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Elastic Problem. Aluminum Wire in Horizontal Circle

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data

    An aluminum wire is 0.850 m long and has a circular cross section of diameter 0.780 mm. Fixed at the top end, the wire supports a 1.20-kg object that swings in a horizontal circle. Determine the angular velocity required to produce a strain of 1.00  10–3.

    2. Relevant equations

    Y of Aluminum = 7.0x1010

    Y = [itex]\frac{Stress}{strain}[/itex]

    Stress = [itex]\frac{F}{A}[/itex]


    Fc = ω2R
    3. The attempt at a solution

    I use Young's Modulus with the definition of stress and I get the equation

    Y = [itex]\frac{F/A}{Strain}[/itex]

    Then I can solve for F

    A = [itex]\frac{∏(0.780)2}{4}[/itex] = 4.77x10-7

    F = Y x Strain x Area

    Okay, now I have the force which will give me the strain that is needed. I'll apply it in an object rotating in a horizontal circle, The force that I used will be the one on the X axis. So

    Fc = Fsinθ

    and also

    R = Lsinθ

    Using the equation of Centripetal Force I get the equation for angular Velocity

    ω = [itex]\sqrt{\frac{Tsinθ}{Lsinθ}}[/itex]

    Finally I get the value of 6.27 rad/s





    I just want to know if I did it right. Because I don't have the correct answer for this. Thanks :D
     
  2. jcsd
  3. Nov 30, 2011 #2

    PhanthomJay

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    Fc = mω2R
     
  4. Nov 30, 2011 #3
    Oops. What a simple mistake :|

    So

    ω = sqrt(Fsinθ/mLsinθ)

    giving an answer of 4.86 rad/s?
     
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