Which is heavier, 1kg of fluffy feathers or 1kg Which is heavier, 1kg of fluffy feathers or 1kg of lead?of lead?

1kg of anything has exactly the same mass : 1kg of anything has exactly the same mass : 1kg... The classic trick question!1kg... The classic trick question!

ButBut in everyday language we would all say in everyday language we would all say that that “lead is heavier than feathers”....“lead is heavier than feathers”....

We need a new word to describe the We need a new word to describe the difference...difference...

DensityDensity

1.1. To understand qualitatively the concept To understand qualitatively the concept of density and how it affects usof density and how it affects us

2.2. To be able to successfully tackle density To be able to successfully tackle density problems including alloys problems including alloys

3.3. To use density investigations as a vehicle To use density investigations as a vehicle for teaching for teaching “How Science Works” “How Science Works” and and “the scientific method”“the scientific method”

Book Reference : Pages 162-163Book Reference : Pages 162-163

DensityDensity: is a measure of how much : is a measure of how much mass is contained in a given unit mass is contained in a given unit volumevolume

Meaning:Meaning: how heavy (in g or kg) one unit how heavy (in g or kg) one unit volume (in cmvolume (in cm33 or m or m33) of the material is.) of the material is.

Something we consider as "heavier" has a higher Something we consider as "heavier" has a higher density, (is more dense). Something we consider as density, (is more dense). Something we consider as "lighter" has a lower density (is less dense)"lighter" has a lower density (is less dense)

Density =Density = massmass

VolumeVolume

Or if you insist on squiggly Greek letters...Or if you insist on squiggly Greek letters...

== m / Vm / V (pronounced roh/roe/ro)(pronounced roh/roe/ro)

Units :Units :

Mass : kg (preferred) or gMass : kg (preferred) or g

Volume : mVolume : m33 (preferred) or cm (preferred) or cm33

Density : kg / mDensity : kg / m33 (preferred) (or g/cm (preferred) (or g/cm33))

In keeping with the “SI” In keeping with the “SI” ((Le Système Le Système International d'Unités)International d'Unités) units used units used throughout Physics, kg/mthroughout Physics, kg/m33 are the preferred are the preferred unit for densityunit for density

However, for many everyday values and also However, for many everyday values and also in the field of chemistry g/cmin the field of chemistry g/cm33 are often used are often used

Take real care converting for square and Take real care converting for square and cubic units! cubic units!

For example...For example...

While there are 100cm in 1m, for 1mWhile there are 100cm in 1m, for 1m33 there there are 100x100x100 = 10are 100x100x100 = 1066 cm cm33 in each m in each m33

Standard prefixes for the SI units of measure:

Litres, (not a correct SI unit) are also a Litres, (not a correct SI unit) are also a minefield.....minefield.....

As the name suggests there are 1000ml in a As the name suggests there are 1000ml in a litre. litre.

Also 1ml Also 1ml 1cm 1cm33

And there are 1000 litres in 1mAnd there are 1000 litres in 1m33

Which adds up since we know that there are Which adds up since we know that there are 101066 cm cm33 (or ml) in 1 m (or ml) in 1 m33

To be able to calculate the density we need To be able to calculate the density we need to know the volume....to know the volume....

Regular solids.... Regular solids....

Cubes, cuboids, cylinders and spheres etc. Cubes, cuboids, cylinders and spheres etc. We measure, (with a ruler, callipers or We measure, (with a ruler, callipers or micrometer and calculate the volume using micrometer and calculate the volume using the appropriate formula:the appropriate formula:Sphere : V = 4/3Sphere : V = 4/3rr33

Cylinder : V = Cylinder : V = rr22hh

Liquids : Liquids : Simply measure the liquid Simply measure the liquid in a measuring cylinder... But...in a measuring cylinder... But...

HSW : Reading a meniscusHSW : Reading a meniscus

Many liquids form either Many liquids form either convex or concave meniscus convex or concave meniscus within vessels.within vessels.

Care must be taken to read at Care must be taken to read at the correct level to avoid the correct level to avoid parallax errorsparallax errors

Irregular solids :Irregular solids :

We cannot simply measure/calculate the volume We cannot simply measure/calculate the volume of such solids, However, we can Archimedes's of such solids, However, we can Archimedes's principle and use a displacement can... 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

Alloys are mixtures of two metals. For example Alloys are mixtures of two metals. For example brass consists of copper (60%) and zinc (40%)brass consists of copper (60%) and zinc (40%)

If we have a volume V of an alloy which is made If we have a volume V of an alloy which is made of two metals A and B then....of two metals A and B then....

If VIf VAA is the volume of A then the mass is given by is the volume of A then the mass is given by AAVVAA. Likewise for B. Likewise for B

So the total mass of the alloy m = So the total mass of the alloy m = AAVVA A ++ BBVVBB

Hence the density Hence the density = m/v = = m/v = AAVVA A ++ BBVVB B

VV