[Leejohnston]

## Buoyancy — Why Things Float Upward

### 1. The Equation

Buoyant force:

F_b = ρ × g × V

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### 2. What Each Symbol Means

- F_b = buoyant force
- ρ = density of the fluid
- g = gravitational acceleration
- V = volume of fluid displaced

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### 3. What the Equation Is Telling Us

An object submerged in a fluid experiences an **upward force** equal to the weight of the fluid it displaces.

Floating is about **displacement**, not weight alone.

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### 4. Where It Comes From (Intuition)

Pressure increases with depth.

The bottom of an object experiences more pressure than the top, creating a net upward force.

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### 5. Worked Example

If an object displaces:
- 0.02 m³ of water
- water density ≈ 1000 kg/m³

F_b = 1000 × 9.8 × 0.02
= **196 newtons**

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### 6. Real-World Applications

- Ships and submarines
- Hot air balloons
- Hydrometers
- Human buoyancy in water

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### 7. Common Misconceptions

- Heavy objects always sink → false
- Shape alone determines floating → false
- Buoyancy only applies in water → false

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### Try It Yourself

Why does a massive steel ship float while a small steel ball sinks?