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Motion, Forces and Energy

Mass, Weight and Density

Cambridge IGCSE Physics

Mass and weight

  • Mass is a measure of the quantity of matter in an object at rest relative to the observer.
  • Weight is a gravitational force on an object with mass.
  • Gravitational field strength is force per unit mass. It is equivalent to the acceleration of free fall.
  • Weights, and so masses, are compared using a balance.
gravitational field strength = weight ÷ massg = W / m

Rearranged: W = m g, m = W / g.

Weight is the effect of a gravitational field on a mass.

Density

Density is mass per unit volume.

density = mass ÷ volumeρ = m / V
  • Rearranged: m = ρ V, V = m / ρ.
  • Mass in g with volume in cm3 gives a density in g/cm3.
QuantitySymbolUnit
weightWN
massmkg
gravitational field strengthgN/kg
densityρkg/m3
volumeVm3

Measuring density

Method: density of an irregular solid that sinks
  1. Measure the mass of the object on a balance.
  2. Pour water into a measuring cylinder and measure the initial volume of water.
  3. Immerse the object in the water.
  4. Read the final volume at the bottom of the meniscus, with the line of sight perpendicular to the scale.
  5. Subtract the initial volume from the final volume to give the volume of the object.
  6. Calculate the density with ρ = m / V.
Line of sight perpendicular to the scale Eye Measuring cylinder Bottom of the meniscus Water Object
Reading the volume in a measuring cylinder: eye level with the bottom of the meniscus.
  • Regular solid: measure the length, width and height with a rule. Repeat in several places and take averages for each dimension. Volume = length × width × height.
  • Liquid: measure the mass of an empty container, then the mass of the container with the liquid, and subtract. Measure the volume of the liquid in a measuring cylinder.

Sources of inaccuracy

  • Air bubbles on the immersed object make the measured volume too large.
  • Graduations on the measuring cylinder too large: use a smaller measuring cylinder.
  • Measuring the dimensions of a regular solid gives a more precise volume than a measuring cylinder with large graduations.

Floating

  • An object floats on water when its average density is less than the density of the water. An object with a greater density than the liquid sinks.
  • A steel ship floats because there are air spaces in the ship, so its average density is less than the density of the water.

Two liquids that do not mix: liquids of lower density float on liquids of higher density.

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