Explanation Given information: The load applied at F is 1.8 kN . 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 B is r B = ( 320 mm ) k . The position of C is r C = − ( 420 mm ) i + ( 320 mm ) k . The position of D is r D = − ( 420 mm ) i + ( 240 mm ) j . The position of E is r E = ( 420 mm ) i . The position of the load is r W = − ( 210 mm ) i + ( 320 mm ) k . Calculate the position of cable BD as shown below. B D → = r D − r B Substitute − ( 420 mm ) i + ( 240 mm ) j for r D and ( 320 mm ) k for r B . B D → = − ( 420 mm ) i + ( 240 mm ) j − ( 320 mm ) k Calculate the length of cable BD as shown below. B D = ( − 420 ) 2 + ( 240 ) 2 + ( − 320 ) 2 = 336 , 400 = 580 mm Calculate the position of cable BE as shown below. B E = r E − r B Substitute ( 420 mm ) i for r E and ( 320 mm ) k for r B . B E → = ( 420 mm ) i − ( 320 mm ) k Calculate the length of cable BE as shown below. B E = ( 420 ) 2 + ( − 320 ) 2 = 278 , 800 = 528.02 mm Calculate the position of cable CD as shown below. C D → = r D − r C Substitute − ( 420 mm ) i + ( 240 mm ) j for r D and − ( 420 mm ) i + ( 320 mm ) k for r C . C D → = − ( 420 mm ) i + ( 240 mm ) j − ( − ( 420 mm ) i + ( 320 mm ) k ) = ( 240 mm ) j − ( 320 mm ) k Calculate the length of cable CD as shown below. C D = ( 240 ) 2 + ( − 320 ) 2 = 160 , 000 = 400 mm Calculate the tension in cable BD ( T B D ) as shown below. T B D = T B D B D → B D Substitute − ( 420 mm ) i + ( 240 mm ) j − ( 320 mm ) k for B D → and 580 mm for B D . T B D = T B D − 420 i + 240 j − 320 k 580 = T B D ( − 0.724 i + 0.414 j − 0.552 k ) Calculate the tension in cable BE ( T B E ) as shown below. T B E = T B E B E → B E Substitute ( 420 mm ) i − ( 320 mm ) k for B E → and 528.02 mm for B E . T B E = T B E 420 i − 320 k 528.02 = T B E ( 0.7954 i − 0.606 k ) Calculate the tension in cable CD ( T C D ) as shown below. T C D = T C D C D → C D Substitute ( 240 mm ) j − ( 320 mm ) k for C D → and 400 mm for C D . T C D = T C D 240 j − 320 k 400 = T C D ( 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 4.123P

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The tension in each cable.

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Chapter 4.3, Problem 4.122P

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Vector Mechanics for Engineers: Statics and Dynamics

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