Eureka! The Discovery of Displacement
Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is exactly equal to the weight of the fluid that the body displaces.
When you weigh an object underwater, it seems to weigh less. This "Apparent Weight" is simply the actual weight of the object pulling it down minus the buoyant force of the water pushing it up. This principle allows scientists to measure the density of irregular objects simply by weighing them in the air and then weighing them while submerged in water.
Practical Uses Today
Archimedes' principle is used constantly in modern engineering:
- Naval Architecture: Designing cargo ships requires precise calculations to ensure the ship displaces exactly enough water to support its own weight plus thousands of tons of cargo without the water line breaching the deck.
- Hydrometers: These devices use Archimedes' principle to float at different heights, instantly measuring the specific gravity (density) of liquids like beer, wine, or battery acid.
- Geology: Identifying the exact density of raw mineral ores or complex meteorites without needing to calculate complex geometric volumes.
The Formula
Example Calculation
A heavy iron anchor weighs exactly $500 , ext{N}$ when hanging in the air. When lowered entirely into the water, it displaces enough water to generate an upward buoyant force of $200 , ext{N}$.
- Subtract Buoyant Force from Actual Weight: $500 - 200 = 300 , ext{N}$.
The apparent weight of the anchor underwater is $300 , ext{N}$, making it significantly easier to lift while submerged than when it breaks the surface.