Explanation Given information: The length of the boom is 2.4 m . The 3.6 kN load applied at A . Calculation: Assumption: Apply the sign convention for calculating the equations of equilibrium as shown below. For the horizontal forces equilibrium condition, take the force acting towards right side as positive ( → + ) and the force acting towards left side as negative ( ← − ) . For the vertical forces equilibrium condition, take the upward force as positive ( ↑ + ) and the downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counterclockwise moment as positive. Draw the free body diagram of the assembly as in Figure (1). Refer Figure (1). Calculate the position vector ( r ) as shown below. The position of A is r A = ( 2.4 m ) k . The position of B is r B = ( 1.2 m ) k . The position of D is r D = − ( 0.8 m ) i + ( 0.6 m ) j . The position of E is r E = ( 0.8 m ) i + ( 1.2 m ) j . Calculate the position of cable AD as shown below. A D → = r D − r A Substitute − ( 0.8 m ) i + ( 0.6 m ) j for r D and ( 2.4 m ) k for r A . A D → = [ − ( 0.8 m ) i + ( 0.6 m ) j ] − [ ( 2.4 m ) k ] = − ( 0.8 m ) i + ( 0.6 m ) j − ( 2.4 m ) k Calculate the length of cable AD as shown below. A D = ( − 0.8 ) 2 + ( 0.6 ) 2 + ( − 2.4 ) 2 = 6.76 = 2.6 m Calculate the position of cable AE as shown below. A E = r E − r A Substitute ( 0.8 m ) i + ( 1.2 m ) j for r E and ( 2.4 m ) k for r A . A E = [ ( 0.8 m ) i + ( 1.2 m ) j ] − [ ( 2.4 m ) k ] = ( 0.8 m ) i + ( 1.2 m ) j − ( 2.4 m ) k Calculate the length of cable AE as shown below. A E = ( 0.8 ) 2 + ( 1.2 ) 2 + ( − 2.4 ) 2 = 7.84 = 2.8 m Calculate the tension in cable AD ( T A D ) as shown below. T A D = T A D A D → A D Substitute − ( 0.8 m ) i + ( 0.6 m ) j − ( 2.4 m ) k for A D → and 2.6 m for A D . T A D = T A D − 0.8 i + 0.6 j − 2.4 k 2.6 = T A D 2.6 ( − 0.8 i + 0.6 j − 2.4 k ) Calculate the tension in cable AE ( T A E ) as shown below. T A E = T A E A E → A E Substitute ( 0.8 m ) i + ( 1.2 m ) j − ( 2.4 m ) k for A E → and 2.8 m for A E . T A E = T A E 0.8 i + 1.2 j − 2.4 k 2.8 = T A E 2.8 ( 0.8 i + 1.2 j − 2.4 k ) Apply the Equations of Equilibrium as shown below. Apply the Equilibrium equation of moment about point C and equate to zero for equilibrium. ∑ M C = 0 r A × T A D + r A × T A E + r A × ( − 3 j ) = 0 Substitute ( 2.4 m ) k for r A , T A D 2.6 ( − 0.8 i + 0.6 j − 2.4 k ) for T A D , and T A E 2.8 ( 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 4.109P

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The tension in each cable and the reaction at C.

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Chapter 4.3, Problem 4.108P

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Chapter 4 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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The tension in each cable and the reaction at C .

The tension in each cable and the reaction at C.

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