Explanation Given information: The length of the wire is 525 mm , force P is ( 341 N) j .and y = 155 mm . Figure-(1) Write Pythagoras Equation for triangle A B O ( A B ) 2 = ( x ) 2 + z 2 + y 2 …… (I) Here, distance in y direction is y , distance in x direction is x and distance in z direction is z from point O. Write coordinate of point A . A = ( 0 , 155 , 0 ) Write coordinate of point B . B = ( 200 , 0 , z ) …… (II) Here, distance of point B from point O is z . Write Equation for vector A B → . A B → = ( 200 mm-0mm ) i ^ + ( 0 mm − 155 mm ) j ^ + ( z - 0mm ) k ^ = ( 200 i ^ − 155 j ^ + z k ^ ) mm …… (III) Write expression for modulus of vector. | D → | = ( x ) 2 + ( y ) 2 + ( z ) 2 …… (IV) Write expression for unit vector A B ^ . A B ^ = A B → | A B → | …… (V) Write Tension vector in wire A B . T → AB = T A B ⋅ ( A B ^ ) …… (VI) Write equilibrium equation for collar A in y direction. ∑ F y = 0 P + ( T AB ) y = 0 ….. (VII) Here, force in y direction is P and component of tension in y direction is ( T AB ) y . Calculation: Substitute 525 mm for A B , 200 mm for x and 155 mm for y in Equation (I) ( 525 mm ) 2 = ( 200 mm ) 2 + z 2 + ( 155 mm ) 2 275625 mm 2 = 40000 mm 2 + z 2 + 24025 mm 2 z 2 = 211600 mm 2 z = 460 mm Substitute 460 mm for z in Equation(II) To determine (b) Magnitude of force Q required to maintain the equilibrium of system.

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 102P

To determine

(a)

The tension in wire AB.

To determine

(b)

Magnitude of force Q required to maintain the equilibrium of system.

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Chapter 2.5, Problem 101P

Chapter 2.5, Problem 103P

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