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Finding the Displacement of a piston in circular motion

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data
    A 1.86 g piston is attached to a rotating disc. The radius is 25.5 cm when the disc is stationary. A spring attached to the piston has a spring constant of 31.3 N/m. The piston is rotating at a frequency of 10 Hz. How har will the piston move outward
    k = 31.3
    r = 25.5 cm = 0.255 m
    Frequency = 10 Hz
    m = 1.86 g



    2. Relevant equations
    1/2kx^2 = Es
    ac = v^2/r
    W = change in Energy


    3. The attempt at a solution

    I really don't even know where to start. Please help. How am I supposed to relate frequency to speed?
     
  2. jcsd
  3. Nov 22, 2009 #2

    Delphi51

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    Does that mean the piston's centrifugal force stretches the spring?
    If so, begin with centrifugal force = spring force
    Fill in the detailed formulas and see if you can find the stretch.
     
  4. Nov 22, 2009 #3
    Okay so

    Fc = -kx
    m*ac = -31.3* x
    0.00186*v^2/0.255 = -31.3* x

    How do I find both v and x?
     
    Last edited: Nov 22, 2009
  5. Nov 22, 2009 #4

    Delphi51

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    You can write another equation using the 10 turns per second.
    That is v = 2πr*10.
    The question is not very clear, but looks like r = 0.255 + x.
    You have a system of two equations to solve.
     
  6. Nov 22, 2009 #5
    I found the strech of the spring to be 1.525 cm. Is that all I have to do for this problem?
     
  7. Nov 22, 2009 #6

    Delphi51

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    The stretch is the answer but that 1.5 cm seems low.
    It would be interesting to see how you worked it out.
     
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