Explanation Given: Tension in line ABAD is 60 lb . Maximum moment about z axis is 279 lb ⋅ ft . Concept used: Draw the diagram to represent the force acting at point A. Write the expression for the position vector for point D with respect to A. d → A D = ( x i ^ − 7.75 j ^ − 3 k ^ ) ft Here, d → A D is the position vector for point D with respect to A. Write the expression for the position vector for point A with respect to C. d → C A = ( 0 i ^ + 7.75 j ^ + 3 k ^ ) ft Here, d → C A is the position vector for point A with respect to C. Write the expression for the magnitude of position vector for point D with respect to A. | d A D | = ( x ) 2 + ( − 7.75 ) 2 + ( − 3 ) 2 = x 2 + 69.0625 Here, | d A D | is the magnitude of position vector for point D with respect to A. Write the expression for unit vector along line AD. n ^ A D = d → A D | d A D | ……. (1) Here, n ^ A D is the unit vector along line AD. Write the expression for representation of tension in cable AD in vector. T → A D = | T | ⋅ n ^ A D …… (2) Here, T → A D is the representation of tension in cable AD in vector and | T | is the magnitude of applied force. Write the expression for representation of tension in cable AB in vector. T → A B = − | 2 T | j ^ …… (3) Here, T → A B is the representation of tension in cable AB in vector. Write the expression for total tension in Line ABAD. T → = T → A B + T → A D …… (4) Here, T → is the total tension in line ABAD. Write the expression for moment about z axis. M z = ( d → C A × T → ) ⋅ k ^ …… (5) Here, M z is the moment about z axis. Calculation: Substitute ( x i ^ − 7.75 j ^ − 3 k ^ ) ft for d → A D and x 2 + 69.0625 for | d A D | in equation (1) n ^ A D = ( x i ^ − 7.75 j ^ − 3 k ^ ) x 2 + 69.0625 Substitute ( x i ^ − 7.75 j ^ − 3 k ^ ) x 2 + 69.0625 for n ^ A D and 60 lb for | T | in equation (2) T → A D = 60 ( x i ^ − 7.75 j ^ − 3 k ^ ) x 2 + 69.0625 = ( 60 x x 2 + 69.0625 i ^ − 465 x 2 + 69.0625 j ^ − 180 x 2 + 69

2nd Edition

ISBN: 9780073398167

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David Mazurek

Publisher: McGraw-Hill Education

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Chapter 3.2, Problem 42P

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The allowable distance x when tension in Line ABAD is 60 lb.

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Chapter 3.2, Problem 41P

Chapter 3.2, Problem 43P

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