### Density: Basics

**Density is the mass per unit volume**of a material:- Objects made from low-density materials typically have a low mass, whilst similar-sized objects made from high-density materials have a high mass

(Think of how heavy a bag full of feathers is compared to a similar bag full of metal)

- Objects made from low-density materials typically have a low mass, whilst similar-sized objects made from high-density materials have a high mass
- Density is related to mass and volume by the following equation:

(Note: The greek letter ρ is used to mean density)

- You can rearrange this equation with the help of the formula triangle:

*Use the formula triangle to help you rearrange the equation*

- The units of density depend on what units are used for mass and volume:
- If the mass is measured in
and volume in*g*, then the density will be in*cm*^{3}*g/cm*^{3} - If the mass is measured in
and volume in*kg*, then the density will be in*m*^{3}*kg/m*^{3}

- If the mass is measured in

#### Exam Tip

- The main thing to remember is that
**density is mass per unit volume** - In Physics, mass is almost always measured in kg

Density is the only topic in which physicists sometimes use grams instead

### Floating

- In general, an object will float in a liquid if the average density of that object is less than the density of the liquid it is placed in
- Water, for example, has a density of about 1 g/cm
^{3}- If an object has a density of less than 1 g/cm
^{3}then it will float in water - If an object has a density that is greater than 1 g/cm
^{3}then it will sink in water

- If an object has a density of less than 1 g/cm

*Diagram showing the relationship between an object’s density and its ability to float in water*

### Measuring Density

- To measure the density of an object, we must measure its mass and volume and then use the following equation:

- The mass of an object can be measured quite simply by placing it on a
**top pan balance**

You ought to state that you will ‘zero’ the balance before using it

*Always zero a top pan balance before taking any measurements*

- In the case of a liquid, the liquid must be placed in a container, the mass of which should be measured both when it is empty and when it contains the liquid:
- The mass of the liquid will be the difference between the two values

- The volume can be determined in a couple of ways:

**Regular shapes** (e.g. cubes, spheres, cylinders):

- The width (and length) can be measured using a ruler or a pair of
**digital calipers** - To make the measurements accurate, several measurements should be taken between different faces or points on the circumference, and an average taken

*When measuring the width (or diameter) take several readings between different points and take an average*

- The volume can then be calculated using an appropriate equation:

(Note: When measuring the width of a sphere or cylinder, divide the measurement by two to find the radius)

**Irregular shapes:**

- The volume can be found using a Eureka can:

*Placing an object in a full Eureka can will displace water equal to its volume*

- Fill the Eureka can with water
- Place an empty measuring cylinder below its spout
- Now carefully lower the object into the Eureka can (use a piece of string, perhaps)
- Measure the volume of displaced water in the measuring cylinder

- Alternatively, the object can be placed in a measuring cylinder containing a known volume of liquid, and the change in volume then measured

*When an irregular solid is placed in a measuring cylinder, the level of the liquid will rise by an amount equal to the volume of the solid*

- Once the mass and volume of the shape is known, its density can be calculated