Explanation Given information: The tension in cable A B is 259 N . The below figure represents the schematic diagram of the arrangement. Write the position of points A , B , C and D with respect to point O . A = ( 0 , 5.6 m , 0 ) B = ( − 4.2 m , 0 , 0 ) C = ( 2.4 m , 0 , 4.2 m ) D = ( 0 , 0 − 3.3 m ) Write the vector A B → . A B → = ( − 4.2 m-0 ) i ^ + ( 0 ft − 5 .6 m ) j ^ + ( 0 -0 ) k ^ = ( − 4.2 i ^ − 5.6 j ^ ) m …… (I) Write the vector A C → . A C → = ( 2.4 m-0 ) i ^ + ( 0 − 5 .6 m ) j ^ + ( 4.2 m-0 ) k ^ = ( 2.4 i ^ − 5.6 j ^ + 4.2 k ^ ) m …… (II) Write the vector A D → . A D → = ( 0 -0 ) i ^ + ( 0 − 5 .6 m ) j ^ + ( − 3.3 m-0 ) k ^ = ( − 5.6 j ^ − 3.3 k ^ ) m …… (III) Write the expression for modulus of the vector. | D → | = ( x ) 2 + ( y ) 2 + ( z ) 2 …… (IV) Here, horizontal distance along x axisis x , horizontal distance along y axis is y and horizontal distance along z axis is z from the point O and the modulus of the vector is | D → | . Write the expression for unit vector A B ^ . A B ^ = A B → | A B → | …… (V) 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 → | …… (VI) 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 → | …… (VII) Here, the unit vector of A D → is A D ^ and the magnitude of A D → is | A D → | . Write the expression for tension T A B → . T A B → = T A B ⋅ A B ^ …… (VIII) Here, the tension vector in cable A B is T A B → and the magnitude of the tension in cable A B is T A B . Write the expressionfor tension T A C → . T A C → = T A C ⋅ A C ^ …… (IX) 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 expressionfor tension T A D → . T A D → = T A D ⋅ A D ^ …… (X) Here, the tension vector in the cable A D is T A D → and the magnitude of tension in cable A D is T A D . Write the expression for the equilibrium equation of forces at the point A . T A B → + T A C → + T A D → + P = 0 …… (XI) Here, the force acting at point A is P . Calculation: Substitute − 4.2 m for x , − 5.6 m for y , 0 for z and A B → for D → in equation (IV) | A B → | = ( − 4.2 m ) 2 + ( − 5.6 m ) 2 + ( 0 ) 2 = 17.64 m 2 + 31.36 m 2 + 0 = 7 m Substitute 2.4 m for x , − 5.6 m for y , 4.2 m for z and A C → for D → in equation (IV) | A C → | = ( 2.4 m ) 2 + ( − 5.6 m ) 2 + ( 4.2 m ) 2 = 5.76 m 2 + 31.36 m 2 + 17.64 m 2 = 7.4 m Substitute 0 for x , − 5.6 m for y , − 3.3 m for z and A D → for D → in equation (IV) | A D → | = ( 0 ) 2 + ( − 5.6 m ) 2 + ( − 3.3 m ) 2 = 0 + 31.36 m 2 + 10

2nd Edition

ISBN: 9780073398167

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

Publisher: McGraw-Hill Education

See similar textbooks

Videos

Question

Chapter 2, Problem 113RP

To determine

The magnitude of force exerted by the balloon at point A.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 112RP

Chapter 2, Problem 114RP

Students have asked these similar questions

Three cables are connected at A, where the force P is applied as shown. Determine the tension each cable.

3. Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in the cable AD is 521 N. 4.20 m 2.40 m T C 4.20 m 5.60 m 3.30 m

Three cables are used to tether a balloon as shown. Knowing that the balloon exerts an 800-N vertical force at A, determine the tension in each cable.

Chapter 2 Solutions

Statics and Mechanics of Materials

Ch. 2.1 - 2.1 and 2.2 Determine graphically the magnitude...Ch. 2.1 - 2.1 and 2.2 Determine graphically the magnitude...Ch. 2.1 - Two structural members B and C are bolted to...Ch. 2.1 - Two structural members B and C are bolted to...Ch. 2.1 - The 300-lb force is to be resolved into components...Ch. 2.1 - The 300-lb force is to be resolved into components...Ch. 2.1 - A trolley that moves along a horizontal beam is...Ch. 2.1 - A disabled automobile is pulled by means of two...Ch. 2.1 - Two forces are applied as shown to a hook support....Ch. 2.1 - A disabled automobile is pulled by means of two...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The magnitude of force exerted by the balloon at point A.

Solution Summary: The author explains the magnitude of force exerted by the balloon at point A. The tension in cable AB is 259.

Videos

The magnitude of force exerted by the balloon at point A.

Want to see the full answer?

Chapter 2 Solutions