Explanation The tension in the cable C F can be represented as T C F , in the cable B E can be represented as T B E and in the cable D G can be represented as T D G . The free body diagram of the given arrangement is given by Figure 1. Figure 1 The position vector of the point B is given as, r B = ( 0.48 m ) i The position vector of the point C is given as, r C = ( 0.48 m ) i − ( 0.14 m ) k The position vector of the point D is given as, r D = ( 0.48 m ) i − ( 0.3 m ) k The vector B E → is given as B E → = ( − 0.48 m ) i + ( 0.2 m ) j , vector D G → is given as D G → = ( − 0.48 m ) i + ( 0.14 m ) k and C F → is given as C F → = ( 0 .48 m ) i . The tension across the cable B E as, T B E = T B E B E → B E Here, T B E is the tension across the cable B E , B E → is the vector along the path of the points, B E is the magnitude of the vector. Substitute ( − 0.48 m ) i + ( 0.2 m ) j for B E → and 0.50 m for B E to get T B E . T B E = T B E 0.5 m ( ( − 0.48 m ) i + ( 0.2 m ) j ) = T B E 25 ( − 24 i + 7 j ) The tension across the cable D G as, T D G = T D G D G → D G Here, T D G is the tension across the cable D G , D G → is the vector along the path of the points, D G is the magnitude of the vector. Substitute ( − 0.48 m ) i + ( 0.14 m ) k for D G → and 0.52 m for D G to get T D G . T D G = T D G 0.52 m ( ( − 0.48 m ) i + ( 0.14 m ) k ) = T D G 13 ( − 12 j + 5 k ) The tension across the cable C F as, T C F = T C F C F → C F Here, T C F is the tension across the cable C F , C F → is the vector along the path of the points, C F is the magnitude of the vector. Substitute ( 0 .48 m ) i for C F → and 0.48 m for C F to get T C F . T C F = T C F 0.48 m ( ( 0 .48 m ) i ) = T C F i The weight is given as, W = − m g j Here, W is the weight, m is the mass and g is the acceleration due to gravity. Substitute 350 N for m g . W = − ( 350 N ) j The force on the point is zero. This means that the sum of the moments of the force will also be zero. r D × W + r B × T B E + r D × T D G + r C × T C F = 0 Substitute the vector values and determine the cross product. | i j k 0.48 0 − 0

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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Chapter 4.3, Problem 4.130P

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The tension in each cable and the reaction at A.

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Chapter 4.3, Problem 4.129P

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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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