Archimedes’ principle describes the upward vertical force that a fluid (liquid or gas) exerts on any immersed body. It is equal to the weight of the volume of fluid displaced by the object. This fundamental law, covered in 9th grade curriculum, explains flotation.
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How to measure it in class
With the FizziQ app, it is possible to explore Archimedes’ principle indirectly.
Steps:
- Use the accelerometer to detect the apparent weight of objects
- Immerse an object attached to the smartphone in water and observe the variation
- Compare the weight in air and the “apparent weight” in water
- Calculate the buoyant force: F_A = P_air - P_apparent
- Verify that F_A = rho_water x V_object x g
Scientific activities on this topic
- Study of flotation: https://www.fizziq.org/en/activities/lighter/
- Measurement of density by hydrostatic weighing
- Submarine and ballast tanks
Learn more
Statement of the principle:
“Any body wholly or partially immersed in a fluid at rest is acted upon by an upward buoyant force equal to the weight of the fluid displaced.”
Flotation condition:
| Condition | Behavior |
|---|---|
| rho_object < rho_fluid | The object floats |
| rho_object = rho_fluid | The object is in equilibrium |
| rho_object > rho_fluid | The object sinks |
Physical origin:
Archimedes’ principle results from the pressure difference between the bottom and top of the object. Pressure increases with depth, so the force on the lower surface is greater than on the upper surface.
Applications:
- Ships float because their average density (hull + air) is less than that of water
- Submarines adjust their density by filling or emptying their ballast tanks
- Helium balloons float in air because rho_He < rho_air
Formula
Archimedes’ principle: F_A = rho_fluid x V_submerged x g
Flotation condition: F_A >= P_object leads to rho_fluid x V_submerged x g >= m_object x g
For a floating object (equilibrium): V_submerged / V_total = rho_object / rho_fluid
where:
- F_A: buoyant force (N)
- rho_fluid: fluid density (kg/m cubed)
- V_submerged: submerged volume (m cubed)
- g: acceleration due to gravity (m/s squared)
Application examples
- An iceberg floats with 90% of its volume underwater (rho_ice/rho_water approximately equals 0.9)
- A swimmer weighs about 1/6 of their actual weight in water (rho_body approximately equals 1050 kg/m cubed)
- Fish adjust their buoyancy using their swim bladder
- The Dead Sea allows easy floating (rho approximately equals 1240 kg/m cubed)
FAQ
Q: Why does a steel ship float when steel is denser than water? A: The hull contains a lot of air. The average density of the ship (steel + interior air) is less than that of water.
Q: Does Archimedes’ principle exist in air? A: Yes! But it is very weak because rho_air is approximately 1.2 kg/m cubed, which is very small. A helium balloon rises because it experiences this force.
Q: How to measure buoyant force with FizziQ? A: Indirectly, by measuring the difference between the weight in air and the apparent weight in water of an object attached to the smartphone.
Q: Does a submarine float differently in freshwater and saltwater? A: Yes, saltwater being denser, the buoyant force is stronger. The ballast tanks must be adjusted accordingly.
Related concepts
Density - Pressure - Flotation - Force Equilibrium - Hydrostatics - Apparent Weight