Explanation Given information : The force F t exerted on the toe is { − 50 i + 80 j − 158 k } N . The moment M t exerted on the toe is { − 6 i + 4 j + 2 k } N ⋅ m . The force F h exerted on the heel is { − 20 i + 60 j − 250 k } N . The moment M h exerted on the toe is { − 20 i + 8 j + 3 k } N ⋅ m . Determine the resultant F R equivalent force using the formula. F R = F t + F h (I) Express the position vector r h of heel in the vector form as follows: r h = ( 0.8 i ) m (II) Express the position vector r t of toe in the vector form as follows: r t = ( 0.92 i ) m (III) Determine the resultant couple moment M R P acting at point P using the formula. M R P = r h × F h + r t × F t + M t + M h (IV) Conclusion : Substitute { − 50 i + 80 j − 158 k } N for F t and { − 20 i + 60 j − 250 k } N for F h in Equation (I). F R = { − 50 i + 80 j − 158 k } + { − 20 i + 60 j − 250 k } = { − 70 i + 140 j − 408 k } N Thus, the resultant F R equivalent force is { − 70 i + 140 j − 408 k } N _ . Substitute ( 0.8 i ) m for r h , { − 20 i + 60 j − 250 k } N for F h , ( 0.92 i ) m for r t , { − 50 i + 80 j − 158 k } N for F t , { − 6 i + 4 j + 2 k } N ⋅ m for M t , and { − 20 i + 8 j + 3 k } N ⋅ m for M h in Equation (IV)

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

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 4.9, Problem 166RP

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The resultant equivalent force and resultant couple moment acting at point P in the form of Cartesian vector.

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Chapter 4.9, Problem 165RP

Chapter 4.9, Problem 167RP

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Chapter 4 Solutions

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

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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The resultant equivalent force and resultant couple moment acting at point P in the form of Cartesian vector .

The resultant equivalent force and resultant couple moment acting at point P in the form of Cartesian vector.

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Chapter 4 Solutions