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Spring with circular motion

  1. Jul 15, 2007 #1
    1. The problem statement, all variables and given/known data
    An object of mass M = 3.00 kg is attached to a spring with spring constant k = 132 N/m whose unstretched length is L = 0.170 m, and whose far end is fixed to a shaft that is rotating with an angular speed of omega = 2.00 radians/s. Neglect gravity and assume that the mass also rotates with an angular speed of 2.00 radians/s as shown.

    [​IMG]

    Question:
    Given the angular speed of omega = 2.00 radians/s, find the radius R([tex]\omega[/tex]) at which the mass rotates without moving toward or away from the origin.

    2. Relevant equations

    [tex]k(R-L)[/tex]
    The amount of force a spring exerts is proportional to the distance it is stretched or compressed with respect to its equilibrium length ( L = 0.170 m in this case).

    so...

    [tex]F_{spring}(R)=k(R-L)[/tex]

    3. The attempt at a solution

    "force a spring exerts is proportional to the distance it is stretched or compressed with respect to its equilibrium length" I am having problems with this part. I cannot figure out what the other side of the equation is.

    I tried [tex]R-L=k(R-L)[/tex] but this does not work.

    Any ideas???

    -- Abarak
     
  2. jcsd
  3. Jul 15, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Apply Newton's 2nd law to the mass. Is it accelerating?
     
  4. Jul 15, 2007 #3
    From what I gather the object is not accelerating so Newton's 2nd law would not apply to this.

    "force a spring exerts is proportional to the distance it is stretched or compressed with respect to its equilibrium length" I don't see how this would apply to Newton's second law or the other side of the equation:

    [tex]???? = k(R-L)[/tex]

    -- Abarak
     
  5. Jul 15, 2007 #4

    Doc Al

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    Staff: Mentor

    Sure it's accelerating--it's going in a circle! (Reread the chapter in your text about circular motion.)
     
  6. Jul 15, 2007 #5
    Oh snap! Talk about a lack of judgment. After applying Newton's 2nd Law everything worked like a charm.

    Thanks again for the help Doc.

    -- Abarak
     
  7. Jan 30, 2008 #6
    how did you do this problem, because i have the same problem and its been bugging me like crazy.
     
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