In order to straighten a crooked tree,a rope is attached horizontally from the top of the tree to a nearby building.A force of 600 N is applied downward at the center of rope.The angle between this downward force and the rope going to the tree is 95 degrees,which is the same as the angle between the downward force and the rope going to the building.The tension in the rope going to the tree is
A)300 N.
B)600 N.
C)1200 N.
D)3442 N.
E)3658 N.

Question

Quizplus · Accepted Answer

Let T be the tension in the rope going to the tree, and let F be the force applied at the center of the rope. Then we can resolve forces horizontally and vertically:

Horizontal forces: T cos(95) = F = 600 N
Vertical forces: T sin(95) = W

where W is the weight of the tree. Since the problem only asks for the tension in the rope, we can ignore W. Solving for T:

T = F / cos(95) = 600 N / cos(95) = 3442 N (rounded to the nearest whole number)

In Order to Straighten a Crooked Tree,a Rope Is Attached