Explanation Write the equation of moment of force about an arbitrary axis. M → 1 = λ 1 ( r → B / A × F → 2 ) (I) Here, the moment of force F → 2 about the line of action of F → 1 is M → 1 , the unit vector along the force F → 1 is λ 1 , the vector line drawn from A to B is r B / A , and the force acting about the line of action of F → 1 is F → 2 . Sketch the force acting about the line of action of F → 1 . Write the equation for the force for F → 1 . F → 1 = F 1 λ 1 Sketch the force acting about the line of action of F → 2 . Write the equation for the force for F → 2 . F → 2 = F 2 λ 2 Replace F 2 λ 2 for F → 2 in equation (I) and rewrite it. M → 1 = λ 1 ( r → B / A × λ 2 ) F 2 (II) Write the equation of moment of force about an arbitrary axis. M → 2 = λ 2 ( r → A / B × F → 1 ) (III) Here, the moment of force F → 1 about the line of action of F → 2 is M → 2 , the unit vector along the force F → 2 is λ 2 , the vector line drawn from B to A is r A / B , and the force in the space is F → 1 . Replace F 1 λ 1 for F → 1 in equation (III) and rewrite it

Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977206

Author: BEER, Ferdinand P., Johnston Jr., E. Russell, Mazurek, David, Cornwell, Phillip J., SELF, Brian

Publisher: McGraw-Hill Education

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Chapter 3.2, Problem 3.63P

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Whether the moment of force F→1 about the line of action of F→2 is equal to the moment of F→2 about the line of action of F→1.

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Chapter 3.2, Problem 3.62P

Chapter 3.2, Problem 3.64P

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Chapter 3 Solutions

Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

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Ch. 3.1 - 3.11 and 3.12The tailgate of a car is supported by...Ch. 3.1 - 3.11 and 3.12The tailgate of a car is supported by...Ch. 3.1 - 3.13 and 3.14It is known that the connecting rod...Ch. 3.1 - 3.13 and 3.14It is known that the connecting rod...Ch. 3.1 - Form the vector product P1 P2 and use the result...Ch. 3.1 - The vectors P and Q are two adjacent sides of a...Ch. 3.1 - A plane contains the vectors A and B. Determine...Ch. 3.1 - A line passes through the points (4 m, 3 m) and (2...Ch. 3.1 - Prob. 3.19P Ch. 3.1 - Determine the moment about the origin O of the...Ch. 3.1 - Before the trunk of a large tree is felled, cables...Ch. 3.1 - The 12-ft boom AB has a fixed end A. 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Determine the...Ch. 3.4 - Determine the single equivalent force and the...Ch. 3.4 - Five separate force-couple systems act at the...Ch. 3.4 - The weights of two children sitting at ends A and...Ch. 3.4 - Three stage lights are mounted on a pipe as shown....Ch. 3.4 - A beam supports three loads of given magnitude and...Ch. 3.4 - A 6 12-in. plate is subjected to four loads as...Ch. 3.4 - Gear C is rigidly attached to arm AB. 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Whether the moment of force F → 1 about the line of action of F → 2 is equal to the moment of F → 2 about the line of action of F → 1 .

Solution Summary: The author compares the moment of force of stackrelto to the unit vector, the vector line, and the force acting about the line of action.

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Whether the moment of force F→1 about the line of action of F→2 is equal to the moment of F→2 about the line of action of F→1.

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Chapter 3 Solutions