Archimedes' Principle

Discover why objects feel lighter in water and how this principle revolutionized our understanding of buoyancy and fluid mechanics!

Setup A: Stone in Air
5.0 N
Weight
5.0 N
Setup B: Stone in Water
3.2 N
Buoyant Force
0.0 N
Weight
5.0 N
Buoyant Force
1.8 N

Understanding Archimedes' Principle

Displaced Volume = Block Volume
Weight
5.0 N
Block
Buoyant Force
5.0 N

Key Concept:

When an object is immersed in a fluid, it displaces a volume of fluid equal to its own volume. The buoyant force equals the weight of this displaced fluid.

Buoyant Force = Weight of Displaced Fluid

The object displaces water equal to its own volume. This creates an upward buoyant force of 5.0 N.

Since the buoyant force equals the weight, the object will float at equilibrium.

Applications of Archimedes' Principle

🚢
Ships & Boats
Ships float because they displace a large volume of water. The buoyant force equals the ship's weight, allowing massive vessels to stay afloat.
🚤
Submarines
Submarines control their buoyancy by filling or emptying ballast tanks with water, allowing them to dive or surface as needed.
🥛
Lactometer
Used to test milk purity. Pure milk has a specific density, and the lactometer floats at different levels based on the milk's composition.
🌡️
Hydrometer
Measures liquid density by observing how deep it sinks in the liquid. Widely used in battery testing and brewing.
🎈
Hot Air Balloons
Float in air because hot air inside is less dense than cold air outside, creating a buoyant force that lifts the balloon.
👑
Density Testing
Archimedes used this principle to test if the king's crown was pure gold by comparing its density with pure gold.

Practice Questions

Q1.
You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
Answer: Your actual mass is slightly more than 42 kg. This is because air exerts a buoyant force on your body, making you appear lighter on the weighing machine. The buoyant force reduces the apparent weight, so the actual mass is greater than the measured value.
Q2.
You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than the other. Can you say which one is heavier and why?
Answer: The bag of cotton is actually heavier than the iron bar. Cotton has a much larger volume than iron for the same apparent mass, so it displaces more air and experiences a greater buoyant force from air. This makes it appear lighter on the weighing machine. Therefore, the actual mass of cotton is greater than that of iron.
Q3.
Why was no further decrease in elongation observed once the stone was fully immersed in water in Activity 9.7?
Answer: Once the stone is fully immersed, it displaces a constant volume of water. According to Archimedes' principle, the buoyant force depends only on the volume of fluid displaced. Since the displaced volume remains constant when fully immersed, the buoyant force remains constant, and no further change in elongation occurs.
Question 1 of 3
Explore Archimedes' Principle
Archimedes' Principle
"When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it."
About Archimedes (287-212 BCE)

"Eureka!" - "I have found it!"

Archimedes was a Greek scientist who discovered this principle after noticing that water in a bathtub overflowed when he stepped into it. He ran through the streets shouting "Eureka!" This knowledge helped him determine the purity of gold in the crown made for the king.

His work in Geometry and Mechanics made him famous. His understanding of levers, pulleys, and wheels-and-axle helped the Greek army in its war with the Roman army.

Key Points to Remember:

  • Buoyant force acts upward on any object in a fluid
  • The magnitude equals the weight of displaced fluid
  • This principle explains why objects feel lighter in water
  • It's the basis for designing ships, submarines, and measuring instruments
  • The principle applies to all fluids - liquids and gases