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Mass suspended from spring in ship - Gravity problem

  1. May 18, 2005 #1
    Hello all just a quick question,


    A mass is suspended from a spring balance in a ship sailing along the equator with a speed v.
    (a) Show that the scale reading will be very close to wo = (1 ± 2ωv/g), where ω is the angular
    speed of Earth, and wo is the weight of the mass with the ship at rest.
    (b) Explain the ± sign
    .


    I have wrapped my head around the question but am having trouble coming up with the given equation.
    -The weight of the mass at rest will be equal to mg- the centripetal force of the rotating earth.
    -The weight of the mass when the ship is sailing will be close to wo, but differ depending of the direction the ship is sailing, hence the ±.
    -As this is the case I recognize that the velocity when calculating the centripetal force on the mass will be ω±v/r.

    What I do not see is how 1 came into 1 ± 2ωv/g, nor where the mass or radius went

    Thank you for any help,
    Lucas
     
  2. jcsd
  3. May 18, 2005 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Your approach is right. The vector sum of the spring force and gravity has to equal the centripetal force. Where [itex]v << \omega R[/itex] you can use the binomial expansion and eliminate the higher order term. The radius is implicit in [itex]\omega = v_{earth}/R[/tex]. It might be useful to think in terms of [itex]\omega R \pm v = R(\omega \pm \Delta \omega)[/itex].

    The answer: 1 ± 2ωv/g is the acceleration. Multiply by m to give the normal force or weight read by the scale.

    AM
     
    Last edited: May 18, 2005
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