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

[Carl Mungan <mungan@usna.edu>]

> 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).

You do have it right. A common error indeed is to focus just on the 
weight of the oil pushing down on the top of the ball and not 
consider that the oil also pushes down on the surface of the water 
and increases the pressure in the water which thereby pushes the 
bottom half of the ball upward.

The quick answer is the ball rises because... before it was only 
partly immersed in liquid and now it's fully immersed in liquids.

-Carl

> 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?


--
Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/