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Homework Help: Why does a log float horizontally?

  1. Feb 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Why does a log float horizontally as opposed to vertically?

    2. Relevant equations

    3. The attempt at a solution
    I can kind of imagine why a vertical log would be in unstable equilibrium, but the thought isn't quite as logically cohesive as I'm comfortable with, so could anyone elaborate using concepts of buoyancy or even energy (which I think does have something to do with it)

    Taken from the "questions" section of Halliday and resnick, chapter 17: fluid statics.
  2. jcsd
  3. Feb 28, 2016 #2

    Simon Bridge

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    The concept you want is "balance" and "stabitity".
    Sketch a log floating vertically - but tipped very slightly - and examine the forces on it: where is the center of mass and what happens?
    Repeat for a log floating horizontally.
  4. Feb 28, 2016 #3
    Ah nvm the center of mass stays above the center of buoyancy, got it. Thanks!
  5. Feb 28, 2016 #4

    Simon Bridge

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    Well done.
  6. Feb 28, 2016 #5


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    No. A floating object of uniform density always has its centre of mass higher than its centre of buoyancy. Sketch the vertical log and the horizontal log and you will find it true for both.
    Stability of floating objects is subtler. If the object is perturbed by a small rotation, its profile in the water can change. This shifts the centre of buoyancy. If it shifts the centre of buoyancy in the same direction as the centre of mass, but further, the resulting torque restore equilibrium.
    See https://en.m.wikipedia.org/wiki/Buoyancy#Stability

    For a long cylinder, its stability about its axis is neutral, i.e. there is no restoring torque, but the no reinforcing torque either.

    In fact, the question is not correct without qualification. A very short fat log will float upright (in the sense that its cylindrical axis is upright), not on its side. There may even be a range of ratios for which the log will be stable at a jaunty angle.
    Last edited: Feb 28, 2016
  7. Feb 28, 2016 #6
    That was a very clear explanation, thanks.
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