Buoyancy

Why a ship of steel floats while a nail sinks. Drop a block into a fluid and the fluid pushes back up with the weight of whatever the block shoves aside — Archimedes' principle, buoyant force B = ρfluid·g·Vsubmerged. Less dense than the fluid and the block floats, settling with just enough of itself under the surface — a fraction equal to ρobjectfluid; denser, and it sinks. Change the block's density and the fluid, drag it under and let it bob back, and watch the two force arrows fight it out. It all runs on your device.

You are in the Physics lab.

Drag the block under the surface and release it to watch it settle
Presets:
Weight W6.86 N
Buoyant force Fb
Net force
Submerged
Apparent weight (submerged)
ResultFloats
Displace your own weight and you float. A fluid pushes up on anything in it with a force equal to the weight of the fluid pushed aside, B = ρfluid·g·Vsubmerged. Sink a little and you displace more fluid and feel more lift, so a floating object settles at exactly the depth where buoyancy balances its weight — a submerged fraction of ρobjectfluid. If the object is denser than the fluid it cannot displace enough even when fully under, so weight wins and it sinks. Density, not size, decides.

Reading the simulation

What the two vectors, the highlighted volume and the density panel are telling you.

1

Two vectors, and the longer one wins

The red arrow is the weight W = ρobject·g·V pulling straight down; the teal arrow is the buoyant force Fb = ρfluid·g·Vsubmerged pushing straight up. They are drawn to the same scale, so whichever arrow is longer is the winner: while the block is settling the buoyant arrow grows as more of the block goes under, until the two match and it floats — or, if weight stays longer even fully submerged, the block sinks. The net force readout is simply Fb − W.

2

The shaded volume sets the fraction

The blue hatched region is the displaced fluid — the part of the block below the waterline. A floating block stops sinking exactly when the fluid it displaces weighs as much as the block, so the submerged fraction settles at ρobjectfluid. Wood at 700 in water at 1000 rides 70% under; ice at 917 sits about 92% under — the iceberg. Change the volume and the fraction does not move: bigger blocks weigh more but displace proportionally more, so density alone sets how deep it floats.

3

Change the fluid and the outcome can flip

The side panel compares the object's density bar to the fluid's, with a dashed float line at the fluid: a bar below the line floats, above it sinks. Steel at 7850 towers over water and drops to the floor — but switch the fluid to mercury at 13600 and the same steel bar falls below the line, so it bobs at the surface. That is why density, not weight or size, decides, and why a dense metal can float on a denser liquid.

How It Works

Displaced fluid pushes back, a floating object finds its level, and density draws the line between floating and sinking.

1

The fluid pushes up

Pressure in a fluid grows with depth, so the fluid presses up on the bottom of a submerged object harder than it presses down on the top. The net is an upward buoyant force, and Archimedes showed it equals the weight of the displaced fluid: B = ρfluid·g·Vsubmerged. The deeper the object sits, the more it displaces and the stronger the push.

2

A float finds its level

If the object is less dense than the fluid, it can displace its whole weight of fluid while still partly above the surface. It sinks until buoyancy exactly balances gravity and then floats there, with the submerged fraction equal to ρobjectfluid. Ice at 920 in water at 1000 sits about 92 percent under — the iceberg's hidden bulk.

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Or it sinks

If the object is denser than the fluid, even fully submerged it cannot displace its own weight, so the buoyant force stays below the weight and the net force is downward — it sinks to the bottom, where it still feels a real buoyant force that makes it seem lighter than in air. Slide the density across the fluid's value to flip between floating and sinking.

What is buoyancy?
Buoyancy is the upward force a fluid exerts on any object placed in it. It arises because pressure in a fluid increases with depth, so the fluid pushes up on the bottom of an object harder than it pushes down on the top, leaving a net upward force. If that force matches the object's weight the object floats; if it is smaller, the object sinks. This simulator draws the buoyant force and the weight as vectors and lets you pick the object's material or density, the fluid and the object's volume.
What is Archimedes' principle?
Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces: B = ρfluid · g · Vsubmerged. Push more of the object under, and it displaces more fluid and feels more lift. An object floats when it can displace its own weight of fluid before it is fully submerged, which happens exactly when its density is less than the fluid's. This tool computes the buoyant force live from the submerged volume and shows it as a vector beside the weight, with the net force read out.
Why do some things float and others sink?
It comes down to density. An object less dense than the fluid can displace its own weight while still partly above the surface, so buoyancy balances gravity and it floats. An object denser than the fluid cannot displace enough even when fully submerged, so its weight wins and it sinks. That is why a steel block sinks in water but the same steel shaped as a hull floats — the hull displaces far more water. Change the densities here to cross the floating-sinking boundary.
What fraction of a floating object is submerged?
For a floating object the submerged fraction equals the ratio of its density to the fluid's density, ρobjectfluid. Ice at about 920 kg/m³ floating in water at 1000 kg/m³ sits with roughly 92 percent submerged — the origin of "the tip of the iceberg". The same object in denser mercury barely dips below the surface. Set the densities in this simulator and read the submerged percentage directly.

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