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Buoyancy of object on telescopic riser with only part of its bottom in water

  1. Sep 21, 2010 #1
    If a cube submerged in water is attached to the floor with a telescopic cylinder taking up part of the surface area on the bottom of the cube, will the buoyant upward force be a fraction of the surface area on the bottom of the cube exposed to water, or will the full buoyancy effect take place, as long as at least a little of the bottom surface area of the cube is exposed.

    Assume the cube is less dense than the water it is in.
    Assume the telescopic cylinder does not create any tensive or vacuum force, and is ridgid. It is just preventing some of the water from contacting part of the bottom surface of the cube.

    From what I have read on the forums, if the ENTIRE bottom of the cube is not in contact with water the cube will have NO buoyant uplift. My question is what if only part of the bottom surface of the cube is in contact with water? Do I calculate buoyant force normally and multiply by the fraction of bottom surface area that water comes in contact with? Or, does the entire normal Buoyant force get applied.
     
  2. jcsd
  3. Sep 21, 2010 #2

    cjl

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    Buoyant force depends on displaced volume, not surface area. It won't change just because there's a cylinder attached (aside from any volume displaced by the cylinder).
     
  4. Sep 23, 2010 #3

    Cleonis

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    Gold Member

    I will refer to 'the basin' for the container of the body of water that the cube is floating in.

    In a sense the cube you describe is not attached to the floor of the basin; your statement about the cilinder implies it exerts neither an upward nor a downward force. All that the cilinder does is prevent sideways motion.

    We have that in order to float the cube must display its weight in water. It follows that the cube-with-cilinder will be immersed more deeply than the same cube without cilinder. The volume taken up by the cilinder is not available for water being displaced.

    Alternatively, you can evaluate the buoyancy by considering pressure gradient. In a fluid like water there is a pressure gradient; the pressure increases linearly with depth. The bottom of the cube is below the surface, the pressure acting upon the bottom of the cube provides the required upward force for buoyancy. As you describe: with the cilinder in place there is less surface area available. Force is pressure times surface area. Less surface area means a larger pressure is required to obtain the same amount of force.
     
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