CIE IGCSE Physics

Revision Notes

1.4.1 Density

Density: Basics

  • Density is the mass per unit volume of a material:
    • Objects made from low-density materials typically have a low mass, whilst similar-sized objects made from high-density materials have a high mass
      (Think of how heavy a bag full of feathers is compared to a similar bag full of metal)
  • Density is related to mass and volume by the following equation:

Density equation, IGCSE & GCSE Physics revision notes            (Note: The greek letter ρ is used to mean density)

 

  • You can rearrange this equation with the help of the formula triangle:

Density triangle (2), IGCSE & GCSE Physics revision notes

Use the formula triangle to help you rearrange the equation

 

  • The units of density depend on what units are used for mass and volume:
    • If the mass is measured in g and volume in cm3, then the density will be in g/cm3
    • If the mass is measured in kg and volume in m3, then the density will be in kg/m3

 

Exam Tip

  • The main thing to remember is that density is mass per unit volume
  • In Physics, mass is almost always measured in kg
    Density is the only topic in which physicists sometimes use grams instead

 

Floating

  • In general, an object will float in a liquid if the average density of that object is less than the density of the liquid it is placed in
  • Water, for example, has a density of about 1 g/cm3
    • If an object has a density of less than 1 g/cm3 then it will float in water
    • If an object has a density that is greater than 1 g/cm3 then it will sink in water

 

Floating, IGCSE & GCSE Physics revision notes

Diagram showing the relationship between an object’s density and its ability to float in water

 

Measuring Density

  • To measure the density of an object, we must measure its mass and volume and then use the following equation:

Density equation 2, IGCSE & GCSE Physics revision notes

  • The mass of an object can be measured quite simply by placing it on a top pan balance
    You ought to state that you will ‘zero’ the balance before using it

top-pan-balance, IGCSE & GCSE Physics revision notes

Always zero a top pan balance before taking any measurements

  • In the case of a liquid, the liquid must be placed in a container, the mass of which should be measured both when it is empty and when it contains the liquid:
    • The mass of the liquid will be the difference between the two values

 

  • The volume can be determined in a couple of ways:

Regular shapes (e.g. cubes, spheres, cylinders):

  • The width (and length) can be measured using a ruler or a pair of digital calipers
  • To make the measurements accurate, several measurements should be taken between different faces or points on the circumference, and an average taken

 

digital calipers, IGCSE & GCSE Physics revision notes

When measuring the width (or diameter) take several readings between different points and take an average

 

  • The volume can then be calculated using an appropriate equation:

Sphere cube cylinder equation, IGCSE & GCSE Physics revision notes

(Note: When measuring the width of a sphere or cylinder, divide the measurement by two to find the radius)

 

Irregular shapes:

  • The volume can be found using a Eureka can:

 

Eureka-can, IGCSE & GCSE Physics revision notes

Placing an object in a full Eureka can will displace water equal to its volume

  • Fill the Eureka can with water
  • Place an empty measuring cylinder below its spout
  • Now carefully lower the object into the Eureka can (use a piece of string, perhaps)
  • Measure the volume of displaced water in the measuring cylinder

 

  • Alternatively, the object can be placed in a measuring cylinder containing a known volume of liquid, and the change in volume then measured

 

Density worked example, IGCSE & GCSE Physics revision notes

When an irregular solid is placed in a measuring cylinder, the level of the liquid will rise by an amount equal to the volume of the solid

  • Once the mass and volume of the shape is known, its density can be calculated

 

Author: Jenna

Jenna studied at Cardiff University before training to become a science teacher at the University of Bath specialising in Biology (although she loves teaching all three sciences at GCSE level!). Teaching is her passion, and with 10 years experience teaching across a wide range of specifications – from GCSE and A Level Biology in the UK to IGCSE and IB Biology internationally – she knows what is required to pass those Biology exams.
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