Explanation Given information : The force value ( F ) is 100 N. The angle value ( θ ) is 60 ° . Show the free body diagram of the board with four way lug wrench as in Figure (1). Using Figure (1), Scalar Analysis: Determine the moment of force F at the x axis. M x = − F sin θ × d 1 + F cos θ × d 2 (I) Here, the horizontal distance for the vertical force F at the x axis is d 1 and the vertical distance for the force F is d 2 . Vector Analysis: Determine the position vector for point AB . r A B = r B − r A = ( x B i + y B j + z B k ) − ( x A i + y A j + z A k ) = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k (II) Here, the position vector for point B is r B , the position vector for point A is r A , the distance of point B from the origin along x direction is x B , the distance of point B from the origin along y direction is y B , the distance of point B from the origin along the z direction is z B , the distance of point A from the origin along x direction is x A , the distance of point A from the origin along y direction is y A , the distance of point A from the origin along z direction is z A , the vector component along x direction is i, the vector component along y direction is j, and the vector component along z direction is k. Determine the force vector. F = F ( cos θ j − sin θ k ) (III) Determine the moment of force F at the x axis. M x = i ⋅ ( r A B × F ) (IV) Conclusion : Substitute 100 N for F , 60 ° for θ , 250 mm for d 1 , and 0 m for d 2 in Equation (I). M x = − 100 sin 60 ° × ( 250 mm × 1 m 1 , 000 mm ) + 100 cos 60 ° × 0 = − 21.7 N ⋅ m The negative sign indicates that M x is directed towards the negative x axis. Thus, the magnitude of the moment of the force at the x axis ( M x ) using scalar analysis is − 21.7 N ⋅ m _ . Substitute 250 mm for x B , 250 mm for x A , 250 mm for y B , 0 m for y A , 0 m for z B , and 0 m for z A in Equation (II)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Die Stock

Die stock is expressed as the type of component which is utilized for fitting purposes while creating or shaping uniform threads on tubes, pipes, or screws. The die stock (die handle) has three screws around the adjustable part of a particular machine th…

Videos

Question

Chapter 4.5, Problem 58P

To determine

The magnitude of the moment produced by the force at the x axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.5, Problem 57P

Chapter 4.5, Problem 59P

Students have asked these similar questions

The small crane is mounted along the side of a pickup bed and facilitates the handling of heavy loads. When the boom elevation angle is q = 40°, the force in the hydraulic cylinder BC is 7 kN, and this force applied at point C is in the direction from B to C (the cylinder is in compression). Determine the moment of this 7 kN force about pivot point O assuming counterclockwise is positive. Express your answer in units of N-m. A 110 mm 785 mm C - 0 B 340 mm 360 mm

The turnbuckle is tightened until the tension in cable AB is 1.1 kN. Calculate the magnitude of the moment about point O of the force acting on point A. 1.4 m 2.3 m 1.3 m 0.9 m Answer: M= kN-m

Q-1 Caleulate the magnitude of the moment about the base point O of the 600-N force in five different ways. 600 N 0-2 Determine the moment of -875 mm- the 800-N force about point A and about point 0. 625 mm 30 F= 800 N F = 120 N 13 20 Q-3 In stendily turning the water pump, a person exerts the 120-N force on the handle as shown. Determine the moment of this force about point O. 150 mm Ans. Mo-14.74 N-m CW

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 magnitude of the moment produced by the force at the x axis.

Solution Summary: The author explains how to determine the magnitude of the moment produced by the force at the x axis.

Concept explainers

Videos

The magnitude of the moment produced by the force at the x axis.

Want to see the full answer?

Chapter 4 Solutions