Re: [Phys-L] Nice question on buoyancy and balance

[Philip Keller <pkeller@holmdelschools.org>]

I admit that this one has me bothered. My first thought was "no change" 
but then I argued myself out of that. So here goes:

First, I decided to change the ball into a cube.  Instead of looking at 
displaced water, we can think of the buoyancy force as the gauge 
pressure times area of the bottom surface.  (Using gauge pressure lets 
us ignore the downward force of air pressure from above.)

Then I imagined adding the oil slowly until the depth of the oil just 
reached the top of the sides of the cube.  If my guess of no change in 
fraction submerged were right, then the bottom surface of the cube would 
be at a higher pressure than initially due to the new layer of 
oil....but then it would rise.

So I guess the cube rises as you add oil.  And once the oil is above the 
top of the cube, no more change.

Getting back to the sphere, it seems strange because 90% of the sphere 
is originally submerged.  It is easy to imaging the oil pushing down on 
the 10% that is still above the water, pushing it down further.  But in 
fact, the increase in the pressure below wins (if I have this right).

On 1/30/2014 12:27 PM, Carl Mungan wrote:
> One more nice problem (I believe it is a Mazur ConcepTest) is:
>
> You have a ball of specific gravity 0.9 and oil of specific gravity 0.8.
>
> A graduated cylinder is about half filled with water. The ball is 
> dropped in and floats on top. You make a mark level with the top of 
> the ball.
>
> Now you carefully pour in enough oil to cover the ball. (The ball 
> continues to float on the water but sinks in the oil because of their 
> specific gravities.)
>
> Is the top of the ball now above, at, or below the mark you made?