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. Suppose that an 83.3-kg climber, who is 1.89m tall and has a center of gravity 1.5m from his feet, rappels down a vertical cliff with his body raised 30.3? above the horizontal. He holds the rope 1.54m from his feet, and it makes a 28.9? angle with the cliff face.

A) What tension does his rope need to support?

B) Find the horizontal component of the force that the cliff face exerts on the climber's feet.

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

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?

Explanation / Answer

T*cos28.9 + Fy = mg

-T*sin28.9 + Fx = 0


T*1.54*sin(88.6) = m*g*1.5*co30.3

A) T = 686.72 N

B) Fx = T*sin28.9 = 331.879 N

C) Fy = mg-T*cos28.9 = (83.3*9.8)-(331.879*cos28.9)= 525.79 N

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