Question

The two trees are 5.2 m apart. A backpacker is trying to lift his 28-kg backpack out of the reach of bears.

A) Calculate the magnitude of the force F that he must exert downward to hold the backpack so that the rope sags at its midpoint by 1.4 m .

B) Calculate the magnitude of the force F that he must exert downward to hold the backpack so that the rope sags at its midpoint by 0.14 m .

Answer 1

weight of backpack = ma (28 kg x 9.8 m/s^2) = 274.4N.

it is supported by two trees. so one tree takes, = 137.2N force.

distance of pack from each tree is (5.2/2) = 2.6m.

a) Angle below horizontal with 1.4 m. sag = arctan. (1.4/2.6) = 28.30 degrees.
The vertical load is 137.2, so rope tension needed = 137.2/ (sin 28.30), = 289.39 N.
I am assuming the rope is being pulled from 1 end.

b) Angle below horizontal with 0.14 m. sag = arctan (0.14/2.6), = 3.08 degrees.
Tension needed = 137.2 / (sin 3.08) = 2553.49 N