Density
Section: Physics | Syllabus: Cambridge IGCSE Combined Science (0653)
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
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