Explanation Given: Magnitude of force Q is 174 lb . Length of rod CD is 23 in . . Length of rod AB is 50 in . Concept used: Draw the diagram for the force acting on the system as shown below: Write the expression for the position vector for point D with respect to A. d → A D = ( 16 i ^ + 8 j ^ − 12 k ^ ) in Here, d → A D is the position vector for point D with respect to A. Write the expression for the position vector for point B with respect to A. d → A B = ( 32 i ^ − 30 j ^ − 24 k ^ ) in Here, d → A B is the position vector for point B with respect to A. Write the expression for the magnitude of position vector for point B with respect to A. | d A B | = ( 32 ) 2 + ( − 30 ) 2 + ( − 24 ) 2 = 50 in Here, | d A B | is the magnitude of position vector for point B with respect to A. Write the expression for unit vector along line AB. n ^ A B = d → A B | d A B | ……. (1) Here, n ^ A B is the unit vector along line AB. Write the expression for the position vector for point H with respect to D. d → D H = ( − 16 i ^ − 21 j ^ − 12 k ^ ) in Here, d → D H is the position vector for point H with respect to D. Write the expression for the magnitude of position vector for point H with respect to D. | d D H | = ( − 16 ) 2 + ( − 21 ) 2 + ( − 12 ) 2 = 29 in Here, | d D H | is the magnitude of position vector for point H with respect to D. Write the expression for unit vector along line DH. n ^ D H = d → D H | d D H | ……. (2) Here, n ^ D H is the unit vector along line DH. Write the expression for representation of tension in cable DH in vector. Q → = | Q | ⋅ n ^ D H …… (3) Here, Q → is the representation of force Q in vector and | Q | is the magnitude of applied force. Write the expression for moment about rod AB due to force Q. M A B = n ^ A B ⋅ ( d → A D × Q → ) …… (4) Here, M A B is the moment about rod AB due to force Q . Calculation: Substitute ( 32 i ^ − 30 j ^ − 24 k ^ ) in for d → A B and 50 in for | d A B | in equation (1) n ^ A B = ( 32 i ^ − 30 j ^ − 24 k ^ ) 50 = ( 0

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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 48P

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Chapter 3.2, Problem 47P

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Statics and Mechanics of Materials

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Solution Summary: The author analyzes the moment about AB due to force Q. The expression for the position vector for point D with respect to A.

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