Physics · Lesson 05
Archimedes' Principle
Why does a massive steel ship float while a tiny pebble sinks? The answer is a 2,200-year-old discovery made in a bathtub — and it explains everything from submarines to hot air balloons.
Who Was Archimedes?
Archimedes of Syracuse (287–212 BC) was an ancient Greek mathematician, physicist, and inventor — one of the greatest scientists of the ancient world. Legend says that King Hiero II of Syracuse asked him to figure out whether a golden crown was pure gold or mixed with cheaper silver, without melting it down. While stepping into a bath, Archimedes noticed the water level rise as he got in, and suddenly understood the answer. He was so excited that he reportedly ran through the streets shouting "Eureka!" — Greek for "I have found it!" Archimedes also designed war machines, calculated the value of π, and invented the Archimedes screw, still used to pump water today.
What is Buoyancy?
Archimedes' Principle — The Big Idea
In plain English: the more water your object pushes aside (displaces), the harder the water pushes back up. A large hollow object displaces a lot of water, so it gets a very strong upward push. A small dense object displaces very little water, so the upward push is weak.
The Two Forces on Every Submerged Object
Every object in a fluid has two forces acting on it vertically:
↓ Weight (gravity) — pulls the object down. Depends on how much mass the object has.
↑ Buoyant Force — pushes the object up. Depends on how much fluid the object displaces.
If the buoyant force is greater than or equal to the weight → the object floats.
If the weight is greater than the buoyant force → the object sinks.
Density — The Key to Sink or Float
The easiest way to predict whether something sinks or floats is to compare its density to the density of the fluid.
Density of Common Materials vs. Water
| Material | Density (g/cm³) | Compared to water | Result in water |
|---|---|---|---|
| 🪵 Pine wood | 0.55 | Floats ✓ | |
| 🧊 Ice | 0.92 | Floats ✓ | |
| 💧 Water | 1.00 | Neutral | |
| 🪨 Granite rock | 2.70 | >max | Sinks ✗ |
| 🔩 Aluminum | 2.70 | >max | Sinks ✗ |
| ⚙️ Steel | 7.85 | >max | Sinks ✗ |
| 🪙 Gold | 19.30 | >max | Sinks ✗ |
Sink or Float Machine
Select an object in the Controls panel, then drop it into the tank.
Buoyancy & Fluid Dynamics (Interactive)
Explore how buoyancy forces depend on object density, mass, and fluid density. Watch real-time fluid dynamics in action:
- Adjust Object Density and Fluid Density with the sliders below
- Watch the Physics Display update in real-time
- Observe how the Net Force determines if an object floats or sinks
- Click the canvas to create ripples and disturb the fluid
Buoyant Force = ρfluid × g × Vobject
If Buoyant Force > Weight Force, the object floats. If Buoyant Force < Weight Force, the object sinks.
How Do Steel Ships Float?
Steel has a density of about 7.85 g/cm³ — nearly 8 times denser than water. So why doesn't a steel ship immediately sink? The answer is shape and air.
A solid steel ball has no air inside. Its overall density is 7.85 g/cm³ — much greater than water. The water cannot push it up hard enough. It sinks.
A ship's hull is hollow and filled with air. The average density of the whole ship (steel + air + everything inside) is much less than 1.0 g/cm³. The ship displaces enough water to balance its weight. It floats.
Submarines: Controlling Buoyancy on Purpose
Submarines can both sink and rise by changing their average density. They carry large tanks called ballast tanks. When the tanks are filled with water, the sub gets denser and dives. When compressed air is pumped into the tanks (pushing the water out), the sub gets less dense and rises. This is pure Archimedes' Principle — on demand.
Archimedes' Principle in the Real World
Buoyancy appears everywhere — from ocean engineering to meteorology to medicine.
Practice Problems
Use ρ = m ÷ V and compare to water (1.0 g/cm³). Round to two decimal places.
Easy1. An object has a density of 0.7 g/cm³. Will it sink or float in water? Type 1 for float, 0 for sink.
Easy2. A rock has a mass of 270 g and a volume of 100 cm³. What is its density in g/cm³? (ρ = m ÷ V)
Medium3. A piece of wood has a mass of 110 g and a volume of 200 cm³. What is its density, and will it sink or float? Enter just the density value.
Medium4. Ice has a density of 0.92 g/cm³. What percentage of an ice cube is below the waterline? (Use: % submerged = object density ÷ fluid density × 100)
Challenge5. A hollow steel sphere has an outer volume of 400 cm³ and a mass of 120 g. What is its average density, and will it float?
Challenge6. The Dead Sea has a density of 1.24 g/cm³. A human body has an average density of about 1.00 g/cm³. What percentage of a person's body floats above the surface? (% above = (1 − body density ÷ fluid density) × 100)