Question

9. A statue is to be scaled down isomorphically (It will have its size changed without changing its shape). It starts with an initial height of 6.75 [m] and ends up with a final height of 2.15 [m]. If the mass of the original statue with a uniform mass density was 44.5 [kg], calculate the mass of the smaller model with the same uniform mass density.

Answer 1

Answer:

   m = 1.45 kg

Explanation:

For this exercise we look for size reduction in height

              Reduction = y / y₀

              Reduction = 2.15 / 6.75

              Reduction = 0.3185

As the statue should not be deformed, all reduction has the same factor.

Let's use the concept of density

       ρ = m / V

Initial statue

         ρ = m₀ / V₀

         

It is reduced

         V = x y z

         V = 0.3185 x₀ 0.3185 y₀ 0.3185 z₀

         V = 0.3185³ V₀

       

Density is

         ρ = m / V

         ρ = m / 0.3185³ V₀

As the density remains constant we can match them

         m₀ / Vo = m / 0.3185³ V₀

         m = 0.3185³ m₀

Let's calculate

        m = 0.3185³ 45

        m = 0.03231   45

        m = 1.45 kg