Explanation Given: The magnitude of force, F 1 = 700 lb , The magnitude of force, F 2 = 600 lb , The magnitude of force, F 3 = 800 lb , The angle between F 1 and x axis is α 1 = 30 ° . Show the magnitude of components force F 1 into x , y , and z direction as in Figure (1). Show the magnitude of components force F 2 into x , y , and z direction as in Figure (2). Show the magnitude of components force F 3 into x , y , and z direction as in Figure (3). Express the force F 1 as a Cartesian vector using Figure (1). F 1 = F 1 x ( + i ) + F 1 y ( + j ) = { F 1 cos 30 ° i + F 1 sin 30 ° j } lb = F 1 [ cos 30 ° i + sin 30 ° j ] lb (I) Express the force F 2 as a Cartesian vector using Figure (2). F 2 = F 2 x ( + i ) + F 2 y ( + j ) + F 2 z ( + k ) = { 0 ( i ) + F 2 cos θ j + F 2 sin θ k } lb = F 2 { cos θ j + sin θ k } lb (II) Express the force F 3 as a Cartesian vector using Figure (3). F 3 = F 3 x ( + i ) + F 3 y ( + j ) + F 3 z ( + k ) = F 3 cos 120 ° i + F 3 cos 60 ° j + F 3 cos 45 ° k = F 3 [ cos 120 ° i + cos 60 ° j + cos 45 ° k ] lb (III) Express the resultant force as a Cartesian vector. F R = F 1 + F 2 + F 3 (IV) Express the magnitude of F R . F R = ( F R ) x 2 + ( F R ) y 2 + ( F R ) z 2 (V) Write the cosines of the coordinate direction angles. cos α = ( F R ) x F R (VI) cos β = ( F R ) y F R (VII) cos γ = ( F R ) z F R (VIII) Conclusion: Substitute 700 lb for F 1 in Equation (I). F 1 = 700 [ cos 30 ° i + sin 30 ° j ] lb = 700 [ 0.866 i + 0.5 j ] = [ 606.2 i + 350 j ] lb Substitute 600 lb for F 2 , 4 / 5 for cos θ , and 3 / 5 for sin θ in Equation (II)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2.6, Problem 81P

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The magnitude of resultant force, FR.

The magnitude of resultant force FR and its coordinate direction angles (α,β,γ).

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Chapter 2.6, Problem 80P

Chapter 2.6, Problem 82P

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The magnitude of resultant force, F R . The magnitude of resultant force F R and its coordinate direction angles ( α , β , γ ) .

Solution Summary: The author explains the magnitude of resultant force F_R and its coordinate direction angles.

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The magnitude of resultant force, FR.

The magnitude of resultant force FR and its coordinate direction angles (α,β,γ).

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Chapter 2 Solutions

The magnitude of resultant force, F R . The magnitude of resultant force F R and its coordinate direction angles ( α , β , γ ) .

Solution Summary: The author explains the magnitude of resultant force F_R and its coordinate direction angles.

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The magnitude of resultant force, FR. The magnitude of resultant force FR and its coordinate direction angles (α,β,γ).

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Chapter 2 Solutions

The magnitude of resultant force, FR.

The magnitude of resultant force FR and its coordinate direction angles (α,β,γ).