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Circular motion of rope and ball

  1. Sep 15, 2009 #1
    1. The problem statement, all variables and given/known data

    A motor is used to rotate a ball attached to a rope in a vertical plane. The mass of the ball is 2kg and the length of the rope is 3m. Ignoroing air resistance and the mass of the rope, calculate:

    a) The minimum motor speed in rpm that will maintain the ball in a circular motion

    b) The total energy of the ball at the top of the circle

    2. Relevant equations

    a

    3. The attempt at a solution

    a) If the motor is providing enough speed to maintain a circular motin then at the balls highest point all hte centripetal accelration is provided by gravity.

    a = g = 9.81 = w2r= w2 x 3

    so

    [tex]\omega=\sqrt{\frac{9.81}{3}} = 1.808 rad/s[/tex] rad/s

    [tex]\omega=\frac{1.808}{2\Pi}=0.288rev/s [/tex]

    [tex]\omega=0.288rev/s . 60 = 17.28 rpm[/tex]


    b)

    v = rw = 3 x 1.808 = 5.424 m/s

    Potential Energy at the top of the circle = mgh = 2 x 9.81 x 3 = 58.86 J
    Kinetic Energy = 1/2 m v^2 = .5 x 2 x 5.424 = 29.42 J

    Total Energy at the top of the circle = 58.86 + 29.42 = 88.28 J



    Hi, just after sanity check and to make sure the assumptions I have made in part a) are correct. I'm not 100% on them.

    Thanks in advance

    Parabol
     
  2. jcsd
  3. Sep 15, 2009 #2

    Redbelly98

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    (a) looks good.

    (b) is probably okay, but the question is ill-posed. They do not say where to take the potential energy to be zero. If we take h=0 at the center of the circle, then you're answer is correct.
     
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