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The rotation of the Earth affects the apparent gravitational acceleration at differ

  1. Feb 16, 2012 #1
    1. The problem statement, all variables and given/known data
    The rotation of the Earth affects the apparent gravitational acceleration at
    different latitudes. At a location on the Equator, a man’s weight is registered
    as 709.7 N on a set of very accurate scales. Assuming a perfectly spherical
    Earth, determine what the same set of scales would register for the same
    man’s weight at the North Pole



    2. Relevant equations
    Not sure I have used f=ma and w=mg but dont think I need these as the Earth is perfectly spherical
    So it might be a=v^2/r


    3. The attempt at a solution
    As far as I can figure if Earth is perfectly spherical then there will be no change in weight due to the force of gravity. But maybe because of the rotation and Centrifugal force this might have a slight effect.
     
  2. jcsd
  3. Feb 16, 2012 #2

    SammyS

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    Re: The rotation of the Earth affects the apparent gravitational acceleration at dif

    Correct.
    So, how much effect ?
     
  4. Feb 16, 2012 #3
    Re: The rotation of the Earth affects the apparent gravitational acceleration at dif

    So if I find the angular velocity first ω=2∏rad/T and then v=rω^2
    Plugged in values
    2*3.14/(24h*3600s/h)=7.3x10^-5 rads
    v=6.378x10^6m/(7.3x10^-5)^2rads=0.034m/s^2
    So the force of gravity will be 0.034m/s^2 less
    and then I can find the weight .
    Dose this seem right
     
  5. Feb 16, 2012 #4

    SammyS

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    Re: The rotation of the Earth affects the apparent gravitational acceleration at dif

    Yes, except for some units and saying force rather than acceleration .

    (Corrected above)
     
  6. Feb 16, 2012 #5
    Re: The rotation of the Earth affects the apparent gravitational acceleration at dif

    Ok thanks A lot SammyS your help is appreciated
     
  7. Feb 16, 2012 #6

    SammyS

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    Re: The rotation of the Earth affects the apparent gravitational acceleration at dif

    And ... I forgot to say,

    Welcome to PF !
     
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