Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

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


    ω = sqrt(Fsinθ/mLsinθ)

    giving an answer of 4.86 rad/s?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook