ = 1 2 Conclusion: From Figure (1), Calculate the force F 1 into its x and y components as a Cartesian vector form. F 1 = { F 1 cos θ ( − i ) + F 1 sin θ ( + j ) } (I) Substitute 60 lb for F 1 and 1 2 for cos θ and sin θ respectively in Equation (I). F 1 = { ( 60 ) 1 2 ( − i ) + ( 60 ) 1 2 ( + j ) } = { − 42.43 i + 42.43 j } lb Calculate the force F 2 into its x and y components as a Cartesian vector form. F 2 = { F 2 sin 60 ° ( − i ) + F 2 cos 60 ° ( − j ) } (II) Substitute 70 lb for F 2 in Equation (II). F 2 = { 70 sin 60 ° ( − i ) + 70 cos 60 ° ( − j ) } = { − 60.62 i − 35 j } lb Calculate the force F 3 into its x and y components as a Cartesian vector form. F 3 = F 3 ( − j ) (III) Substitute 50 lb for F 3 in Equation (III). F 3 = 50 ( − j ) = { − 50 j } lb Calculate the vector resultant force F R . F R = ∑ F = F 1 + F 2 + F 3 (IV) Substitute { − 42.43 i + 42.43 j } lb for F 1 , { − 60

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 2.4, Problem 41P

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The magnitude of resultant force FR and its direction θ measured counterclockwise from the positive x axis.

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Chapter 2.4, Problem 40P

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Chapter 2 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

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 magnitude of resultant force F R and its direction θ measured counterclockwise from the positive x axis.

The magnitude of resultant force FR and its direction θ measured counterclockwise from the positive x axis.

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Chapter 2 Solutions