In this chapter we’re going to be exploring. You shall understand arrangement and permutation problems, calculating permutations when there is a repeated object. Ordering r objects from n. You should have some prior knowledge of basic probability.
What is Density?
Density is the measurement or comparison of how heavy different types of materials are. Instead of measuring how heavy a material is, we measure how heavy a cube of each material would be. Consider this; What weighs more, a tonne of gold or a tonne of feathers. You would think that a tonne of gold weighs more but you would be wrong. Both materials weigh the same 1 tonne. For example 10 cm3 of gold weighs 79.2 grams. What would 1 cm3 of gold weigh?
1 cm3 of gold would weigh 7.92 grams.
That means gold has 7.92 grams for every centimetre cube or 7.92g per cm3 We say that it has a density of 7.92 g/cm3
Difference between weight and mass
The two terms weight and mass are similar, they describe how heavy an object is. Although they are similar they are not the same.
Mass is the measure of how much substance there is in an object, and weight is the measure of how heavy an object is.
Weight depends on gravity and would vary depending on where you’re in the universe. An object that feels very heavy on planet earth will weigh differently on the moon or Mars. Meaning that it might be impossible to lift a car on earth but it will be easy on the moon. Mass is different in that, it stays the same no matter what planet or where you’re in the universe.
454 grams of cheese make up a block of 4cm by 6cm by 10cm. What is the density of cheese in g/cm3.
The information that we require here is grams and cm3. We know that cm3 refers to volume. We need to find volume first.
Now we know that 454g is in the 240cm3 cubes.
The density is the number of grams per cm3, so the density of the cheese is;
Some times we know how dense different materials are per cm3, for example the density of Aluminium is 2.79g/cm3 and the density of diamond is 3.52g/cm3. We can use these values to find the mass when the volume is more than one or for different volumes. In some cases we have to find the volume first.