Density

Master Segun: I'm happy to welcome you again to my class 

Density

Definition: Density is the amount of mass per unit volume of a substance.

Formula: Density = Mass / Volume

Units: kg/m³ (kilograms per cubic meter)


Key Points:

- Density is a scalar quantity, meaning it has no direction.

- Density is a physical property of a substance, meaning it can be measured and quantified.

- Density is often used to identify a substance, as different substances have unique densities.

- Density is affected by temperature and pressure, but not by the shape or size of the substance.


Types of Density:

- Absolute Density: The density of a substance in its pure state.

- Relative Density: The density of a substance relative to the density of water.

Measurements:

- Mass: Measured in kilograms (kg)

- Volume: Measured in cubic meters (m³)

- Density: Calculated by dividing mass by volume


Examples:

- Lead: 11,340 kg/m³

- Copper: 8,960 kg/m³

- Water: 1,000 kg/m³

- Air: 1.2 kg/m³


Applications:

- Density is used in engineering to determine the strength and stability of structures.

- Density is used in chemistry to identify substances and determine their properties.

- Density is used in physics to understand the behavior of objects in different environments.


Formulas:

- Density = Mass / Volume

- Mass = Density x Volume

- Volume = Mass / Density

Examples:

1. A metal cube has an edge length of 5 cm and a mass of 1.2 kg. What is its density?

Answer:

Volume = edge length³ = 5 cm x 5 cm x 5 cm = 125 cm³

Density = Mass / Volume = 1.2 kg / 125 cm³ = 0.0096 g/cm³


2. A liquid has a density of 1.5 g/ml and a volume of 500 ml. What is its mass?

Answer:

Mass = Density x Volume = 1.5 g/ml x 500 ml = 750 g

Derivations:

- Density = Mass / Volume (definition)

- Mass = Density x Volume (rearranging the definition)

- Volume = Mass / Density (rearranging the definition)

Additional Concepts:

- Specific Gravity: The ratio of the density of a substance to the density of water.

- Buoyancy: The upward force exerted on an object by a fluid (such as water or air) when the object is partially or fully submerged.

- Archimedes' Principle: The principle that states that the buoyancy force on an object is 

equal to the weight of the fluid displaced by the object.


Practice Problems:

1. What is the density of a substance that has a mass of 50 kg and a volume of 0.5 m³?

2. A block of wood has a density of 0.8 g/cm³ and a volume of 200 cm³. What is its mass?

3. A gas has a density of 0.0012 g/l and a volume of 2.5 l. What is its mass?

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