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Homework Help: Please help rotational motion

  1. Jul 24, 2010 #1
    Please help....rotational motion

    1. The problem statement, all variables and given/known data
    A stuntman swings from the end of 4 m long rope along the arc of a vertical circle. If his mass is 70kg, find the tension in the rope required to make him follow his circular path, assuming he starts from rest when the rope is horizontal:
    a) at the beginning of his motion

    b) at the bottom of his arc


    2. Relevant equations

    centripetal acceleration = v^2/r

    F = mv^2/r

    3. The attempt at a solution
    For part a) at the beginning of his motion, is the tension equal to zero? The tension of the rope is pointing to the center and therefore the equation is F = mv^2/r. However, v is equal to 0 because he starts from rest. is that right?

    For part b) at the bottom of the arc, tension in the rope and mg causes acceleration and therefore the equation is F - mg = mv^2/r. But what's v???

    Can someone help me please?
     
  2. jcsd
  3. Jul 24, 2010 #2

    Doc Al

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    Re: Please help....rotational motion

    Right.

    You'll need to figure out the speed at the bottom. (What's conserved?)
     
  4. Jul 24, 2010 #3
    Re: Please help....rotational motion

    Kinetic energy
     
  5. Jul 24, 2010 #4

    Doc Al

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    Re: Please help....rotational motion

    Total mechanical energy is conserved as man swings, not just kinetic.
     
  6. Jul 24, 2010 #5
    Re: Please help....rotational motion

    Ok. In that case:

    KEmiddle + PEmiddle = KEbottom +PEbottom
    1/2mv^2 +mgh = 1/2mv^2 +mgh
    0 + mgr = 1/2mv^2 + 0
    mgr = 1/2mv^2
    (70)(9.8)(4) = 1/2(70)v^2

    therefore, v = square root off 2gr = 8.9m/s

    F1 - mg = mv^2/r
    F1 = mv^2/r +mg
    = (70)(8.9)^2/4 + (70)(9.8)
    = 2.07 x 10^3 N

    Can you confirm if this is right? THANKS
     
  7. Jul 24, 2010 #6

    Doc Al

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    Re: Please help....rotational motion

    Looks good! (Don't round off until the end.)
     
  8. Jul 24, 2010 #7
    Re: Please help....rotational motion

    Thanks for your help! =)
     
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