Problem 9.08 Part A The two trees in (Fioure 1) are 7.2 m apart. A backpacker is

Question

Problem 9.08 Part A The two trees in (Fioure 1) are 7.2 m apart. A backpacker is trying to lift his 17-kg backpack out of the reach of bears. Calculate the magnitude of the force F that he must exert downward to hold the backpack so tnat the rope sags at its midpoint by 1.5 m Express your answer to two significant figures and include the appropriate units. F-Value Units Submit My Answers Give Up Part 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 0.15 m Express your answer to two significant figures and include the appropriate units. FValue Units Submit My Answers Give Up Continue | Figure 1 of 1

Explanation / Answer

(17 x 9.81) = 166.77 N. weight. Halve it, = 83.385 N. needs to be supported by each 1/2 rope.
The pack is (7.2/2) = 3.6m. from each tree.
a) Angle below horizontal with 1.5m. sag = arctan. (1.5/3.6), = 22.62 degrees.
The vertical load is 83.385 N., so rope tension needed = 83.385 / (sin 22.62), = 216.8 N.  

b) Angle below horizontal = arctan (0.15/3.6), = 2.386 degrees.
Tension needed = 83.385/ (sin 2.386), = 2003.77 N.

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