Explanation Given information : The forces acting on the pipe F 1 , F 2 , and F 3 are 300 N, 200 N, and 100 N. The anticlockwise moment acting about point A ( M A ) is 100 N ⋅ m . The clockwise moment acting about point B ( M B ) is 180 N ⋅ m . Determine the position vector for point A . r A = ( x A i + y A j + z A k ) (I) Here, the position vector for point A is r A , the distance of point A from the origin along the x direction is x A , the distance of point A from the origin along the y direction is y A , the distance of point A from the origin along the z direction is z A , the vector component along the x direction is i , vector component along the y direction is j, and vector component along the z direction is k. Determine the position vector for point B . r B = ( x B i + y B j + z B k ) (II) Here, the position vector for point B is r A , the distance of point B from the origin along the x direction is x B , the distance of point B from the origin along the y direction is y B , and the distance of point B from the origin along the z direction is z B . Force vector at point A : F 1 = F 1 k (III) Force vector at point B : F 2 = F 2 ( cos θ i − sin θ k ) (IV) Here, the angle for the force F 2 is θ . Force vector at point C : F 3 = F 3 j (V) Write the moment in the Cartesian vector form at point A: M 1 = M A k (VI) Write the moment in the Cartesian vector form at point B : M 2 = M B ( cos θ i − sin θ k ) (VII) Determine the equivalent force at point O . F R = F 1 + F 2 + F 3 (VIII) Determine the couple moment at point O . ( M R ) O = r A × F 1 + r B × F 2 + M 1 + M 2 (IX) Conclusion : Substitute 0 m for x A , 0.5 m for y A , and 0 m for z A in Equation (I). r A = { 0 i + 0.5 j + 0 k } m Substitute 0 m for x B , 1.1 m for y B , and 0 m for z B in Equation (II). r B = { 0 i + 0.5 j + 0 k } m Substitute 300 N for F 1 in Equation (III). F 1 = { 300 k } N Substitute 200 N for F 2 and 45 ° for θ in Equation (IV). F 2 = 200 ( cos 45 ° i − sin 45 ° k ) = { 141.42 i − 141.42 k } N Substitute 100 N for F 3 in Equation (V). F 3 = { 100 j } N Substitute 100 N ⋅ m for M A in Equation (VI). M 1 = { 100 k } N ⋅ m Substitute 180 N ⋅ m for M B and 45 ° for θ in Equation (VII). M 2 = 180 ( cos 45 ° i − sin 45 ° k ) = { 127.28 i − 127.28 k } N ⋅ m Substitute { 300 k } N for F 1 , { 141.42 i − 141.42 k } N for F 2 , and { 100 j } N for F 3 in Equation (VIII). F R = { 300 k } + { 141.42 i − 141.42 k } + { 100 j } = 141

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works …

Videos

Question

Chapter 4.8, Problem 134P

To determine

The equivalent resultant force and the couple moment acting at point O.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.8, Problem 133P

Chapter 4.8, Problem 135P

Students have asked these similar questions

500 Q3: The attachment shown in Fig.3 is made of 1040 HR. The static force is 30 kN. Specify the weldment (give the pattern, electrode number, type of weld, length of weld, and leg size). Fig. 3 All dimension in mm 30 kN 100 (10 Marks)

(read image) (answer given)

A cylinder and a disk are used as pulleys, as shown in the figure. Using the data given in the figure, if a body of mass m = 3 kg is released from rest after falling a height h 1.5 m, find: a) The velocity of the body. b) The angular velocity of the disk. c) The number of revolutions the cylinder has made. T₁ F Rd = 0.2 m md = 2 kg T T₂1 Rc = 0.4 m mc = 5 kg ☐ m = 3 kg

Chapter 4 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The equivalent resultant force and the couple moment acting at point O .

Solution Summary: The author explains how to determine the equivalent resultant force and the couple moment acting at point O.

Concept explainers

Videos

The equivalent resultant force and the couple moment acting at point O.

Want to see the full answer?

Chapter 4 Solutions