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Fluid Statics - net upward force

  1. Nov 29, 2014 #1
    1. The problem statement, all variables and given/known data
    Find magnitude of net upward force on a cube in terms of l, ρ (rho), g and h. then show that h = m/ρl2

    A solid cube, mass m, side length l, is placed in a liquid of uniform density, ρ(rho), at a depth h0 below the surface of the liquid, which is open to the air.
    The upper and lower faces of the cube are horizontal.

    (this is from previous question https://www.physicsforums.com/threads/force-exerted-by-fluid.784711/)

    2. Relevant equations
    pressure, p = ρ g h
    mass = ρ x volume of liquid displaced

    3. The attempt at a solution
    Net force, Fn = (pbottom x area of cube face) - (ptop x area of cube face)
    p at top face = (pT) x ρliquid x h x g
    p at bottom face = (pB) x ρliquid x (h+l) x g
    so
    Fn = (ρgh + ρlg - ρgh)
    Fn = ρlg

    Net force - fine.
    Er! how do I show that h = m/ρl2
    I know m = ρ x v . . .
     
  2. jcsd
  3. Nov 29, 2014 #2

    haruspex

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    I can only make sense of the question if h is different from h0. (Your working all has h, but the question used h0.)
    A reasonable meaning for h would be that the block is released and floats level with depth h immersed.
     
  4. Nov 29, 2014 #3
    I have looked at the question and unscrewed the bits of paper I attempted my answers on and the h0 seems to be a complete typo, it all says just plain h. I will try to work through with that in mind, as you say.
     
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