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String tension with an attached whirling mass

  1. Dec 6, 2009 #1

    MZA

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    1. The problem statement, all variables and given/known data
    A 0.40 kg mass, attached to the end of a .75 m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum speed can the mass have if the string is not to break?


    2. Relevant equations
    F=m*a
    T=r*F*sin(theta)
    v=r*omega

    3. The attempt at a solution
    I have absolutely no idea where to even begin with this. My idea was to find the acceleration when the force is 450 N, but that yields the linear acceleration not the angular one which does nothing for me. I am stumped.
     
  2. jcsd
  3. Dec 6, 2009 #2

    Oddbio

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    Gold Member

    Well even with the object being swung around at a constant (angular) speed you will still have a force. Because the direction of the velocity vector is changing, and acceleration is change in velocity. So you are looking for the acceleration inward, which is the centripetal acceleration, the force vector would be pointing from the object toward the center of the circle as it spins.

    So the equations you are missing are:
    [tex]a_{centripetal}=\frac{v^{2}}{r}[/tex]
    OR equivalently:
    [tex]a_{centripetal}=\omega^{2}r[/tex]
     
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