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two trees in (Figure 1) are 5.2 m apart. A backpacker is to lift his 15 kg backp

ID: 1552854 • Letter: T

Question

two trees in (Figure 1) are 5.2 m apart. A backpacker is to lift his 15 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 that the rope sags at its midpoint by 1.1 m Express your answer to two significant figures and include the appropriate units. Calculate the of the force F that he must exert downward to hold the backpack so that the rope sags at its midpoint by 0.11 m. Express your answer two significant figures and include the appropriate units.

Explanation / Answer

(15 x 9.8) = 147 N. weight. Halve it, = 73.5 N. needs to be supported by each 1/2 rope.
The pack is (5.2/2) = 2.6 m. from each tree.
a) Angle below horizontal with 1.1 m. sag = arctan(1.1/2.6), = 22.93 degrees.
The vertical load is 73.2 N., so rope tension needed = 73.5/ (sin 22.93) = 188.65 N.

b) Angle below horizontal = arctan (0.11/2.6) = 2.42 degrees.
Tension needed = 73.5/ (sin 2.42) = 1740.7 N.