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Homework Help: Liquid mirror problem

  1. Jun 5, 2010 #1
    A concave astronomical telescope mirror may be made by rotating a circular tank of mercury. Find an expression for the shape of the surface in terms of the density of mercury, the radius from the centre and the rotaion rate

    so far ive come up with:
    KE=1/2MV^2
    In the case of circular motion the relation v = ωr holds, hence
    KE=1/2MW^2R^2
    The gravitational potential energy is given by
    potential energy= mgh
    where g is the acceleration of gravity and h is the height of the mercury's surface above some arbitrary elevation, for instance, we can set h = 0 to be the lowest mercury surface.

    We set the potential energy equal to the kinetic energy to find the mirror's shape:
    H=(1/2g)W^2R^2
    which is by definition a parabola

    im unsure how to include a density term into this formula any help appreciated
    Thanks.
     
  2. jcsd
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