# Density

## Key Stage 3

### Meaning

Density is the amount of mass per unit volume of an object.

The unit of density is kg/m3.
An object with a large amount of mass in a small volume is said to have a high density.
An object with a small amount of mass spread over a large volume is said to have a low density. Solids are the most dense state of matter because there are a large number of particles in a certain volume and gases are the least dense state of matter because there are a small number of particles in a the same volume.

### Density and Floating

If an object is more dense than water it will sink.
If an object is less dense than water it will rise through water and float on the surface.

### Equation

Density = Mass/volume

$$\rho = \frac{m}{V}$$

Where:

ρ = The density of the object.
m = The mass of the object.
V = The volume taken up by the object.

### Example Calculations

 5000kg of Iron has a volume of 0.635m3. Calculate the density of Iron. A 50,000cm3 container of water is full with a 50kg mass of water. Calculate the density of water. A 200,000cm3 volume of air has a mass of 245g. Calculate the density of air. Mass = 5000kg Volume = 0.635m3 $\rho = \frac{m}{V}$ $\rho = \frac{5000}{0.635}$ $\rho = 7874kg/m^3$ Mass = 50kg Volume = 50,000cm3 = 0.05m3 $\rho = \frac{m}{V}$ $\rho = \frac{50}{0.05}$ $\rho = 1000kg/m^3$ Mass = 245g = 0.245kg Volume = 200,000cm3 = 0.2m3 $\rho = \frac{m}{V}$ $\rho = \frac{0.245}{0.2}$ $\rho = 1.225kg/m^3$

## Key Stage 4

### Meaning

Density is the amount of mass per unit volume of an object.

The SI Unit of density is kg/m3.
Density is a scalar quantity as it has magnitude but does not have a direction.
An object with a large amount of mass in a small volume is said to have a high density.
An object with a small amount of mass spread over a large volume is said to have a low density.

### Finding the Density

#### Finding The Density of a Regular Object

A regular object is a solid in the shape of a cuboid.
1. Measure the mass of the cuboid using an Electronic Balance or Measuring Scale.
2. Measure the length, width and height of the cuboid.
3. Multiply the length, width and height to calculate the volume.
4. Divide the mass by the volume of the cuboid to calculate the density.

#### Finding The Density of an Irregular Object

An irregular object is a solid whose shape prevents the sides being measured by a ruler.
1. Measure the mass of the object using an Electronic Balance or Measuring Scale.
2. Fill a measuring cylinder with enough water to submerse the object.
3. Take a reading of the volume of water in the Measuring Cylinder.
4. Place the object in the Measuring Cylinder and ensure it is submersed.
5. Take a reading of the volume of water + object in the Measuring Cylinder.
6. Subtract the volume of water from the volume of water + object to find the volume of the object.
7. Divide the mass by the volume of the object to calculate the density. Solids are the most dense state of matter because they have the largest amount of matter per unit volume and gases are the least dense state of matter because they have the smallest amount of matter per unit volume.

### Density and Floating

If an object is more dense than water it will sink.
If an object is less dense than water it will rise through water and float on the surface.

### Equation

Density = Mass/volume

$$\rho = \frac{m}{V}$$

Where:

ρ = The density of the object.
m = The mass of the object.
V = The volume taken up by the object.

### Example Calculations

#### Finding Density from Mass and Volume

 5000kg of Iron has a volume of 0.635m3. Calculate the density of Iron correct to two significant figures. A 200,000cm3 volume of air has a mass of 245g. Calculate the density of air correct to two significant figures. 1. State the known quantities in SI Units Mass = 5000kg Volume = 0.635m3 1. State the known quantities in SI Units Mass = 245g = 0.245kg Volume = 200,000cm3 = 0.2m3 2. Substitute the numbers into the equation and solve. $$\rho = \frac{m}{V}$$ $$\rho = \frac{5000}{0.635}$$ $$\rho = 7874kg/m^3$$ $$\rho \approx 7900kg/m^3$$ 2. Substitute the numbers into the equation and solve. $$\rho = \frac{m}{V}$$ $$\rho = \frac{0.245}{0.2}$$ $$\rho = 1.225kg/m^3$$ $$\rho \approx 1.2kg/m^3$$

#### Finding Volume from Mass and Density

 Gold has a density of 19320kg/m3. 31g of Gold is used to make a coin. Calculate the volume of this coin correct to two significant figures. A 1.3ton rock with a density of 2650kg/m3 is dropped into a swimming pool. Calculate the volume of water displaced by the rock, correct to two significant figures. 1. State the known quantities in SI Units ρ = 19320kg/m3 m = 31g = 31x10-3kg 1. State the known quantities in SI Units ρ = 2650kg/m3 m = 1.3ton = 1.3x103kg 2. Substitute the numbers and evaluate. $$\rho = \frac{m}{V}$$ $$19320 = \frac{31 \times 10^{-3}}{V}$$ 2. Substitute the numbers and evaluate. $$\rho = \frac{m}{V}$$ $$2650 = \frac{1.3 \times 10^{3}}{V}$$ 3. Rearrange the equation and solve. $$19320V = 31 \times 10^{-3}$$ $$V = \frac{31 \times 10^{-3}}{19320}$$ $$V = 1.60455 \times 10^{-6}m^3$$ $$V \approx 1.6 \times 10^{-6}$$ 3. Rearrange the equation and solve. $$2650V = 1.3 \times 10^{3}$$ $$V = \frac{1.3 \times 10^{3}}{2650}$$ $$V = 0.490566m^3$$ $$V \approx 0.49m^3$$

#### Finding Mass from Volume and Density

 A car is filled with 32 litres of gasoline, which has a density of 719.7kg/m3. Calculate the mass of gasoline added to the car, correct to two significant figures. A 2,500,000 litre swimming pool is filled with Chlorinated water which has a density of 993kg/m3. Calculate the mass of Chlorinated water in this swimming pool, correct to two significant figures. 1. State the known quantities in SI Units ρ = 719.7kg/m3 V = 32 litres = 32x10-3m3 1. State the known quantities in SI Units ρ = 993kg/m3 V = 2,500,000 litres = 2,500m3 2. Substitute the numbers and evaluate. $$\rho = \frac{m}{V}$$ $$719.7 = \frac{m}{32\times10^{-3}}$$ 2. Substitute the numbers and evaluate. $$\rho = \frac{m}{V}$$ $$993 = \frac{m}{2500}$$ 3. Rearrange the equation and solve. $$m = 719.7 \times 32 \times 10^{-3}$$ $$m = 23.0304kg$$ $$m \approx 23kg$$ 3. Rearrange the equation and solve. $$m = 993 \times 2500$$ $$m = 2482500kg$$ $$m \approx 2500000kg$$