Question 1162039
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Vertical component of the force T is  {{{T*(sqrt(3)/2)}}}.


The sum of vertical components of the force T exerted to two ropes is  {{{sqrt(3)*T}}}.


Since the magnitude of T is equal to the weight w,  the sum of vertical components of the force T  exerted to two ropes is {{{sqrt(3)*w}}}.


The "box is held at rest" means that


     F + w = {{{sqrt(3)*w}}},


It implies that


    F = {{{sqrt(3)*w}}} - {{{w}}} = {{{(sqrt(3)-1)*w}}} = {{{(sqrt(3)-1)*9.6*g}}} = {{{(sqrt(3)-1)*9.6*9.81}}} = 68.75 N.



<U>ANSWER</U>.  The closest option is E).
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Solved, explained and answered.