Archimedes' Principle — Why Objects Float

Archimedes' Principle — Why Objects Float

Buoyancy is the upward force exerted by a fluid on an immersed object. Archimedes discovered that this force equals the weight of the fluid displaced by the object.

What you'll learn

An object floats when the buoyant force equals its weight; sinks when its weight exceeds the maximum buoyant force possible (when fully submerged). The key insight: F_buoyant = weight of displaced fluid.

The principle

F_buoyant = ρ_fluid × V_displaced × g

Where ρ_fluid is fluid density, V_displaced is the volume of fluid pushed aside, and g is gravitational acceleration.

Floating vs. Sinking

• Floating: Object density < fluid density. At equilibrium, the submerged fraction equals ρ_object / ρ_fluid.
• Sinking: Object density > fluid density. Even fully submerged, F_buoyant < W_object.
• It's average density that counts: spread a fixed mass over a bigger volume (a hull, a hollow shape) and its average density falls below water — so even steel floats. Drag the volume slider to see the same lump switch from sinking to floating.

Measured quantities

• ρ_water = 997 kg/m³ — density of water at 25°C
• g = 9.80665 m/s² — standard gravitational acceleration
• ρ_pine = 500 kg/m³ — density of pine wood
• ρ_steel = 7850 kg/m³ — density of steel
• V_block = 0.001 m³ — volume of the block (10 cm cube)

Sources

NIST Chemistry WebBook, Standard Reference Database 69, 'Water, liquid' (accessed 2023-10-27). Available at: https://webbook.nist.gov/cgi/cbook.cgi?ID=C7732185

CODATA Recommended Values of the Fundamental Physical Constants: 2018. National Institute of Standards and Technology (NIST). Available at: https://physics.nist.gov/cuu/Constants/

Forest Products Laboratory. (2010). Wood Handbook: Wood as an Engineering Material. General Technical Report FPL-GTR-190. U.S. Department of Agriculture.

ASM Handbook, Volume 1: Properties and Selection: Irons, Steels, and High-Performance Alloys. (1990). ASM International.