Combining Substances in a Certain Ratio to Give a Set Density
Substances are often combined to make new substances. Metal alloys are made by mixing metals together in certain proportions to give certain properties of strength, hardness, density or some other quality. If it is required that the density be a certain value then we can calculate the proportions in which the metals should be combined (this calculation applies to all mixing of substances, not just metals).
Suppose that metal 1 has a density
then a volume
of this metal has a mass
Suppose that metal 2 has a density
then a volume
of this metal has a mass
The two metals are mixed, so the total mass is
and the total volume is
The density of the mixture will be
and this density will be somewhere betweenand
depending on the ratio of metal 1 to metal 2 in the mixture.
Suppose the ratio is
by mass then the mass of metal 1 in the mixture is
and the mass of metal 2 is
Also
and
so that
Then
Suppose that the two metals have densities of
and
and are mixed in the mass ratio 3:5. Then
Suppose the ratio isby volume then the volume of metal 1 in the mixture is
and the volume of metal 2 is
Also
and
so that
Then
Suppose that the two same metals with densities ofandare mixed in the volume ratio 3:5 . Then