# Density

## Density Revision

**Density**

**Density** measures how compact a substance is. It relates how much **mass** a substance has to the **volume** that it takes up. Different materials have different densities.

**Density**

**Density **is defined as an object or substances mass per unit **volume**. This can be seen in the density equation:

\textcolor{aa57ff}{\text{Density} = \dfrac{\text{Mass}}{\text{Volume}}}

This can also be written as:

\textcolor{aa57ff}{\rho = \dfrac{m}{V}}

- \textcolor{aa57ff}{\rho} is the
**Densit****y**in kilograms per metre cubed \left(\textcolor{aa57ff}{\textbf{kg/m}^{3}}\right) . - \textcolor{aa57ff}{m} is the
**Mass**in kilograms \left(\textcolor{aa57ff}{\textbf{kg}}\right). - \textcolor{aa57ff}{V} is the
**Volume**in metres cubed \left(\textcolor{aa57ff}{\textbf{m}^3 }\right).

An object with particles in a **closer arrangement** will have a higher density. So a** solid** will be more dense than a liquid and a gas.

**Required Practical**

**Measuring the density of regular and irregular objects**

Calculating the **density** of some objects is easier than others, depending on how easy it is to calculate the shape’s volume. For example, calculating the volume of an object with a regular shape, like a box, is a lot easier than calculating the volume of an irregular shaped object like a rock.

**Doing the experiment**

For** regular** objects, like a box, finding the **density** is very simple:

- Measure the length, width and height of the box and multiply them together to get the
**volume**. - Place the box on a balance to find the
**mass**of the box. - Use the mass and volume in the
**density equation**\left( \rho = \dfrac{m}{V} \right) to calculate the density of the rock.

For **irregular** objects, a **displacement technique** can be used to measure the volume and calculate the density:

- Use a
**balance**to measure the**mass**of the object (in this case it is a rock). - To find the
**volume**of the rock, set up a eureka can filled with water just up until the spout. - Place a measuring cylinder underneath the spout, and place the rock in the eureka can. The rock will displace water into the measuring cylinder.
- Record the volume of water in the measuring cylinder because this is the volume of the rock.
- Use the mass and volume in the
**density equation**\left( \rho = \dfrac{m}{V} \right) to calculate the density of the rock.

** Example: Calculating Density**

A solid metal cube has a mass of \text{\textcolor{10a6f3}{5 kg}} and sides of length \text{\textcolor{00bfa8}{0.5 \: m}} . Calculate the density of the metal cube.

**[2 marks]**

Find the volume of the cube by multiplying the length of each side:

\textcolor{00bfa8}{0.5} \times \textcolor{00bfa8}{0.5} \times \textcolor{00bfa8}{0.5} =0.125 \: \text{m}^3

Using \rho = \dfrac{m}{V} = \dfrac{\textcolor{10a6f3}{5}}{0.125}

\rho = 40 \: \text{kg/m}^3

## Density Example Questions

**Question 1: **A rock has a mass of \text{0.6 kg} and a volume of \text{0.15 m}^3 . Calculate it’s density.

**[2 marks]**

Using \bold{\rho = \dfrac{m}{V} = \dfrac{0.6}{0.15}}

\bold{\rho = 4} \: \textbf{kg/m}^3**Question 2: **A cube box has a density of \text{25 kg/m}^3 and a mass of 8 \: \text{ kg} .

Calculate the length of each side of the box.

**[3 marks]**

We know that the box is a cube so:

length of sides = \bold{\sqrt[3]{V} = \sqrt[3]{0.32} = 0.68} \: \textbf{m} \text{ (2 sf)}

**Question 3: **A student wants to find out the density of a rock. Describe an experiment they could perform to determine the density of this rock.

**[6 marks]**

Because it is an **irregularly shaped object**, we cannot just measure the dimensions to find the volume.

- First, fill up a
**eureka can**just up to the spout. - Set up a
**measuring cylinder**to catch any water that comes out of the spout. - Use a balance to record the
**mass**of the rock, and the place the rock into the water. - The
**volume**of the water in the measuring cylinder is the same as the**volume**of the rock. Record this volume. - Use \rho = \dfrac{m}{V} to find the
**density**of the piece of rock.

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