Buoyancy Simulator
Submerge objects of different densities in a fluid. See buoyant force, weight, and net force and predict whether objects float or sink.
About Buoyancy and Archimedes' Principle
Archimedes' principle states that any object immersed in a fluid experiences an upward buoyant force equal to the weight of fluid displaced. This principle explains why ships float despite being made of dense steel, and why a stone sinks in water.
Key Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| ρ_obj | Object Density | kg/m³ | Mass per unit volume of the object |
| ρ_fluid | Fluid Density | kg/m³ | Mass per unit volume of the fluid |
| V | Object Volume | m³ | Total volume of the object |
| V_sub | Submerged Volume | m³ | Volume of object below the fluid surface |
| F_b | Buoyant Force | N | Upward force from the displaced fluid |
| F_w | Weight Force | N | Downward gravitational force on the object |
| F_net | Net Force | N | F_b − F_w; positive = floats, negative = sinks |
| g | Gravitational acceleration | m/s² | Standard value 9.81 m/s² |
Floating vs Sinking Condition
- Floats: ρ_obj < ρ_fluid. Only part of the object is submerged. The submerged fraction is ρ_obj/ρ_fluid.
- Neutral buoyancy: ρ_obj = ρ_fluid. The object floats at any depth without rising or sinking.
- Sinks: ρ_obj > ρ_fluid. The net force is downward and the object accelerates toward the bottom.
Worked Example — Floating
A wooden block (ρ = 600 kg/m³, V = 0.01 m³) in fresh water (ρ_fluid = 1000 kg/m³):
At equilibrium, F_b = F_w exactly — the object floats with 60% submerged.
Worked Example — Sinking
An iron ball (ρ = 7874 kg/m³, V = 0.001 m³) in water (ρ_fluid = 1000 kg/m³):
Key Formulas
Archimedes' Principle (Buoyant Force)
Weight Force
Net Force
Floating Equilibrium (Submerged Fraction)
| Formula | Description | Notes |
|---|---|---|
| F_b = ρ_f g V_sub | Buoyant force | ρ_f = fluid density, V_sub = submerged volume |
| F_w = m g = ρ_obj V g | Weight of object | Total weight, not just submerged portion |
| F_net = F_b − F_w | Net vertical force | Positive upward; zero at floating equilibrium |
| V_sub/V = ρ_obj/ρ_fluid | Fraction submerged | Only valid when floating (ρ_obj < ρ_fluid) |
| ρ = m/V | Density | Key property determining float/sink behaviour |
Frequently Asked Questions
Why does a ship made of steel float?
A steel ship is hollow — it encloses a large volume of air. The average density of the ship (steel + air) is less than water. What matters is not the density of the material but the average density of the entire object including any air spaces.
Does the shape of the object affect buoyancy?
No — only the volume of fluid displaced matters, as Archimedes' principle states. F_b = ρ_fluid × V_submerged × g regardless of shape. Shape does affect stability (tendency to tip over), but not the magnitude of the buoyant force.
What happens if the fluid is denser, like the Dead Sea?
The Dead Sea has salinity around 34%, giving ρ ≈ 1240 kg/m³. Because the fluid is denser, the required submerged fraction ρ_obj/ρ_fluid is smaller — you float higher. That is why people float effortlessly in the Dead Sea.
What is neutral buoyancy and how do submarines use it?
Neutral buoyancy means ρ_obj = ρ_fluid, so F_net = 0. The object neither rises nor sinks. Submarines achieve this by pumping seawater into or out of ballast tanks, changing their average density to match the surrounding water at a desired depth.
Does buoyancy work in air?
Yes! Helium balloons and hot-air balloons use buoyancy in air. Air has ρ ≈ 1.2 kg/m³. Helium (ρ ≈ 0.17 kg/m³) is less dense than air, so a helium-filled balloon experiences a net upward buoyant force and rises.