Explanation Concept used: Draw the diagram for the system as shown below: Write the coordinate of point A as ( 0 , 0 , 0 ) in . Write the coordinate of point B as ( 12 , 0 , 0 ) in . Write the expression for the position vector for B. d → B = [ 12 i ^ + 0 j ^ + ( 0 ) k ^ ] in Here, d → B is the position vector of point B. Write the coordinate of point D as ( 12 , 0 , − 16 ) in . Write the expression for the position vector for D. d → D = [ 12 i ^ + 0 j ^ − ( 16 ) k ^ ] in Here, d → D is the position vector of point D. Write the coordinate of point E as ( 12 , 0 , − 24 ) in . Write the expression for the position vector for E. d → E = [ 12 i ^ + 0 j ^ − ( 24 ) k ^ ] in Here, d → E is the position vector of point E. Write the coordinate of point F as ( 12 , 0 , − 32 ) in . Write the expression for the position vector for F. d → F = [ 12 i ^ + 0 j ^ + ( − 32 ) k ^ ] in Here, d → F is the position vector of point F. Write the coordinate of point G as ( 0 , 0 , 19 ) in . Write the expression for the position vector for G. d → G = [ 0 i ^ + 0 j ^ + ( 19 ) k ^ ] in Here, d → G is the position vector of point G. Write the coordinate of point J as ( 0 , 0 , − 24 ) in . Write the expression for the position vector for J. d → J = [ 0 i ^ + 0 j ^ + ( − 24 ) k ^ ] in Here, d → J is the position vector of point J. Write the coordinate of point H as ( 0 , 16 , − 16 ) in . Write the expression for the position vector for H. d → H = [ 0 i ^ + 16 j ^ + ( − 16 ) k ^ ] in Here, d → H is the position vector of point H. Write the coordinate of point C as ( 12 , 0 , − 8 ) in . Write the expression for the position vector for C. d → C = [ 12 i ^ + 0 j ^ + ( − 8 ) k ^ ] in Here, d → C is the position vector of point H. Write the expression for the position vector for point B with respect to G. d → B G = [ − 12 i ^ + 9 k ^ ] in Here, d → B G is the position vector of for point B with respect to G. Write the expression to calculate the magnitude of position vector of point for B with respect to G. | d → B G | = d x 2 + d y 2 + d z 2 ....... (1) Here, | d → B G | is the magnitude of position vector of point for B with respect to G d x is the x component of position vector, d y is the y component of position vector and d z is the z component of position vector. Write the expression for the unit vector along BG. n ^ B G = d → B G | d → B G | ....... (2) Here, n ^ B G is the unit vector along BG. Write the expression for the position vector for point D with respect to H. d → D H = ( − 12 i ^ + 16 j ^ ) in Here, d → D H is the position vector of for point D with respect to H. Write the expression to calculate the magnitude of position vector of point for D with respect to H. | d → D H | = d x 2 + d y 2 + d z 2 ....... (3) Here, | d → D H | is the magnitude of position vector of point D with respect to H d x is the x component of position vector, d y is the y component of position vector and d z is the z component of position vector. Write the expression for the unit vector along DH. n ^ D H = d → D H | d → D H | ....... (4) Here, n ^ D H is the unit vector along DH. Write the expression for the position vector for point F with respect to J. d → F J = ( − 12 i ^ + 16 j ^ ) in Here, d → F J is the position vector of for point F with respect to J.. Write the expression to calculate the magnitude of position vector of point for F with respect to J. | d → F J | = d x 2 + d y 2 + d z 2 ....... (5) Here, | d → F J | is the magnitude of position vector of point F with respect to J d x is the x component of position vector, d y is the y component of position vector and d z is the z component of position vector. Write the expression for the unit vector along FJ. n ^ F J = d → F J | d → F J | ....... (6) Here, n ^ F J is the unit vector along FJ. Write the expression to represent the moment about A. d → B × T B G n ^ B G + d → D × T D H n ^ D H + d → F × T F J n ^ F J + d → E × ( − 24 j ^ ) + d → C × ( − 24 j ^ ) = 0 ....... (7) Here, T → B G , T → D H and T → F J is the tension in cable BG, DH, and FJ in vector form Write the expression for net force. ( R x i ^ + R y j ^ + R z k ^ ) + T B G n ^ B G + T D H n ^ D H + T F J n ^ F J + ( − 24 j ^ ) + ( − 24 j ^ ) = 0 ....... (8) Here, R x , R y , and R z reaction at A in x , y , and z respectively. Calculation: Substitute − 12 in for d x , 0 in for d y and 9 in for d z in equation (1) | d → B G | = ( − 12 ) 2 + ( 0 ) 2 + ( 9 ) 2 = 15 in Substitute 15 in for | d → B G | and ( − 12 i ^ + 9 k ^ ) in for d → B G in equation (2) n ^ B G = ( − 12 i ^ + 9 k ^ ) 15 = ( − 0.8 i ^ + 0

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 4, Problem 108RP

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The tension in the cable BG, DH, and FJ and the reaction at R.

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Chapter 4, Problem 107RP

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Statics and Mechanics of Materials

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