Explanation Given information: The load applied at C is 60 lb . 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 bent rod as in Figure (1). Refer Figure (1). Calculate the position vector ( r ) as shown below. The position of A is r A = ( 7 in . ) i . The position of B is r B = ( 16 in . ) i . The position of D is r D = ( 16 in . ) i + ( 24 in . ) k . The position of E is r E = ( 24 in . ) k . The position of F is r F = ( 11 in . ) j + ( 16 in . ) k . The position of C with respect to A is r C / A = ( 9 in . ) i + ( 10 in . ) k . The position of B with respect to A is r B / A = ( 9 in . ) i . Calculate the position of cable BF as shown below. B F → = r F − r B Substitute ( 16 in . ) i for r B and ( 11 in . ) j + ( 16 in . ) k for r F . B F → = ( ( 11 in . ) j + ( 16 in . ) k ) − ( ( 16 in . ) i ) = − ( 16 in . ) i + ( 11 in . ) j + ( 16 in . ) k Calculate the length of cable BF as shown below. B F = ( − 16 ) 2 + ( 11 ) 2 + ( 16 ) 2 = 633 = 25.16 in . Calculate the position of AE as shown below. A E = r E − r A Substitute ( 7 in . ) i for r A and ( 24 in . ) k for r E . A E → = ( 7 in . ) i − ( 24 in . ) k Calculate the length of cable AE as shown below. A E = ( 7 ) 2 + ( − 24 ) 2 = 625 = 25 in . Calculate the tension in cable BF ( T ) as shown below. T = T B F → B F Substitute − ( 16 in

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 4.136P

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The tension in the cable.

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Chapter 4.3, Problem 4.135P

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Vector Mechanics for Engineers: Statics and Dynamics

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