Between 1975 and 1985, the volume of all iron and steel in a given automobile model decreased from 0.165 m3m3 to 0.118 m3m3. In the same time frame, the volume of all aluminum alloys increased from 0.012 m3m3 to 0.023 m3m3. Using the densities of pure FeFe and AlAl, estimate the mass reduction resulting from this trend in materials substitution.

Answer: 340.19kg

Explanation:

The reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. It is referred to as a quantity which allows the two-body problem to be solved as if it were a one-body problem. You should note, however, that the mass determining the gravitational force is not reduced. In the computation or calculation, one mass can be replaced with the reduced mass, if this is compensated by replacing the other mass with the sum of both masses.

It has the dimensions of mass, and SI unit kg.

Given two bodies, first with mass m1 and the other with mass m2, the equivalent one-body problem, with the position of one body with respect to the other referred to as the unknown, is that of a single body of mass.

The density of Iron (Fe) = 7.87Mg/m^3

The volume of Iron decreased from = (0.165 - 0.118) m^3 = 0.047m^3

Therefore,

The weight of Iron decreased = (0.047m^3) x (7.87Mg/m^3) = 0.36989Mg

The density of aluminium = 2.70Mg/m^3

The volume of aluminum increased = (0.023 - 0.012) m^3 = 0.011m^3

The weight of aluminium is = (0.011m^3) * (2.70Mg/m^3) = 0.0297Mg

Therefore,

The mass reduction is:

The weight of Iron decreased minus the weight of Aluminium:

0.36989Mg - 0.0297Mg = 0.34019Mg

0.34019Mg * 1000

= 340.19Kg

Therefore, the mass reduction resulting from the trend is = 340.19kg