Explanation Given information: The value of force P is 164 N . The tension in both the cables is same. The below figure represents the given system. Figure-(1) Write the position vector of points A , B , C and D with respect to point O . O = ( 0 , 0 , 0 ) A = ( 0 , 400 , 0 ) B = ( − 130 , 0 , 160 ) C = ( − 150 , 0 , − 240 ) Write vector A B → . A B → = ( − 130 mm-0 mm ) i ^ + ( 0 mm − 400 mm ) j ^ + ( 160 mm-0 mm ) k ^ = ( − 130 i ^ − 400 j ^ + 160 k ^ ) mm …… (I) Write vector A C → A C → = ( − 150 mm-0 mm ) i ^ + ( 0 mm − 400 mm ) j ^ + ( − 240 mm-0 mm ) k ^ = ( − 150 i ^ − 400 j ^ − 240 k ^ ) mm …… (II) Write the expression for modulus of vector. | D → | = ( x ) 2 + ( y ) 2 + ( z ) 2 …… (III) Here, horizontal distance is x along x axis, horizontal distance is y along y axis and horizontal distance is z along z axis, from point O . Write expression for unit vector A B ^ . A B ^ = A B → | A B → | …… (IV) Here, the magnitude of the vector A B → is | A B → | . Write expression for unit vector A C ^ . A C ^ = A C → | A C → | …… (V) Here, the unit vector of A C → is A C ^ and the magnitude of A C → is | A C → | . Write the equation for tension T A B → . T A B → = T A B ⋅ A B ^ …… (VI) Here, the tension vector in cable A B is T A B → , the magnitude of tension in cable A B is T A B . Write the equation for tension T A C → . T A C → = T A C ⋅ A C ^ …… (VII) Here, the tension vector in cable A C is T A C → and the magnitude of tension in cable A C is T A C . Write the expression for equilibrium at point A . P + Q + W + T A B → + T A C → = 0 …… (VIII) Calculation: Substitute A B → for D → and − 130 mm for x , − 400 mm for y and 160 mm for z in Equation (III) | A B → | = ( − 130 mm ) 2 + ( − 400 mm ) 2 + ( 160 mm ) 2 = ( 16900 + 160000 + 25600 ) mm 2 = 450 mm Substitute A C → for D → and 0 in for x , 60 in for y and 32 in for z in Equation (III) | A C → | = ( − 150 mm ) 2 + ( − 400 mm ) 2 + ( − 240 mm ) 2 = ( 22500 + 160000 + 57600 ) mm 2 = 490 mm Substitute ( − 130 i ^ − 400 j ^ + 160 k ^ ) mm for A B → and 250 mm for | A B → | in Equation (IV) A B ^ = ( − 130 i ^ − 400 j ^ + 160 k ^ ) mm 250 mm = 1 450 ( − 130 i ^ − 400 j ^ + 160 k ^ ) = − 0

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 95P

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The magnitude of W and Q.

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The magnitude of W and Q .

Solution Summary: The author explains the magnitude of W and Q. The value of force P is 164 and the tension in both the cables is same.

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