Density
Section: Motion, Forces & Energy | Syllabus: Cambridge IGCSE Physics (0625)
Density Definition & Equation
- Density (ρ) is defined as the mass per unit volume of a substance:
- density measures how tightly packed the matter within an object is
- it is a scalar quantity
- common SI units are kilograms per cubic metre (kg/m^3) and grams per cubic centimetre (g/cm^3)
- unit conversion: 1 g/cm^3 = 1000 kg/m^3
- Formula:
- ρ = (m/V)
- Where:
- ρ = density (kg/m^3 or g/cm^3)
- m = mass (kg or g)
- V = volume (m^3 or cm^3)
Density triangle showing the relationship between density, mass, and volume:
Determining Density Experimentally
1. Finding the density of a liquid:
- To find the density of a liquid, you need to measure its mass and volume. To do this you can:
- place an empty measuring cylinder on a digital balance and record its mass (m_1)
- pour a specific volume (V) of liquid into the measuring cylinder and read the volume at eye level from the bottom of the meniscus
- reweigh the cylinder containing the liquid to find the total mass (m_2)
- calculate the mass of the liquid: m = m_2 - m_1
- calculate density using: ρ = (m/V)
Diagram showing the procedure for finding the density of a liquid using a measuring cylinder and a digital balance
2. Finding the density of a regularly shaped solid:
- To find the density of a regularly shaped solid, you need to
- measure the mass (m) of the solid using a digital balance
- measure the dimensions (length, width, height, or radius) using a ruler, vernier calipers, or a micrometer
- calculate the volume (V) using the appropriate geometric formula (e.g. V = l × w × h for a rectangular block, or V = π r^2 h for a cylinder)
- calculate density using: ρ = (m/V)
3. Finding the density of an irregularly shaped solid which sinks in a liquid (displacement method):
- To find the density of an irregularly shaped solid which sinks in a liquid, you need to:
- this method only works if the solid sinks and can be fully submerged, if it floats, its volume cannot be found this way
- measure the mass (m) of the solid using a digital balance
- fill a measuring cylinder with a known initial volume of water (V_1)
- gently lower the solid into the water so it is completely submerged, and record the new volume (V_2)
- calculate the volume of the solid displaced: V = V_2 - V_1
- alternatively, fill a Eureka (displacement) can to the spout and lower the object in; collect the overflowing water in a measuring cylinder to directly read volume V
- calculate density using: ρ = (m/V)
Diagram illustrating the displacement method using a measuring cylinder and a Eureka can to find the volume of an irregular solid
Floating and Sinking
- Floating vs. sinking for solids:
- an object will float in a liquid if its density is less than the density of the liquid
(_object < _liquid) - an object will sink in a liquid if its density is greater than the density of the liquid
(_object > _liquid) - example: wood (ρ ≈ 0.7 g/cm^3) floats on water (ρ = 1.0 g/cm^3), whereas steel (ρ ≈ 7.8 g/cm^3) sinks
- an object will float in a liquid if its density is less than the density of the liquid
Diagram illustrating that less dense objects like wood float on water, while denser objects like steel sink
Liquids Floating on Liquids
Extended Only
- Behaviour of immiscible liquids (liquids that do not mix):
- when two or more unmixable liquids are placed in the same container, they form distinct layers based on their densities
- the liquid with the lowest density floats to the top layer
- the liquid with the highest density sinks to the bottom layer
- example: oil (ρ ≈ 0.9 g/cm^3) floats on top of water (ρ = 1.0 g/cm^3)
A density column displaying stacked liquids of different densities showing the least dense liquid on top and the most dense at the bottom
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