Welcome to the World of Density!
Hi there! Ever wondered why a giant cruise ship made of metal can float, but a tiny little pebble sinks straight to the bottom? Or why a hot air balloon rises up into the sky? The answer to these cool questions is all about a single, super important idea in science: Density.
In these notes, we're going to explore what density is, how we can measure and calculate it, and how it explains why some things float and others sink. Don't worry if this sounds tricky at first – we'll break it all down with simple examples from everyday life. Let's get started!
What is Density, Really?
Before we can understand density, we need to quickly remember two other key ideas: Mass and Volume.
Quick Review: Mass and Volume
- Mass is the amount of 'stuff' (or matter) in an object. We usually measure it in grams (g) or kilograms (kg). Think of it as how heavy something feels. A bowling ball has a lot of mass; a balloon has very little mass.
- Volume is the amount of space an object takes up. We often measure it in cubic centimetres (cm³). A big, empty box has a large volume, and a small marble has a small volume.
So, what is Density?
Density is the relationship between an object's mass and its volume. It's a measure of how much 'stuff' is packed into a certain amount of space.
Imagine you have two boxes of the exact same size (same volume):
- One box is filled with feathers.
- The other box is filled with rocks.
Which one would be heavier? The box of rocks, of course! Even though they take up the same amount of space, the box of rocks has more mass packed inside. This means the rocks are more dense than the feathers.
In simple terms: Density is the "packed-in-ness" of a substance.
Key Takeaway
Density tells us how much mass is squeezed into a certain volume. An object is dense if it has a lot of mass in a small space.
The Density Formula: Let's Do Some Maths!
Don't worry, the maths for density is quite simple! There's a special formula we use to calculate it.
The Formula
The formula for density is:
$$ \text{Density} = \frac{\text{Mass}}{\text{Volume}} $$The standard units we use are:
- Mass in grams (g)
- Volume in cubic centimetres (cm³)
- So, Density is in grams per cubic centimetre (g/cm³)
A Memory Aid: The Density Triangle
A great way to remember the formula is the "Density Triangle". Just cover up the thing you want to find!
- Want to find Density? Cover 'D'. You are left with M over V. (Mass ÷ Volume)
- Want to find Mass? Cover 'M'. You are left with D next to V. (Density × Volume)
- Want to find Volume? Cover 'V'. You are left with M over D. (Mass ÷ Density)
(Imagine a triangle with M at the top, and D and V at the bottom.)
Step-by-Step Calculation
Let's calculate the density of a block of aluminium.
Problem: An aluminium block has a mass of 81 g and a volume of 30 cm³. What is its density?
- Write down what you know:
Mass = 81 g
Volume = 30 cm³ - Write down the formula:
Density = Mass / Volume - Put the numbers in:
Density = 81 g / 30 cm³ - Calculate the answer (and don't forget the units!):
Density = 2.7 g/cm³
It's that easy! You just need to remember to divide the mass by the volume.
Common Mistake Alert!
A common mistake is dividing the volume by the mass. Always remember: Mass goes on top! Think of a broken heart shape – M is on top of V. (M/V)
Key Takeaway
To find density, you divide the mass of an object by its volume. The formula is D = M/V, and the common unit is g/cm³.
Finding the Density of Irregular Shapes
It's easy to find the volume of a cube (length × width × height), but what about a rock or a plasticine model? How do you find the volume of something with a weird shape?
The Water Displacement Method
We can find the volume of an irregularly shaped object by seeing how much water it pushes out of the way. This is called displacement.
Step-by-Step Guide:
- Pour some water into a measuring cylinder and write down the starting volume. (Let's say it's 50 cm³).
- Carefully lower the object (e.g., a rock) into the water, making sure it's fully submerged.
- The water level will rise. Write down the new volume. (Let's say it's now 75 cm³).
- To find the volume of the object, just subtract the starting volume from the new volume!
Volume of object = New water level - Starting water level
Volume of our rock = 75 cm³ - 50 cm³ = 25 cm³
Now that you have the volume (25 cm³) and you've measured its mass on a balance (let's say 65 g), you can calculate its density: Density = 65 g / 25 cm³ = 2.6 g/cm³.
Key Takeaway
To find the volume of an irregular object, use the water displacement method in a measuring cylinder. The volume of the object is the amount the water level rises.
Sink or Float? It's a Density Showdown!
This is where density gets really interesting. Whether an object sinks or floats depends on its density compared to the density of the liquid it is in.
For most everyday situations, that liquid is water. The density of pure water is very easy to remember: it's about 1 g/cm³.
The Golden Rules of Floating and Sinking:
- If an object is MORE DENSE than water (> 1 g/cm³), it will SINK.
- If an object is LESS DENSE than water (< 1 g/cm³), it will FLOAT.
Let's look at some examples:
- An iron nail has a density of about 7.8 g/cm³. This is much more than water's 1 g/cm³, so it sinks!
- A piece of wood might have a density of 0.8 g/cm³. This is less than water, so it floats!
- A plasticine ball has a density of about 1.9 g/cm³, so it sinks. But if you shape it into a hollow boat shape, the average density (including the air inside) becomes less than 1 g/cm³, and it floats! This is how big metal ships work!
Did you know? The Density Column!
If you carefully pour different liquids that don't mix well into a glass, they will form layers based on their density. You could have honey (very dense) at the bottom, then water, and then oil (least dense) floating on the very top. You can then drop small objects in and see where they float!
Key Takeaway
An object floats if it is less dense than the fluid it's in. It sinks if it is more dense. For water, the magic number is 1 g/cm³.
Extension: How Temperature Changes Density
(This is a slightly more advanced idea, but it connects back to how particles behave!)
Have you ever heard the saying "heat rises"? This is because of density!
What happens when you heat something?
Remember that all matter is made of tiny particles. When you heat a substance (like a liquid or a gas), you give its particles more energy. They start to move faster and spread further apart.
- The amount of 'stuff' (mass) stays the same.
- But it now takes up more space (its volume increases).
What does this do to the density? Let's use the formula: D = M/V. If the mass (M) stays the same but the volume (V) gets bigger, the density (D) must get smaller!
Heating a substance generally makes it expand and become LESS dense.
Real-World Example: The Hot Air Balloon
This is exactly how a hot air balloon works! The air inside the balloon is heated with a burner. This makes the air particles spread out, so the air inside becomes less dense than the cooler air outside the balloon. Because it's less dense, it floats upwards, carrying the basket with it!
The same thing happens with water. Hot water is less dense than cold water, which is why in a lake, the warmer water is often at the surface while the colder, denser water is at the bottom.
Key Takeaway (Extension)
When most substances are heated, they expand, and their density decreases. When they are cooled, they contract, and their density increases. This is all explained by the particle theory!