Mountaineers often use a rope to lower themselves down the face of a cliff (this

Question

Mountaineers often use a rope to lower themselves down the face of a cliff (this is called rappelling). They do this with their body nearly horizontal and their feet pushing against the cliff (the figure (Figure 1) ). Suppose that an 78.0-kg climber, who is 1.95 m tall and has a center of gravity 1.5 m from his feet, rappels down a vertical cliff with his body raised 43.9 ? above the horizontal. He holds the rope 1.35 m from his feet, and it makes a 27.6 ? angle with the cliff face.

Part A

What tension does his rope need to support?

Express your answer using two significant figures.

T=

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 =

Part C

Find the vertical component of the force that the cliff face exerts on the climber's feet.

Express your answer using two significant figures.

FV =

Part D

What minimum coefficient of static friction is needed to prevent the climber's feet from slipping on the cliff face if he has one foot at a time against the cliff?

Express your answer using two significant figures.

?s =

Explanation / Answer

part(A)

net torque about the feet = 0

torque due to tension = torque due to weight

T*cos27.6*1.35*cos43.9 + T*sin27.6*1.35*sin43.9 = 78*9.8*1.5*cos43.9

T = 637.6 N

B)

along horizantal

-Tx + FH = 0

FH = Tx = T*sin27.6 = 637.6*sin27.6 = 295.4 N

(c)

along vertical

Fv + Ty - Fg = 0

Fy + 637.6*cos27.6 - 78*9.8 = 0

Fv = 199.4 N

(d)

us = Fv/FH = 199.4/295.4 = 0.67

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