Hw 4 - PROBLEM 2.99 Three cables are used to tether a...

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PROBLEM 2.99 Three cables are used to tether a balloon as shown. Determine the vertieal force P exerted by the balloon at A knowing that the tension in cable AD is 259 N. , SOLUTION '"I.to ... 1;" \ o TAB' T ,.Ie. TAD' and P The forces applied at A are: where P = Pj. To express the other forces in tenns of the unit vectors I, j, k. we write AD = -(4.20 m)I-(5.60m)j AB=7.00m AC = (2.40 m)i - (5.60 m)j + (4.20 m)k AC=7.40rn AD =-(5.60 m)j -(3.30 m)k AD=6.50m and TAB =T,lBl.A.B = TAB AD = (-O.6i-O.8j)T AB AD T AC = TACA-A.C =. T AC AC = (0.32432 - O.75676j +O.56757k)~c AC T,,w =T,wl. . .w =T,w AD = (-O.86154j-O.50769k)T,w AD
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PROBLEM 2.99 (Continued) Equilibrium condition LF=O: TAB +T,IC+TAD+Pj=O Substituting the expressions obtained for T.411' T AC ' and TAD and factoring i, j. and k: (-O.6T AB + 0.32432T Ac )1 + (--C.ST AB -0. 75676T AC - O.86154T AD + P)J +(O.56757T AC - O.50769T .w)k ~ 0 Equating to zero the coefficients of I, j, k: -O.6T AB + O.32432T AC =: 0 (I) -O.ST AB -O.75676T AC -O.86154T.w + p=o (2) O.56757T AC - 0.507697:w = 0 (3) Setting TAB = 259 N in (1) and (2), and solving tbe resulting set of equations gives T Ae =479.15 N TAn = 535.66 N
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, PROBLEM 2.109 ~A A transmission tower is held by three guy wires attached to a pin at A
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