Explanation Given: The tension in wire A E is 75 lb . The below figure represents the schematic diagram of the system. Write the position vector of points A , B , C and D with respect to point O . A = ( 0 , − 60 in , 0 ) B = ( − 17.5 in , 0 , 0 ) C = ( 0 , 0 , 25 in ) D = ( 80 in,0,0 ) E = ( 0 , 0 , − 45 in ) Write the vector A B → . A B → = ( − 17.5 in-0 ) i ^ + ( 0 − ( − 60 in ) ) j ^ + ( 0 -0 ) k ^ = ( − 17.5 i ^ + 60 j ^ ) in …… (I) Write the vector A C → A C → = ( 0 − 0 ) i ^ + ( 0 − ( − 60 in ) ) j ^ + ( 25 in-0 ) k ^ = ( 60 j ^ + 25 k ^ ) in …… (II) Write the vector A D → A D → = ( 80 in − 0 ) i ^ + ( 0 − ( − 60 in ) ) j ^ + ( 0 -0 ) k ^ = ( 80 i ^ + 60 j ^ ) in …… (III) Write the vector A E → A E → = ( 0 − 0 ) i ^ + ( 0 − ( − 60 in ) ) j ^ + ( − 45 in-0 ) k ^ = ( 60 j ^ − 45 k ^ ) in …… (IV) Write the expression for modulus of the vector. | D → | = ( x ) 2 + ( y ) 2 + ( z ) 2 …… (V) Here, horizontal distance along x axisis x , horizontal distance along y axis is y and horizontal distance along z axisis z , from point O . Write the expression for unit vector A B ^ . A B ^ = A B → | A B → | …… (VI) Here, the unit vector of A B → is A B ^ and the magnitude of A B → is | A B → | . Write the expression for unit vector A C ^ . A C ^ = A C → | A C → | …… (VII) Here, the unit vector of A C → is A C ^ and the magnitude of A C → is | A C → | . Write the expression for unit vector A D ^ . A D ^ = A D → | A D → | …… (VIII) Here, the unit vector of A D → is A D ^ and the magnitude of A D → is | A D → | . Write the expression for unit vector A E ^ . A E ^ = A E → | A E → | …… (IX) Here, the unit vector of A E → is A E ^ and the magnitude of A E → is | A E → | . Write the expression for tension T A B → . T A B → = T A B ⋅ A B ^ …… (X) Here, the tension vector in the cable A B is T A B → and the magnitude of tension in cable A B is T A B . Write the expression for tension T A C → . T A C → = T A C ⋅ A C ^ …… (XI) Here, the tension vector in the cable A C is T A C → and the magnitude of tension in cable A C is T A C . Write the expression for tension T A D → . T A D → = T A D ⋅ A D ^ …… (XII) Here, the tension vector in the cable A D is T A D → , the magnitude of tension in cable A D is T A D . Write the equation for T A E → . T A E → = T A E ⋅ A E ^ …… (XIII) Here, the tension vector in the cable A E is T A E → and the magnitude of tension in cable A E is T A E . Write the expression for the equilibrium equation of forces at point A . T A B → + T A C → + T A D → + T A E → + P = 0 …… (XIV) Here, the force acting at point A is P . Calculation: Substitute − 17.5 in for x , 60 in for y , 0 for z and A B → for D → in equation (V) | A B → | = ( − 17.5 in ) 2 + ( 60 in ) 2 + ( 0 ) 2 = 306.25 in 2 + 3600 in 2 + 0 = 62.5 in Substitute 0 for x , 60 in for y , 25 in for z and A C → for D → in equation (V) | A C → | = ( 0 ) 2 + ( 60 in ) 2 + ( 25 in ) 2 = 0 + 3600 in 2 + 625 in 2 = 65 in Substitute 80 in for x , 60 in for y , 0 for z and A D → for D → in equation (V) | A D → | = ( 80 in ) 2 + ( 60 in ) 2 + ( 0 ) 2 = 6400 in 2 + 3600 in 2 + 0 = 100 in Substitute 0 for x , 60 in for y , − 45 in for z and A E → for D → in equation (VI) | A E → | = ( 0 ) 2 + ( 60 in ) 2 + ( − 45 in ) 2 = 0 + 3600 in 2 + 2025 in 2 = 75 in Substitute ( − 17 To determine (b) The tension in the cable B A C and the tension in the cable A D .

2nd Edition

ISBN: 9780073398167

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David Mazurek

Publisher: McGraw-Hill Education

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Chapter 2.5, Problem 97P

To determine

(a)

The magnitude of load P.

To determine

(b)

The tension in the cable BAC and the tension in the cable AD.

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Chapter 2.5, Problem 96P

Chapter 2.5, Problem 98P

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