Part A Mountaineers often use a rope to lower themselves down the face of a clif

Question

Part A Mountaineers often use a rope to lower themselves down the face of a cliff (this is called rappeling). They do this with their body nearly horizontal and their feet pushing against the cliff Eigure 1). Suppose that an 81.7-kg climber, who is 1.95 m tal and has a center of gravity 1.0 n from his feet, rappels down a vertical clitf wilth his body raised 36.1 above the horizontal. He holds the rope 1.49 m from his feet, and it makes a 27.5 angle with the clit face. What tension does his rope need to support? Express your answer using two significant figures. Submit My Answers Give Up Part B Find the horizontal component of the force that the cliff face exerts on the climber's feet. Express your answer using two significant figures. FH Submit My Answers Give U Part C Find the vertical component of the force that the ciff face exerts on the cimber's feet Express your answer using two significant figures

Explanation / Answer

1) The rope makes an angle with his body of
= 90º + 36.1º - 27.5º = 98.6º

Sum the moments about his feet (so that we can ignore the forces there):
M = 0 = mgdcos36.1º - TDsin98.6º
0 = 81.7kg * 9.8m/s² * 1.0m * cos36.1º - T * 1.49m * sin98.6º
and so
tension T = 439.11 N

2) Fx = T*sin27.5º = 202.76 N

3) Fy = mg - Tcos27.5º = 81.7kg * 9.8m/s² - 439.11N * cos27.5º = 411.16 N

4) min µ = Fy / Fx = 2.03

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