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

[Robert Cohen <Robert.Cohen@po-box.esu.edu>]

Interesting variation in the solutions.  I solved it much like Antti did.  How about the following variation?

Each beaker has an equal amount of water.  You then take two ping-pong balls that are filled with water, not air.

For the right beaker, you suspend the ping-pong ball from a crane, with the ball submerged in the water.

For the left beaker, you break open the ping-pong ball, empty its contents into the beaker, reconstruct the now-empty ping-pong ball and tie it to the bottom of the beaker, keeping it submerged.

Which way does the balance tip, if at all?  Does this make the solution easier or harder?


Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@esu.edu    http://www.esu.edu/~bbq 


-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Philip Keller
Sent: Wednesday, January 29, 2014 11:30 AM
To: Phys-L@phys-l.org
Subject: Re: [Phys-L] Nice question on buoyancy and balance (correction)

I know JD wants me to think in terms of momentum flow, but at my level, I hope to understand mechanics problems by thinking about objects being pushed by forces.

We have two pans.  Both are being pushed down by equal amounts of water.
 One is also being pulled up by a string.

I don't have to worry about the history that led up to this state if I don't feel like it.  But if I do feel like it here is one history:

On each pan, there were empty beakers.  And next to them, each pan had identical large beakers of water.  One beaker also had a ping pong ball, tied to its bottom surface by a short cord, say 1/3 as long as the beaker height.  The extra mass of the ping pong ball causes the balance to tip that way. The other beaker has a steel ball suspended from a crane, about
1/3 of the way down but it iis not yet part of the story.

We pour half of the water from each supply beaker into the empty beakers.
 The ping pong ball is now more than submerged but the water hasn't reached the steel ball.  Transferring this mass of water changes nothing.  The ping pong ball side is still slightly heavier.

We continue to transfer water.  The level reaches and passes the steel ball.  Now the downward force (reaction to the buoyancy force on the steel
ball) matters.  And I know that force is greater than the additional weight of the ping pong ball because I know that ping pong balls float.  So the balance tips the other way.

I still like my first answer better:  same water pushing down, one string pulling up.




On Wed, Jan 29, 2014 at 10:39 AM, Savinainen Antti < antti.savinainen@kuopio.fi> wrote:

> Hi again,
>
> I reread my posting and realized that it contains some embarrassing 
> language mistakes. I wrote:
>
> "The ping pong ball displaces the amount of water which equals its weigh.
> This is
> "under the water" volume if the ping pong ball were floating. So one 
> can image that this the amount of water is poured to the LHS whereas 
> the water poured to the RHS is equal to the volume of the steel ball."
>
> Instead, I should have written (well, it might still contain English 
> mistakes; hopefully no physics mistakes :-)):
>
> "If the ping pong ball were floating,  it would displace the amount of 
> water equal to its weigh (the displaced water is equal to the "under 
> the surface level volume of the ping pong ball"). So one can imagine 
> that this is the amount of water poured to the LHS, whereas the water 
> poured to the RHS is equal to the volume of the steel ball."
>
> Antti
> --
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> virustorjuntaohjelmistolla.
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