Density

Key Stage 3

Meaning

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

About Density

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.

The units of density are kg/m³.

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 = density

m = mass

V = volume

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.

About Density

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.

The units of density are kg/m³.

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 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 = density

m = mass

V = volume

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 \[\rho = \frac{m}{V}\] \[\rho = \frac{0.245}{0.2}\] \[\rho = 1.225kg/m^3\]