Question

an alloy consists of 70% aluminium and 30% magnesium by mass what would we expect its density to be when density of aluminium is equal to 2700 kg per metre cube and density of magnesium is equal to 1740 kg per metre cube

Answer 1

Answer:

Density of alloy = 2412 kg per m³

Explanation:

We can solve this problem using weighted average.

Let w1 be the weight of aluminium

Let d1 be the density of aluminium

Let w2 be the weight of magnesium

Let d2 be the density of magnesium

The density of the alloy is given by (w1*d1 + w2*d2) / (w1 + w2)

Here, w1 and w2 are the "weights" of aluminium and magnesium, expressed as a fraction.

ATQ,

w1 = 0.7              (70% is expressed as 0.7 as a fraction)

d1 = 2700 kg per m³

w2 = 0.3

d2 = 1740 kg per m³

Density of alloy = [(0.7 * 2700) + (0.3 * 1740)] / (0.7 + 0.3)

                          = (1890 + 522) / (1)

                          = 2412

Density of alloy = 2412 kg per m³

Please note that "weights" in this case show relative importance of that metal in the alloy.

It is intutive that the density of the alloy will be closer to that of the metal that has a higher proportion (or weight) in that alloy. You can see that happening in this case. The density of the alloy (2412) is closer to that of aluminium (2700) than magnesium (1740) because aluminium has a higher "weight/share/proportion" of 70% than magnesium that has 30%.

You can also express w1 and w2 as 70 and 30. We have used 0.7 and 0.3, because no further division by the denominator is required. The denominator becomes "1" which is easier to handle.