thomas (08/13/82)
The original problem: Here's a good paradox: Imagine a lock (of the sort in the Panama Canal) with a ship in it which almost fills the lock. (Cross Section Picture) | | | | |--| |--| <--- Water level | | | | | | | | | | | | | | | | | | | | | +-------------+ | +-------------------+ Clearly we can make the fit tight enough to leave an arbitrarily small amount of water in the lock if the ship were removed. So, the question is: If the ship must displace an amount of water equal to its weight in order to float, but the amount of water in the lock is much less than the weight of the ship, WHY is it floating???? ---------------------------------------------------------------- Why it floats: If we want to remove the ship, but keep the water level the same, we must add an amount of water to the lock equal to the volume of the ship which is below water: (Cross Section Picture) | | | | |--|-------------|--| <--- Water level | | fill this | | | | volume with | | | | water | | | | | | | | | | | +-------------+ | +-------------------+ this is the water which is 'displaced' by the ship, and it's weight is equal to the weight of the ship. For further information see: Koehl, G.B., "Archimedes' Principle and the Hydrostatic Paradox - Simple Demonstrations", Am J Phys, 17, 579 (1949). Dodd, L., "The Hydrostatic Paradox: Phases I and II", Am J Phys, 23, 113 (1955). (References courtesy "The Flying Circus of Physics" by Jearl Walker.) =Spencer