Explanation Given information : The force vector at point A F A is { 500 i } N . The force vector at point B F B is { 800 k } N . The force vector at point C F C is { 300 j } N . Show the free body diagram of the forces acting on the plate by a wrench as in Figure (1). Using Figure (1), Write the resultant force vector. F R = F A + F B + F C (I) Determine the resultant force F R . F R = ( F A ) 2 + ( F C ) 2 + ( F B ) 2 (II) Determine the unit vector for the force. u F R = F R F R (III) Assumption : Anticlockwise is positive. Determine the couple moment about x axis. ( M R ) x ′ = ∑ M x ′ = F B l y (IV) Here, the length of the force B about x axis is l y . Determine the couple moment about y axis. ( M R ) y ′ = ∑ M y ′ = F A x + F C x (V) Determine the couple moment about z axis. ( M R ) z ′ = ∑ M z ′ = F A y + F C ( l B C − x ) (VI) Here, the length of the point BC is l B C . Conclusion : Substitute { 500 i } N for F A , { 300 j } N for F C , and { 800 k } N for F B in Equation (I). F R = { 500 i + 300 j + 800 k } N Substitute { 500 i } N for F A , { 300 j } N for F C , and { 800 k } N for F B in Equation (II). F R = ( 500 ) 2 + ( 300 ) 2 + ( 800 ) 2 = 990 N Thus, the magnitude of resultant force F R is 990 N _

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 4.8, Problem 137P

To determine

The magnitude of resultant force, couple moment for the wrench, and the line of action of force to intersect the plate.

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Chapter 4.8, Problem 136P

Chapter 4.9, Problem 37FP

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Chapter 4 Solutions

Engineering Mechanics: Statics

Ch. 4.4 - F41. Determine the moment of the force about point...Ch. 4.4 - F42. Determine the moment of the force about point...Ch. 4.4 - F43. Determine the moment of the force about point...Ch. 4.4 - Neglect the thickness of the member.Ch. 4.4 - F45. Determine the moment of the force about point...Ch. 4.4 - F46. Determine the moment of the force about point...Ch. 4.4 - F47. Determine the resultant moment produced by...Ch. 4.4 - F48. Determine the resultant moment produced by...Ch. 4.4 - F49. Determine the resultant moment produced by...Ch. 4.4 - Express the result as a Cartesian vector.

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