More brain teasers

[Chris B]

Ok, I couldn´t resist so I checked the website for the answer (wont reveal anything though) and I really don´t get it. Could someone explain please???

PS: I believe this post should put me over the top.... yay me

[cjolley]

Q1. damage and agallag are correct - The rock will never displace more than it's own weight of water, so the lake level will either sink (if the rock sinks) or stay the same (if the rock floats). The situation is not symmetrical because the water/air boundary is a surface and not a continuum.

Q2. If the balloon makes it down past the surface of the water it will continue to sink. The buoyancy of the brick is always negative because neither the brick nor the water is compressible. The balloon, on the other hand, only becomes less buoyant as it is dragged down past the surface, because buoyancy is the difference between the weight of the water dissplaced by the balloon minus the weight of the balloon (which is constant). The water pressure on the balloon goes up continuously as the balloon sinks and PV=k for the balloon, so there is no equilibrium point below the surface. The buoyancy of the brick/balloon system therefore decreases with depth.
In other words the "...some arbitrary depth" is always 0 and therefore is not arbitrary.
Unless, of course, it's a floating brick. Which would negate the problem at the very begining.
The skin-diving thing does not count because it is filled after the diver reaches the desired depth.
Is the horse dead yet?
chuck



[This message has been edited by cjolley (edited 30 November 2000).]