Problem 9.08 The two trees in (Figure 1) are 5.8 m apart. A backpacker is trying

Question

Problem 9.08 The two trees in (Figure 1) are 5.8 m apart. A backpacker is trying to lift his 23-kg backpack out of the reach of bears of 1 Figure 1 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 1.5 m Express your answer to two significant figures and include the appropriate units. 115.64 N My Answers Give Up Submit Incorrect, Try Again, 4 attempts remaining Part B Calculate the magnitude of the force E 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.

Explanation / Answer

a.)
distance between trees: 5.8m
half distance between trees (b) = 2.9m
sag at mid point (a) = 1.5m
mid portion of rope = h (hypotenuse)
I drew a right triangle with a as the height, b as the base, and h as the hypotenuse.
h = ( b^2 +a^2) = ( 2.9^2 + 1.5^2) = 3.26m
w = m * g = 23 * 10 = 230 N
--> 2F cos = w ( = the angle between the rope and vertical)
2 * F * (1.5/3.26) = 230
---> F = 249.93 N

b.) a = 0.15m
h = ( b^2 + a^2) = (2.9^2 +0.15^2) = 2.90m
--> 2F cos = w
2 * F * (0.15/2.90) = 190
---> F = 1836.66 N

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