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Uniform Circular Motion; Need help with deriving equations.

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi I'm doing a physics lab about uniform circular motion to measure frequency and to compare it to mass,radius and force tension.

    (A & B) I did
    (C,D, E) I need help

    (a) What variables are being measured / manipulated in this lab? What type of relationship is being tested? (radius, mass, force tension/force causing centripetal force)

    (b) Graph the relationship between the frequency of revolution and each of the following:
    • the magnitude of the tension force [force causing the circular motion(centripetal force)]
    • the radius of the circular path
    • the mass of the object

    **■→(c) Find the proportionalities between frequency of revolution and the variables in radius, mass, and force of tension/centripetal force.

    **■→(d) Derive an equation for the frequency in terms of the tension, the radius, and the mass by combining your results from (c) and using your results from (b) to verify.

    **■→(e) The following relationship gives the magnitude of the net force causing the acceleration of an object in uniform circular motion:
    Fc = 4π²mrf²
    Rearrange this equation to isolate the frequency. Compare this result with the equation you derived in (d). Indicate the likely causes for any discrepancies.

    Data: http://i.imgur.com/dLpyP.png

    Frequency vs Force Graph: http://i.imgur.com/fyFci.png

    Frequency vs Mass Graph: http://i.imgur.com/GJ2ms.png

    Frequency vs Radius Graph: http://i.imgur.com/JtxbR.png

    2. Relevant equations
    Fc = 4π²mrf²


    3. The attempt at a solution
    C) and D) Im stuck at

    E)
    Fc = 4π²mrf²
    [itex]\sqrt{}\frac{Fc}{4π²mr}[/itex]
     
  2. jcsd
  3. Apr 14, 2012 #2

    PeterO

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    Homework Helper

    Your graphs are not extensive enough - they must include the origin (0,0) - not necessarily as a point, but with the axes long enough for them to show up.

    With graphical analysis, the only line you can confidently interpret is a straight line passing through the origin.

    if y vs x is not straight, you can try y vs 1/x or y vs x2 or or y vs 1/x2 or y vs x2 of y vs √x or y vs 1/√x to see if any of them are a straight line through the origin [or close - there may be uncertainties in your measurements]

    suppose y vs 1/√x was such a straight line.

    That means y is proportional to 1/√x or y = k/√x or y2x = k
     
  4. Apr 15, 2012 #3
    uhmm.. time for one cycle is 1/frequency.
     
  5. Apr 15, 2012 #4

    PeterO

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    Homework Helper

    Looking at your results, I am not sure the figure you call frequency is in fact frequency.
    It looks more like the Period to me - ie the time for one cycle.
    You possibly need to follow the step you mention above.
     
  6. Apr 15, 2012 #5
    Yes exactly, that's what I said. The graphs are obviously wrong because he has used time period instead of frequency.
    peter, I didn't ask this question..n3w ton did. :P
     
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