Explanation The tension in the cable F J can be represented as T F J , in the cable D H can be represented as T D H and in the cable B G can be represented as T B G . The free body diagram of the given arrangement is given by Figure 1. Figure 1 The position vector of the point B with respect to A is given as, r B = ( 12 in . ) i The position vector of the point F with respect to A is given as, r F = ( 12 in . ) j − ( 32 in . ) k The position vector of the point D with respect to A is given as, r D = ( 12 in . ) i − ( 16 in . ) k The position vector of the point E with respect to A is given as, r E = ( 12 in . ) i − ( 24 in . ) k The vector B G → is given as B G → = ( − 12 in . ) i + ( 9 in . ) k , vector D H → is given as D H → = ( − 12 in . ) i + ( 16 in . ) j and F J → is given as F J → = ( − 12 in . ) i + ( 16 in . ) j . The tension across the cable B G as, T B G = T B G B G → B G Here, T B G is the tension across the cable B G , B G → is the vector along the path of the points, B G is the magnitude of the vector. Substitute ( − 12 in . ) i + ( 9 in . ) k for B G → and 15 in . for B G to get T B G . T B G = T B G 15 in . ( ( − 12 in . ) i + ( 9 in . ) k ) = T B G ( − 0.8 i + 0.6 k ) The tension across the cable D H as, T D H = T D H D H → D H Here, T D H is the tension across the cable D H , D H → is the vector along the path of the points, D H is the magnitude of the vector. Substitute ( − 12 in . ) i + ( 16 in . ) j for D H → and 20 in for D H to get T D H . T D H = T D H 20 in ( ( − 12 in . ) i + ( 16 in . ) j ) = T D H ( − 0.6 i + 0.8 j ) The tension across the cable F J as, T F J = T F J F J → F J Here, T F J is the tension across the cable F J , F J → is the vector along the path of the points, F J is the magnitude of the vector. Substitute ( − 3 m ) i + ( 1.25 m ) j for F J → and 20 in for F J to get T F J . T F J = T F J 20 in ( ( − 12 in . ) i + ( 16 in . ) j ) = T F J ( − 0.6 i + 0.8 j ) The force on the point is zero. This means that the sum of the moments of the force will also be zero. r B × T B G + r D × T D H + r F × T F J + r C × ( − 24 j ) + r E × ( − 24 j ) = 0 Substitute the vector values and determine the cross product

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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

Publisher: McGraw-Hill Education

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Vector Mechanics for Engineers: Statics and Dynamics

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The tension in each cable and the reaction at A .

Solution Summary: The author explains the tension in each cable and the reaction at A. The free body diagram of the given arrangement is given by Figure 1.

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The tension in each cable and the reaction at A.

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