Science Puzzle
Pirogue Displacement
A wooden pirogue (flat-bottomed boat) is floating in a calm section of a river. The boat is loaded with heavy river rocks. You throw all the rocks overboard into the river. The rocks sink to the bottom.
Does the water level in the river rise, fall, or stay exactly the same?
The Answer
Falls. When the rocks are in the boat, they are floating. A floating object displaces water equal to its own weight. Rocks are dense, so their weight corresponds to a large volume of water displaced.
When the rocks are thrown overboard and sink, they displace water equal only to their own volume, which is much less than the volume of water their weight was displacing before.
The boat itself becomes lighter and rides higher, displacing less water too. The net effect is that the total volume of water displaced goes down, so the river level falls. This is a direct consequence of Archimedes' principle applied twice: once to the floating loaded boat, and once to the submerged rocks.
The principle: Archimedes' principle applied twice. A floating object displaces water equal to its weight. A submerged object displaces water equal to its volume. Dense objects displace more as floaters than as sinkers.