Density, Relative Density & Archimedes’ Principle
Density of regular and irregular solids, density of liquids, relative density using hydrometers, Archimedes’ principle, upthrust, and the law of flotation.
In Ghana, oil companies at the Jubilee and TEN fields measure the API gravity (relative density) of crude oil using hydrometers. Dense, heavy crude sells at different international prices than light, sweet crude.
Key Syllabus Learning Objectives
- 1Define density and relative density and convert between g/cm³ and kg/m³
- 2Determine the density of irregular solids and liquids experimentally using displacement cans and relative density bottles
- 3State Archimedes’ principle and the law of flotation and use them to solve upthrust problems
- 4Explain the operation of a hydrometer and how modern ships made of dense steel can float
Archimedes’ Principle & Buoyancy Calculations
- Apparent Weight Loss: A stone weighs less when weighed immersed in water than in air because the upward buoyant force partially supports its weight.
- Upthrust Formula: U = Weight in air - Weight in liquid. By Archimedes’ principle: U = mass of displaced liquid × g = (Volume × Density of liquid) × g.
- Why steel ships float: A solid block of steel sinks because its density (~7,800 kg/m³) is far greater than water (1,000 kg/m³). However, a ship is hollowed out, containing vast volumes of air, making the average density of the entire vessel much less than water.
Wooden fishing canoes at James Town in Accra displace a volume of seawater whose weight exactly equals the combined weight of the canoe, fishermen, and catch.
Upthrust strictly equals the weight of the fluid displaced by the immersed portion of the body.
The Relative Density Bottle & Hydrometer Applications
- Pycnometer method: Mass of empty dry bottle (m₁); Mass of bottle + liquid X (m₂); Mass of bottle + pure water (m₃).
- Relative Density of liquid X = (m₂ - m₁) / (m₃ - m₁).
- Hydrometer in Dairy & Brewing: Used as a lactometer to test whether fresh cow milk has been diluted with water, and as a saccharometer to measure sugar fermentation in Ghanaian breweries.
Automobile mechanics at Abossey Okai use battery hydrometers (battery syringes) to measure the relative density of sulfuric acid in car batteries to determine battery charge level.
The relative density bottle measures R.D. by comparing the mass of a substance to the mass of an identical volume of water.
- Never attach units to Relative Density; writing "R.D. = 2.5 g/cm³" is penalized heavily by WAEC examiners.
- When using Eureka cans, always ensure water fills the can until it overflows through the spout and stops dripping before introducing the solid.
- Remember to state Archimedes’ principle precisely: "When a body is wholly or partially immersed in a fluid..."
- Confusing density (has units kg/m³ or g/cm³) with relative density (dimensionless ratio).
- Forgetting that Archimedes’ principle applies to all fluids (both liquids and gases), not just water.
- Dividing by 1,000 instead of multiplying by 1,000 when converting g/cm³ to kg/m³.
- Can I convert 2.7 g/cm³ into kg/m³?
- Can I outline the experimental steps to determine the density of an irregular stone using a Eureka can?
- Can I state the Law of Flotation and apply it to an iceberg or floating timber log?
- Can I calculate the relative density of a liquid using a 50 cm³ density bottle?
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