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

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

Neglecting the mass and volume of submerged string, and assuming both balls to be at rest or moving at negligible velocity relative to the water they are in:

Define the system to be the beaker plus the water in the beaker.  Draw three identical free body diagrams, numbered 1, 2, and 3 respectively, of the system.  Each has a normal force exerted by the balance upward on the bottom of the beaker and a gravitational force, equal to the mass of the water-plus-beaker times g, acting downward on the system.

Modify diagram 2 to include the table-tennis ball and string as part of the system.  Add the downward gravitational force exerted by the earth on the table-tennis ball.

Modify diagram 3 to include the force exerted downward on the water by the steel ball.  By Newton's 3rd law, this is equal in magnitude to the buoyant force exerted on the ball by the water.  By Archimedes' principle we know this to be equal to the buoyant force on the totally-submerged table-tennis ball.  From experience, we know that table-tennis balls float meaning that when totally submerged, the buoyant force on a table-tennis ball is of greater magnitude than that of the gravitational force on the tennis ball.  Thus the downward contact force exerted on the water by the steel ball in diagram 3 is greater than the downward gravitational force on the table-tennis ball in diagram 2.  Hence the side in which the steel ball is submerged goes down.

Using a momentum flow approach, the story would go the same way except that the increase in the flow rate of downward gravitational momentum  resulting from the inclusion of the table-tennis ball in the system in diagram 2 would be smaller than the increase in the flow rate of downward momentum from the steel ball (part of the surroundings in diagram 3) to the system in diagram 3.

I don't see how the momentum flow approach makes the problem simpler.  I disagree with John Denker's statement that there are no other momentum flows crossing the boundary.  I think that on the steel ball side there is momentum flow from the steel ball, part of the outside world, across the boundary and into the system.  This momentum flow is associated with the contact interaction between the steel ball and the water.

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Savinainen
> Antti
> Sent: Wednesday, January 29, 2014 4:36 AM
> To: phys-l@phys-l.org
> Subject: [Phys-L] Nice question on buoyance and balance
>
> Hi,
>
> a former studen of mine send me a link to a nice question:
> <http://wealthmanagement.com/question/puzzler-odd-balance>.
>
> I usually ask a variation of this question in my class. It is, in my opinion, a good
> example of conceptual reasoning which goes well beyond rote
> memorization. Probably many of you have seen this question before but I
> thought it might be worth sharing.
>
> Regards,
>
> Antti
>
> --
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