Materials : Density

1. Materials : Density Which is heavier, 1kg of fluffy feathers or 1kg of lead?

2. 1kg of anything has exactly the same mass : 1kg... The classic trick question! But in everyday language we would all say that “lead is heavier than feathers”.... We need a new word to describe the difference... Density

3. Learning Objectives To understand qualitatively the concept of density and how it affects us To be able to successfully tackle density problems including alloys To use density investigations as a vehicle for teaching “How Science Works” and “the scientific method” Book Reference : Pages 162-163

4. Density: Concepts Density: is a measure of how much mass is contained in a given unit volume Meaning: how heavy (in g or kg) one unit volume (in cm3 or m3) of the material is. Something we consider as "heavier" has a higher density, (is more dense). Something we consider as "lighter" has a lower density (is less dense)

5. Density: Calculations • Density = mass • Volume • Or if you insist on squiggly Greek letters... • = m / V (pronounced roh/roe/ro) • Units : • Mass : kg (preferred) or g • Volume : m3 (preferred) or cm3 • Density : kg m-3(preferred) (or g cm-3)

6. Density: Warning on Units 1 In keeping with the “SI” (Le Système International d'Unités)units used throughout Physics, kg m-3are the preferred unit for density However, for many everyday values and also in the field of chemistry g cm-3are often used Take real care converting for square and cubic units!

7. Density: Warning on Units 2 For example... While there are 100cm in 1m, for 1m3 there are 100x100x100 = 106 cm3 in each m3 Standard prefixes for the SI units of measure:

8. Density: Warning on Units 3 Litres, (not a correct SI unit) are also a minefield..... As the name suggests there are 1000ml in a litre. Also 1ml  1cm3 And there are 1000 litres in 1m3 Which adds up since we know that there are 106 cm3 (or ml) in 1 m3

9. Density: Measuring Volumes 1 To be able to calculate the density we need to know the volume.... Regular solids.... Cubes, cuboids, cylinders and spheres etc. We measure, (with a ruler, callipers or micrometer and calculate the volume using the appropriate formula: Sphere : V = 4/3r3(NB micrometer measures diameter) Cylinder : V = r2h

10. Density: Measuring Volumes 2 Liquids : Simply measure the liquid in a measuring cylinder... But... HSW : Reading a meniscus Many liquids form either convex or concave meniscus within vessels. Care must be taken to read at the correct level to avoid parallax errors

11. Density: Measuring Volumes 3 Irregular solids : We cannot simply measure/calculate the volume of such solids, However, we can Archimedes's principle and use a displacement can... Carefully lower the irregular object into the “brimmed” can The volume of the displaced water is equal to the volume of the object

12. Density: Alloys Alloys are mixtures of two metals. For example brass consists of copper (60%) and zinc (40%) If we have a volume V of an alloy which is made of two metals A and B then.... If VA is the volume of A then the mass is given by AVA. Likewise for B So the total mass of the alloy m = AVA +BVB Hence the density  = m/v = AVA +BVB V