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Tention in a String

  1. Oct 31, 2007 #1
    1. The problem statement, all variables and given/known data

    A ball at the end of a string is revolved at a uniform rate in a vertical circle of radius 72cm. If its speed is 4m/s and its mass is 0.300kg, calculate the tentsion in the string when the ball is (a) at the top of its path and (b) at the bottom of its path.

    2. Relevant equations

    F=ma, and variations thereof to include the sum of all forces

    3. The attempt at a solution

    I got (a) by using mg+FsubT=m(v^2/r) and I came up with 6.66N-2.94N=3.72N, but for some reason I can't get (b). I'm doing this for practice for an exam, so I'm doing the problems that have the answers in the back so that I can check myself, and the answer for (b) is supposed to be 9.61N, but I can't figure out how to get there.

    The equation that I'm using for (b) is mg-FsubT=m(v^2/r), because that looked right from my free body diagram (with x reference frame point down), but I keep ending up with 2.94N-6.66N=-3.72N ...

    This is obviously not right... the answer is positive and 3x the magnitude on top of it, so... I don't know what I'm doing wrong. Any help is greatly appreciated.
     
  2. jcsd
  3. Oct 31, 2007 #2

    learningphysics

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    Homework Helper

    "mg-FsubT=m(v^2/r)"

    your signs/directions are wrong here.

    If you take upwards positive... downwards negative...

    FsubT - mg = mv^2/r

    now solve for FsubT
     
  4. Oct 31, 2007 #3
    Excellent. Many thanks.
     
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