- Judah L Schwartz
Suppose you have an iron (density 7.8 gm/cc) object floating in a pool of mercury (density 13.6 gm/cc).[you can vary the situation by using the density sliders]Does the object rise or fall as if you pour water into the container? Why? What happens if you pour an even denser liquid than water into the container? Why? [see further challenges below]
Would the iron object float in mercury if the container were narrower - just a tiny bit wider that the object itself? Suppose the container were also shallower - its bottom being just a bit below the bottom of the floating object; would the object still float? If the answers to these two questions are yes - then it is clear that the usual statement about the laws of floating and sinking are not correct. The object does not need to displace its own weight in the fluid - it can float in an arbitrarily small amount of fluid. If the answers to the two questions above are no - then it seems that the floating and sinking of an object depends on the shape of the container. But how does the object know what the shape of the container is?