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Circular motion of ball and string

  1. Feb 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Part A : A 0.5 Kg ball is attached to a cord 80 cm long. The ball is whirled in a vertical circle at a constant speed. If the ball takes 0.4 seconds to go around once, what is the tension in the cord at the top and bottom of the circle?

    Part B How long does it take for the ball to go around once if the tension in the cord at the top of the circle is zero?

    2. Relevant equations
    v=2Pi*R/T
    T=m(g+v^2/r) (bottom of the circle)
    T=m(g-v^2/r) (top of the circle)


    3. The attempt at a solution

    For part A i used both of the circular motion formulas to fin the tension and i got totally different answers from what it suppose to be for top and bottom. Top it suppose to be 93.8N and bottom it suppose to be 104 N i got 92.7N top and 102.7 N bottom. ( I do not know if the answer is a print error).

    For part A I tried to use v=2Pi*R/T to get the time and i keep getting the same time in part A which is 0.4 secs. But the answer is 1.8 seconds.

    Can someone explain to be what I'm doing wrong??? thanks!
     
  2. jcsd
  3. Feb 13, 2012 #2
    the formula for top of the circle should be

    T=m(v^2/r - g) (top of the circle)

    for part a, the time is 12.57 second

    g = 9.81

    try to put the numbers in your calculator more carefully, the result should come out correct
     
  4. Feb 13, 2012 #3
    for part b, tension must equal zero yet F=ma must be obeyed

    F = m * a

    T + mg = m * v^2/r (the downward force consist of tension and weight)

    mg = m*v^2/r (T=0)

    g = v^2/r

    v = 2.8 m s^-1

    now try the v=2Pi*R/T again
     
  5. Feb 13, 2012 #4
    Thanks it worked!!!
     
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