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

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

John:

In the beaker in which the steel ball is suspended, with your system consisting of the steel ball, part of the string segment suspending the steel ball, the beaker, and the water, you have downward momentum flowing in via gravity, downward momentum flowing out via contact with the scale, and downward momentum flowing out via contact of the lower part of the string (the part inside the boundary) with the upper part of the string segment (the part outside the boundary). 

As compared to the case in which all we had was a beaker plus water; now, on the left, downward momentum is flowing into the system via gravity at a greater rate because we have added the table-tennis ball to the system.  On the right, downward momentum is flowing into the system via gravity at a greater rate because we have added the steel ball to the system but we also have downward momentum flowing out of the system at a greater rate because in addition to the outflow via the contact of the beaker with the pan, we also have momentum flowing out via the string.  I think your argument is incomplete.  To show that the right side goes down, you need to show that the net increase in the inflow of downward momentum on the right is greater than the net increase in the inflow of downward momentum on the left.

Could you please spell out your complete momentum flow argument leading up to and including the statement that the right side goes down.

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
> Sent: Wednesday, January 29, 2014 2:10 PM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] Nice question on buoyance and balance
>
> On 01/29/2014 10:34 AM, Jeffrey Schnick wrote:
> > 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.
>
> That's a poor choice of "the system".
>
> At one point I explicitly said to draw a dotted line around the beaker.
> Everything inside the dotted line is "the system".
> The dotted line is the boundary.
>
> On the left there are two flows crossing the boundary.  On the right there are
> three.  Simple.
>
> Previously I said I didn't see how to mess up the analysis.
> Now I know.  You can mess it up by drawing a super-complicated convoluted
> boundary.
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