Mountaineersoften use a rope to lower themselvesdown the face of a cliff (this is called rappelling).They do this with their body nearly horizontaland their feet pushing against the cliff. Suppose that an 82.0 kg climber,who is 1.90 m tall and has a center of gravity1.1 m from his feet, rappels down a verticalcliff with his body raised 35.0° above the horizontal.He holds the rope 1.40 m from his feet,and it makes a 25.0° angle with the cliff face.(a) What tension does his rope need to support?(b) Find the horizontal and vertical componentsof the force that the cliff face exerts on theclimber’s feet. (c) What minimum coefficientof static friction is needed to prevent the climber’sfeet from slipping on the cliff face if he hasone foot at a time against the cliff?
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 82.0 kg climber,
who is 1.90 m tall and has a center of gravity
1.1 m from his feet, rappels down a vertical
cliff with his body raised 35.0° above the horizontal.
He holds the rope 1.40 m from his feet,
and it makes a 25.0° angle with the cliff face.
(a) What tension does his rope need to support?
(b) Find the horizontal and vertical components
of the force that the cliff face exerts on the
climber’s feet. (c) 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?
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