Density My Teacher Once Asked Me, “is Wool Heavier Or

DENSITY My teacher once asked me, “Is wool heavier or iron?” We all said, “Iron” in one voice. He smiled and then told us, “Depends on how much of each you take!”. Simple isn’t it! It isn’t fair comparing two things of unequal volumes; so we compare same volumes. In everyday language, lead is said to be ‘heavier’ than wood. By this, it is meant that a certain volume of lead is heavier than the same volume of wood. In science, such comparisons are made using the term density. Density is defined as the mass per unit volume i.e., if I take one unit of the volume of a substance (say 1cc) and find its mass, it is called density. density =

mass volume

For example, the density of water is 1g per cc while that of mercury is 13.6g per cc. What we mean by this is that if I take one cc of both water and mercury, water would weigh 1g while mercury would weigh 13.6g. Remember we compare equal volumes.

mass density

volume

Knowing the density of a substance, the mass of any volume can be calculated. This enables engineers to work out the weight of a structure if they know from their plans the volumes of certain materials to be used and their densities. Strong foundations can then be made. The SI unit of density is kilogram per cubic meter. To convert density from g/cm3 to kg/m3 we multiply by 1,000. The table below shows the densities of some common substances. SOLID DENSITY (g/cm3) Aluminium 2.7 Copper 8.9 Iron 7.9 Gold 19.3 Glass 2.5 Teak wood 0.80 Ice 0.92 Polythene 0.90 LIQUID Paraffin Petrol Pure water Mercury

DENSITY g/cm3 0.80 0.80 1.0 13.6

DENSITY g/cm3 1.3 0.09 2.0

GAS Air Hydrogen carbon dioxide

SIMPLE DENSITY MEASUREMENTS: (a) REGULARLY SHAPED SOLIDS: To find out the density of an object we need to know its mass and volume. The mass of a solid can be found using a common balance. The volume of a regularly shaped solid can be found by knowing its dimensions and on application of the formula. Then density can be found using the formula. Take for example the cuboid given below which weighs 600g.

4 cm

8 cm

6 cm

Volume of the cuboid = l x b x h = 8 x 4 x 6 = 192 cm3. Now, density = mass / volume =600/192 Listed below in the table are the volumes of some regular shapes SHAPE Cube Cylinder Cone Sphere

FORMULA FOR VOLUME a3 Πr2h 1/3 Πr2h 4/3Πr3

(b) IRREGULARLY SHAPED SOLIDS (eg: pebble) It is not possible to find the volume of an unknown solid using any formulae as its dimensions are not regular. So we use Archimedes’ principle to find the volume. The mass of the object is found using a balance. A measuring cylinder half-filled with water is taken. Note its initial volume (V 1). Immerse the solid into the water by tying it with a thread. The water raises up as the pebble takes up space inside the water. Note the final volume (V2). The difference in volumes (V2–V1) gives the volume of the pebble. Substitute the values in the formula for density to find the density.

Readings: Mass of the object = m grams Initial volume of water = V1 cm3 Final volume of water = V2 cm3

Volume of object = Difference in volume = (V2–V1) cm3 Density = mass / volume

PRECAUTIONS TO BE TAKEN: First find the mass of the object and then the volume; not the other way around (a wet object weighs more leading to erroneous results). Drop the object carefully tightly tied with a thread. Avoid parallax error in taking readings by keeping the eye line parallel to the reading. FLOATING AND SINKING: We have seen objects float and objects sink. It makes us wonder why some float while some others sink. Well, the answer lies in density. If an object is denser than the liquid it will sink. If the liquid is denser than the object, the object floats. Look at Table 1 and list the things that will float on water and will sink in water. People float in the Dead Sea as it is very dense. A big ship which is made up of iron floats on water and does not sink as its average density is less than the density of sea water. EXERCISES 1. Taking the density of copper as 9g/cm3, find (a) the mass of 5cm3 (b) the volume of 63g 2. If the density of wood is 0.5g/ cm3, what is the mass of (a) 1 cm3 (b) 2 cm3 (c) 10 cm3 3. What is the density of a substance of (a) Mass 100g and volume 10 cm3 (a) Volume of 3m3 and mass 9kg 4. The density of gold is 19g/cm3. Find the volume of

(a) 38g (a) 95g of gold 5. A piece of steel has a volume of 12cm3 and a mass of 96g. What is its density in (a) g/cm3 (b) kg/m3 6. What is the mass of 5m3 of cement of density 3000 kg/m3? 7. What is the mass of air in a room measuring 10m x 5m x 2m if the density of air is 1.3 kg/m3? 8. When a golf ball is lowered into measuring cylinder of water, the water level rises by 30cm3. If the ball weighs 33g in air, find its density. 9. A rectangular block of metal is 50mm long, 35mm wide and has a thickness of 3.0 mm. it weighs 0.15N. Calculate (a) the volume of the piece of metal (b) the density of the metal. 10. A can weighs 5N empty and 35N when completely full of petrol. The capacity of the can is 4 x 10-3 m3. Calculate (a) the mass of petrol in the can when it is full. (b) the density of the petrol. 11. A measuring cylinder contains 30cm3 of water. When a stone of weight 0.92N is dropped into the water, it sinks to the bottom and the liquid level rises to the 70cm3 mark. (a) Calculate the mass of the stone. (b) the density of the stone (c) Explain why it would not be possible to use this method to determine the density of cork. 12. A pupil carries out an experiment with beaker and some liquid and obtains the following results. The mass of the beaker = 96g Mass of the beaker containing 100cc of the liquid = 184g What was the density of the liquid? 13. The table shows the results of an experiment in which a sample of solid material is placed in five different liquids. What is the density of the sample? LIQUID mercury sea-water pure water paraffin organic solvent

DENSITY OF LIQUID kg/m3 14000 1100 1000 700 550

OBSERVATION Floats Floats Floats Sinks Sinks