While camping in denali national park in alaska, a wise camper hangs his pack of food from a rope tied between two trees, to keep the food away from the bears. if the 50.-n bag of food hangs from the center of a rope that is 3.0 m long, and the rope sags 6.0 cm in the middle, what is the tension in the rope?

The tension in each of the ropes is 625 N.

Draw a free body diagram for the bag of food as shown in the attached diagram. Since the bag hangs from the midpoint of the rope, the rope makes equal angles θ with the horizontal. The tensions T in both the ropes are also equal.

Resolve the tension T in the ropes into horizontal and vertical components T cosθ and T sinθ respectively, as shown in the figure. At equilibrium,

    ......(1)

Calculate the value of sinθ  using the right angled triangles from the diagram.

Substitute the value of sinθ in equation (1) and simplify to obtain T.

Thus the tension in the rope is 625 N.

trig 15.3 cos