Explanation Given: The magnitude of component force, F 1 = 50 N The magnitude of component force, F 2 = 80 N The magnitude of component force, F 3 = 30 N The angle between the magnitude of component forces, F 2 and y axis , θ = 15 ° Show the magnitude of component of force F 1 , F 2 , and F 3 into x and y -axis components as in Figure (1). Show the resultant force as in Figure (2). Resolve the vector force F 1 into x and y components using unit vectors i and j . F 1 = ( F 1 ) x i + ( F 1 ) y j = ( F 1 cos θ ) i + ( F 1 sin θ ) j (I) Resolve the vector force F 2 into x and y components using unit vectors i and j . F 2 = − ( F 2 ) x i − ( F 2 ) y j = − ( F 2 sin 15 ° ) i − ( F 2 cos 15 ° ) j (II) Resolve the vector force F 3 into x and y components using unit vectors i and j . F 3 = ( F 3 ) x i = F 3 i (III) Use Figure (1) and find out the cos θ and sin θ from the component force F 1 . cos θ = 3 5 sin θ = 4 5 Express the resultant force. F R = F 1 + F 2 + F 3 (IV) Write the magnitude of the resultant force. F R = ( F R ) x 2 + ( F R ) y 2 (V) Express the directional angle θ measured clockwise from the positive x axis. θ = tan − 1 ( F R ) y ( F R ) x (VI) Conclusion: Substitute 50 N for F 1 , 3 / 5 for cos θ , and 4 / 5 for sin θ in Equation (I). F 1 = ( 50 N ( 3 5 ) ) i + ( 50 N ( 4 5 ) ) j = [ 30 i + 40 j ] N Thus, the vector force F 1 is [ 30 i + 40 j ] N _ . Substitute 80 N for F 2 in Equation (II). F 2 = − ( 80 Nsin 15 ° ) i − ( 80 N c o s 15 ° ) j = − ( 80 N ( 0

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ISBN: 9781323327067

Author: HIBBELER

Publisher: PEARSON C

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Chapter 2.4, Problem 38P

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Each forces in Cartesian vector form (F1,F2,F3).

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

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Chapter 2.4, Problem 37P

Chapter 2.4, Problem 39P

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Each forces in Cartesian vector form ( F 1 , F 2 , F 3 ) . The magnitude of the resultant force ( F R ) and its direction ( θ ) measured clockwise from positive x axis.

Solution Summary: The author explains the force in Cartesian vector form (F_R) measured clockwise from positive x axis.

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Each forces in Cartesian vector form (F1,F2,F3).

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

Want to see the full answer?

Chapter 2 Solutions

Each forces in Cartesian vector form ( F 1 , F 2 , F 3 ) . The magnitude of the resultant force ( F R ) and its direction ( θ ) measured clockwise from positive x axis.

Solution Summary: The author explains the force in Cartesian vector form (F_R) measured clockwise from positive x axis.

Videos

Each forces in Cartesian vector form (F1,F2,F3). The magnitude of the resultant force (FR) and its direction (θ) measured clockwise from positive x axis.

Want to see the full answer?

Chapter 2 Solutions

Each forces in Cartesian vector form (F1,F2,F3).

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