SOLUTION: Please help? (Multiple Choice) A 9.6 kg box is held at rest by two ropes that form 30° angles with the vertical. An external force F acts vertically downward on the box. The fo

Algebra ->  Vectors -> SOLUTION: Please help? (Multiple Choice) A 9.6 kg box is held at rest by two ropes that form 30° angles with the vertical. An external force F acts vertically downward on the box. The fo      Log On


   

Question 1162039: Please help? (Multiple Choice)
A 9.6 kg box is held at rest by two ropes that form 30° angles with the vertical. An external force F acts vertically downward on the box. The force exerted by each of the two ropes is denoted by T. The force F is adjusted so that the magnitude of force T is equal to the weight w. The magnitude of force F, for which this occurs, is closest to:
A) 81 N
B) 78 N
C) 75 N
D) 72 N
E) 69 N
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

Vertical component of the force T is  T%2A%28sqrt%283%29%2F2%29.


The sum of vertical components of the force T exerted to two ropes is  sqrt%283%29%2AT.


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%283%29%2Aw.


The "box is held at rest" means that


     F + w = sqrt%283%29%2Aw,


It implies that


    F = sqrt%283%29%2Aw - w = %28sqrt%283%29-1%29%2Aw = %28sqrt%283%29-1%29%2A9.6%2Ag = %28sqrt%283%29-1%29%2A9.6%2A9.81 = 68.75 N.



ANSWER.  The closest option is E).

Solved, explained and answered.