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



Here's how I do it from the force point of view:

1) Start with just the scale and the beakers of water. Everything
is 100% symmetrical. The scale is in balance.

2) A crane on the left supports the ping-pong ball above the water.
A crane on the right supports the steel ball above the water.
The geometry is nice and symmetrical, the only difference being
the mass of the ball. The scale is still in balance.

3a) The crane on the left lowers the ping-pong ball onto the water.
The load on the left side of the scale increases by the /weight/
of the ping-pong ball. At this point you can remove the left
crane, since it is no longer doing anything.

3b) The crane on the right lowers the steel ball into the water.
The load on the left side of the scale increases by the /displacement/
of the steel ball, i.e. the weight of the displaced water. We
know that since the water pushes up on the ball by that much, so
by N3 (conservation of momentum) the ball must push down on the
water by the same amount. Working out the microscopics of how
and where this happens is a mess, but it can be done.

4) Fiddle with the string on the left to pull the ping-pong ball
below the surface. This gives rise to an /internal/ force-pair
that doesn't change the balance situation in any way.

Since the load on the right is now far greater than the load on
the left, the scale tips.

===

If the ping-pong ball were being pushed below the surface by a
dowel coming in from somewhere /external/, the answer would be
completely different.

=====================

I still think the momentum-flow approach is easier, more intuitive,
and more reliable. Two sentences:

The gravitational field is pouring more momentum into the region
bounded by the right beaker. The crane takes away some of this,
but not all.

That's all there is to it. I don't see any way to mess this up.
http://www.av8n.com/physics/force-intro.htm