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Circular Motion, an object attached by a string to a motor

  1. Oct 24, 2016 #1
    1. The problem statement, all variables and given/known data

    A pendulum traveling at constant speed along a circular path
    Determine the angle that the string makes with the vertical.

    T
    he length of the string was measured to be 60 cm.
    The period was measured to be 1.41 s
    The frequency was found to be 0.709


    2. Relevant equations

    Is it possible to find the radius with only the Period T and frequency f?

    3. The attempt at a solution

    I believe that it should be possible to use the period and frequency to find the velocity, and from there the radius. Once I have the radius, I can find the angle.

    Using:
    v = 2(pi)r / T, v = 2 (pi)fr,
    v = (2 x pi x radius)/period, v = 2 x pi x frequency x radius

    a = v^2/r = (2(pi)f)^2r =(2(pi)/T)^2 r
    a = velocity squared / radius = (2 x pi x frequency) squared x radius
    = ((2 x pi) / T))squared x radius

    I have tried solving for "r" and substituting the solution in order to find velocity, .... but I end up circling back the an equation with both the two unknown variables that I am trying to find, v and r.

    with advanced thanks for any advise,
    D.T.
     
  2. jcsd
  3. Oct 24, 2016 #2

    Doc Al

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    Staff: Mentor

    How about drawing a free body diagram of the pendulum? Identify all forces acting and apply Newton's 2nd law.
     
  4. Oct 24, 2016 #3

    gneill

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    Referring to the thread title, I'm not seeing where the motor comes in....
     
  5. Oct 24, 2016 #4

    Doc Al

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    I'm guessing the string of the pendulum is tied to some spinning axis--driven by the motor.
     
  6. Oct 24, 2016 #5

    gneill

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    Staff: Mentor

    Ah. Alrighty then. :smile:
     
  7. Oct 24, 2016 #6
    Air resistance is not considered scan0002.jpg

    I understand that that force (net) = ma = (mv^2)/r
    and that mass "cancels out" so Force(net) = a = v^2 / r.

    Velocity is not known. Neither is the radius, or angle

    (the length of the string providing the tension, the period and the frequency are known.)

    I thought that I could solve for velocity, and from velocity, solve for radius, ... but am now wondering if there is enough info to so do
     
    Last edited: Oct 24, 2016
  8. Oct 24, 2016 #7

    Doc Al

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    Staff: Mentor

    Apply Newton's 2nd law to vertical and horizontal force components separately.
     
  9. Oct 24, 2016 #8

    thank you
     
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