Problem 9.08 The two trees in (Figure 1) are 6.8 m apart. A backpacker is trying

Question

Problem 9.08

The two trees in (Figure 1) are 6.8 m apart. A backpacker is trying to lift his 18-kg backpack out of the reach of bears.

Part 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 2.0 m . Express your answer to two significant figures and include the appropriate units.

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 0.20 m . Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

m = 18 kg , d = 6.8 m

weight of backpack = 18*9.8 = 176.4 N

Half weight needs to be supported by each 1/2 rope. w =176.4/2 = 88.2 N

The pack is (6.8/2) = 3.4 m. from each tree.

a) Angle below horizontal with 2m. sag = arctan. (2/3.4), = 30.46 degrees.

The vertical load is 88.2 N., so rope tension needed = 88.2/ (sin 30.46), = 174 N.

T =170 N

b) Angle below horizontal = arctan (0.2/3.4), = 3.37 degrees.

Tension needed = 88.2/ (sin 3.37), = 1502 N.

T =1500 N

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