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Centripetal force with circular motion

  1. Oct 20, 2008 #1
    This problem seems simple, but I can't get the answer:
    1. The problem statement, all variables and given/known data

    Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.0 m long. His speed at the bottom of the swing is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1000 N. What is the largest mass that Tarzan can have and still make it safely across the river.

    2. Relevant equations

    Fc=(m*v2)/(r)

    3. The attempt at a solution

    1000 N=(m*(8 m/s)2)/(10 m)



    The answer is apparently 62 kg, and what I'm getting is over double that, so I'm obviously doing something wrong. I'm really not sure what I'm missing.
     
  2. jcsd
  3. Oct 20, 2008 #2

    hage567

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    Homework Helper

    The 1000 N is not Fc. It is the breaking strength (so the maximum tension the vine can withstand). There are two forces to consider. You have neglected to take into account Tarzan's mass on the vine. Draw a diagram to see it.
     
  4. Oct 20, 2008 #3
    Ft is not the only force in this example.


    mv2/r = Fc
    Fc= Ft-Fg
     
  5. Oct 20, 2008 #4
    I'm still not getting the right answer.

    Using this, I've come up with

    m=[10m*(1000 N-9.81m/s2*kg)]/(8.0m2/s2), which keeps working out to around 154 kg, still way off. What am I missing here?
     
  6. Oct 21, 2008 #5
    Nevermind, I got it. Thanks guys.
     
  7. Dec 17, 2010 #6
    maximum tension is the tension at the lowest point
    and
    tension at the lowest point = mv2/r + mg
    works to around 61.72 by taking g = 9.8m/s
     
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