What is Archimedes' Principle?

S6-SA3-0047

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Archimedes' Principle states that when an object is partially or fully submerged in a fluid, it experiences an upward force called buoyant force. This buoyant force is equal to the weight of the fluid displaced by the object. This principle helps us understand why some objects float and others sink.

Simple Example

Quick Example

Imagine you are at a swimming pool and you try to push a large, empty plastic water bottle (like a Bisleri bottle) down into the water. You feel a strong upward push from the water. That upward push is the buoyant force, and it's equal to the weight of the water that the bottle moves out of its way.

Worked Example

Step-by-Step

Let's find the buoyant force on a stone submerged in water.

Step 1: A stone weighs 500 grams in air. This means its mass is 0.5 kg.

--- Step 2: When the stone is fully submerged in water, it displaces 200 cubic centimeters (cm³) of water. We need to convert this to volume in cubic meters (m³): 200 cm³ = 0.0002 m³.

--- Step 3: The density of water is approximately 1000 kg/m³.

--- Step 4: Calculate the mass of the displaced water: Mass = Density x Volume = 1000 kg/m³ x 0.0002 m³ = 0.2 kg.

--- Step 5: Calculate the weight of the displaced water (which is the buoyant force). Use g = 9.8 m/s²: Weight = Mass x g = 0.2 kg x 9.8 m/s² = 1.96 Newtons.

--- Step 6: So, the buoyant force acting on the stone is 1.96 Newtons.

ANSWER: The buoyant force on the stone is 1.96 Newtons.

Why It Matters

Understanding Archimedes' Principle is crucial for engineers designing ships, submarines, and even hot air balloons. It's also vital in fields like marine biology to study how aquatic life floats, and in medicine for understanding blood flow dynamics. Many careers, from naval architecture to aerospace engineering, rely on this principle.

Common Mistakes

MISTAKE: Thinking buoyant force depends on the object's total weight. | CORRECTION: Buoyant force depends only on the weight of the fluid displaced, not the object's total weight.

MISTAKE: Confusing density with weight when determining if an object floats. | CORRECTION: An object floats if its average density is less than the fluid's density. Its weight is only compared to the buoyant force (weight of displaced fluid).

MISTAKE: Assuming the buoyant force is constant for an object regardless of how much it is submerged. | CORRECTION: The buoyant force increases as more of the object is submerged, up to the point where it is fully submerged. After that, it remains constant.

Practice Questions

Try It Yourself

QUESTION: A block of wood with a volume of 0.05 m³ is floating in water. If 80% of its volume is submerged, what is the volume of water displaced? | ANSWER: 0.04 m³ (80% of 0.05 m³)

QUESTION: A boat displaces 5000 kg of water. What is the buoyant force acting on the boat? (Take g = 10 m/s²) | ANSWER: 50,000 Newtons (Weight = mass x g = 5000 kg x 10 m/s²)

QUESTION: A solid metal sphere weighs 100 N in air. When fully submerged in water, it weighs 80 N. What is the buoyant force acting on the sphere? What is the weight of the water displaced? | ANSWER: Buoyant force = 20 N (100 N - 80 N). Weight of water displaced = 20 N (By Archimedes' Principle, buoyant force equals weight of displaced fluid).

MCQ

Quick Quiz

Which of the following factors directly determines the buoyant force on an object submerged in a fluid?

The mass of the object

The volume of the object

The density of the object

The weight of the fluid displaced by the object

The Correct Answer Is:

Archimedes' Principle states that the buoyant force is exactly equal to the weight of the fluid displaced by the object. Options A, B, and C relate to the object itself, not directly to the buoyant force.

Real World Connection

In the Real World

This principle helps us understand why a huge cargo ship, carrying thousands of tonnes of goods (like electronics or cars from Mumbai port), floats easily on the sea. The ship displaces a massive amount of water whose weight is equal to the ship's total weight, including its cargo, creating enough buoyant force to keep it afloat.

Key Vocabulary

Key Terms

BUOYANT FORCE: The upward push exerted by a fluid on a submerged object | FLUID: A substance that flows and takes the shape of its container (liquids and gases) | DISPLACED FLUID: The fluid that is pushed aside by an object when it enters the fluid | DENSITY: Mass per unit volume of a substance

What's Next

What to Learn Next

Great job understanding Archimedes' Principle! Next, you can explore the concept of Relative Density. This will help you predict whether an object will float or sink in a specific fluid, building directly on what you've learned here.