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



Your solution is fine except that the water pushes down on the beaker, not on the pan. The force in question is a contact force and the water is not in contact with the pan.

I have students do a lab exercise in which there are three carts on a track. Call them the back, middle, and front carts respectively. The front and back carts have force sensors on them. The middle cart is in contact with the force sensor on each of the other carts. The carts are not connected together. I ask students to predict how the force sensor readings will compare if a person grabs the rear cart and pushes it forward in such a manner that all three carts are accelerating forward as one. Many say that the force readings will be the same. I think they think that the force of the rear cart on the middle cart is the same force that is acting on the the front cart--not just that it has the same magnitude and direction but that it is the same force. As teachers I think we should be careful to avoid instilling or reinforcing this misconception.

-----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.