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Cambridge IGCSE0625

Density

Physics 0625 Chapter Notes

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Density
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In this chapter

  1. 1Density and its equation
  2. 2Density of a liquid and of a regularly shaped solid
  3. 3Density of an irregularly shaped solid
  4. 4Floating and sinking
  5. 5One liquid floating on another

1. Density and its equation

Density is mass per unit volume. In words, density equals mass divided by volume.

The unit of density is a unit of mass divided by a unit of volume, such as g/cm³ or kg/m³. N/m³ is not a possible unit of density.

To find a mass or a volume, rearrange the equation before putting the numbers in.

ρ = m/V

Examiner insight

“The syllabus defines density as ‘mass per unit volume’. Many candidates selected option A indicating that many thought that ‘per’ means ‘multiplied by’ rather than ‘divided by’, in spite of the equation immediately following the definition.” “A few candidates did not correctly rearrange the density equation to make volume the subject.”

Worked example 11 mark

The density of steel is 7900 kg / m³. The mass of a solid steel cube is 110 kg. Calculate the volume of the steel cube.

  1. 1

    V = m/ρ = 110/7900

  2. 2

    = 0.0139 = 0.014 m³ [1]

2. Density of a liquid and of a regularly shaped solid

Measure the mass with a balance. Zero the balance before the measurement.

For a liquid, a measuring cylinder measures the volume. Use the balance to find the mass of the empty measuring cylinder, then the mass of the cylinder and liquid. The difference is the mass of the liquid. Read the volume from the bottom of the meniscus, with your eye level with the liquid surface.

For a regularly shaped solid such as a block, measure the length, width and height with a ruler and calculate the volume. Then density = mass ÷ volume.

V = l × w × h

ρ = m/V

Examiner insight

“Answers not scoring full credit usually lacked detail and precision, e.g., failing to state that the balance is used to find the mass of the empty measuring cylinder.” “Common errors were using the measuring cylinder to measure mass, not measuring the volume, not making it clear that it was the mass of the liquid that was required and confusing mass, volume and density.”

Worked example 13 marks

The mass of one disc is 24 g. The volume of the disc is 20 cm³. Calculate the density of the disc.

  1. 1

    density = mass ÷ volume [1]

  2. 2

    density = 24 ÷ 20 [1]

  3. 3

    = 1.2 g/cm³ [1]

3. Density of an irregularly shaped solid

An irregularly shaped solid which sinks has its volume found by displacement.

Partly fill a measuring cylinder with water and measure the volume of water. Put the solid in so that it is submerged and measure the new volume. The volume of the solid is the difference in volumes.

With a displacement can, fill the can to the top with water and add the solid. Collect and measure the displaced water in a measuring cylinder. Its volume equals the volume of the solid. Measure the mass with a balance, then density = mass ÷ volume.

V = V₂ - V₁

Examiner insight

“Other candidates put the piece of metal into the measuring cylinder before the water. A number of candidates did not use the word ‘volume’ for the measurements in the measuring cylinder. Reading, height and measurement were common incorrect answers.” “Some candidates referred to a measurement made from below the meniscus. This answer is incorrect because there are many places to take a measurement below the meniscus, none of which are correct.”

Worked example 13 marks

A solid metal sphere has a volume of 31 cm³. Describe how a student determines the volume of the sphere using a measuring cylinder.

  1. 1

    Add water to the measuring cylinder and measure the volume of water, V₁. [1]

  2. 2

    Measure the water volume in the measuring cylinder after the sphere is added, V₂. [1]

  3. 3

    Volume of sphere = difference in water volume = V₂ - V₁. [1]

4. Floating and sinking

An object sinks in a liquid if it is denser than the liquid. It floats if it is less dense than the liquid. Compare the two densities, not the masses.

A solid steel cube sinks in sea water, but a steel ship floats. The ship is not solid steel: the volume of the ship includes air. The average density of the steel and air is less than the density of sea water.

Examiner insight

“A few candidates attempted an explanation in terms of quantities other than density, for example, steel is heavier.” “Many candidates linked air with a vague lowering of density. Answers needed to compare the overall density of the ship with the density of sea water.”

Worked example 11 mark

The table shows the densities of three liquids.

oil 0.8 g / cm³ · water 1.0 g / cm³ · brine 1.2 g / cm³

A student has four balls with different masses and volumes. Which ball would float on brine but sink in oil and in water?

A 26 g, 20 cm³ · B 28 g, 32 cm³ · C 30 g, 38 cm³ · D 34 g, 30 cm³

  1. 1

    The ball must be denser than water and less dense than brine: between 1.0 and 1.2 g / cm³.

  2. 2

    A: 26 ÷ 20 = 1.3. B: 28 ÷ 32 = 0.88. C: 30 ÷ 38 = 0.79. D: 34 ÷ 30 = 1.1.

  3. 3

    D [1]

5. One liquid floating on another

When two liquids do not mix, the less dense liquid floats on the denser liquid.

Oil has a lower density than water, so the oil ends up on top of the water.

Examiner insight

“Almost all candidates correctly described the final position of oil as being on top of the water and explained that this is due to the lower density of the oil.”

Recap

  • Density = mass per unit volume: ρ = m/V.
  • Units: g/cm³ or kg/m³, a mass unit divided by a volume unit.
  • Mass: balance. Volume of a liquid: measuring cylinder. Volume of a block: length × width × height.
  • Irregular solid: volume by displacement, the difference in the two water volumes.
  • An object floats if it is less dense than the liquid and sinks if it is denser.
  • A steel ship floats because its average density, steel and air, is less than that of sea water.
  • Extended: when two liquids do not mix, the less dense liquid floats on the denser one.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Define density.1 mark
  2. A student writes the density of a rock as 2.6 cm³ / g. State the correct unit for this value.1 mark
  3. A metal block has a mass of 0.54 kg and a volume of 200 cm³. Calculate the density of the metal in g / cm³.3 marks
  4. A metal has a density of 8.9 g / cm³. Calculate the mass of 25 cm³ of the metal.2 marks
  5. An empty measuring cylinder has a mass of 96 g. A student pours 60 cm³ of oil into it. The mass of the measuring cylinder and oil is 147 g. Calculate the density of the oil.3 marks
  6. A wooden block is 5.0 cm long, 4.0 cm wide and 2.5 cm high. Its mass is 30 g. Calculate the density of the wood.3 marks
  7. A measuring cylinder contains 40 cm³ of water. A student lowers five identical steel nuts into the water. The new volume reading is 52 cm³. The total mass of the five nuts is 94 g. Calculate the density of the steel.4 marks
  8. A solid ball has a mass of 46 g and a volume of 50 cm³. The density of oil is 0.85 g / cm³. The density of water is 1.00 g / cm³. Determine whether the ball floats or sinks in each liquid.4 marks
  9. Oil, water and mercury do not mix. The density of oil is 0.85 g / cm³, of water is 1.00 g / cm³ and of mercury is 13.6 g / cm³. The three liquids are poured into one tall jar. State the order of the liquids from top to bottom and give the reason.2 marks
  10. A cook makes a salad dressing from olive oil and vinegar, which do not mix. 250 cm³ of the olive oil has a mass of 0.23 kg. 150 cm³ of the vinegar has a mass of 153 g. (a) Calculate the density of each liquid in g / cm³. (b) State which liquid forms the top layer. (c) A seed of density 0.97 g / cm³ is dropped into the dressing. State and explain where the seed comes to rest.5 marks

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