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Static equilibrium Cliff Climber

  1. Mar 30, 2009 #1
    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.
    "[URL [Broken]

    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
    [tex]\sum[/tex][tex]\tau[/tex]=0
    [tex]\sum[/tex]Fx=0
    [tex]\sum[/tex]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.

    [tex]\sum[/tex][tex]\tau[/tex]= 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

    Please advice thanks
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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