# Static equilibrium Cliff Climber

1. Mar 30, 2009

### electricblue

1. The problem statement, all variables and given/known data

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 (Intro 1 figure) ). Suppose that an 84.7-{\rm kg} climber, who is 1.75 {\rm m} tall and has a center of gravity 1.1 {\rm m} from his feet, rappels down a vertical cliff with his body raised 40.7^\circ above the horizontal. He holds the rope 1.54 {\rm m} from his feet, and it makes a 25.5^\circ angle with the cliff face.

Part A
What tension does his rope need to support?

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

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?

2. Relevant equations
$$\sum$$$$\tau$$=0
$$\sum$$Fx=0
$$\sum$$Fy=0

3. The attempt at a solution

For Part A i did 3 times and got the wrong solution... but i still cannot figure out why.

$$\sum$$$$\tau$$= 1.1 x mg x cos40.7 - T cos 71.8 x 1.54
answer i got was T = 1439.15
actual answer T = 472N

Part B i used n = Fx = 472 x cos 67.5 = 180.62
actual answer n = 200N

Last edited by a moderator: May 4, 2017