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Maximum Tension Question

  1. Feb 9, 2014 #1
    1. The problem statement, all variables and given/known data
    The maximum tension the string can have without breaking is Tmax. Derive an expression for Vmax, the maximum speed the ball can have at point Q without breaking the string.


    2. Relevant equations
    F=ma
    Vc=(mv^2)/r
    T=mg+ma
    3. The attempt at a solution
    I thought I could do T+mg=mv^2/r because mv^2/r-mg would give you the max speed to keep the same tension and anything great would produce a greater tension that the string doesn't have causing it to break. So, I pulled out a common factor in m and got a common denominator giving me m((v^2-gr)/r)=T


    IMG_3397.jpg
     
  2. jcsd
  3. Feb 9, 2014 #2
    Sorry for the size of the pic. If you click on it it will expand.
     
  4. Feb 9, 2014 #3
    Careful, the equation you have is incorrect -- tension and weight force act in opposite directions at point Q, so this needs to be reflected in their signs.
     
  5. Feb 9, 2014 #4
    Thats what I thought at first but wanted to try something new. So is it the same thing I have put down but with a plus sign?
     
  6. Feb 9, 2014 #5
    What I mean is that you have this:

    but T and mg cannot have the same sign. There has to be a negative somewhere on the left.
     
  7. Feb 9, 2014 #6
    -T+mg=mv^2/r ?
     
  8. Feb 9, 2014 #7
    No, you're mixing up your signs. Start with this:

    At Q, which way do both forces point, and which way does the acceleration point?
     
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