Question

When a crown of mass 14.7 kg is submerged in water, an accurate scale reads only 13.4 kg. What material is the crown made of?

Answer 1

Answer:

  ρ = 1.13 10⁴  km/m³

Explanation:

For this exercise we use Newton's equilibrium equation

        B –W + W_scale = 0

Where B is the thrust and W_scale is the balance reading

The push is given by Archimedes' law

        B = ρ_water g V

        B = W- W_scale

        B = m g - m_scale g  

       

Let's calculate

         B = 14.7 9.8 - 13.4 9.8

         B = 12.74 N

         ρ_water g V = 12.74

         V = 12.74 / ρ_water g

         V = 12.74 / 1000 9.8

         V = 0.0013 m³

Let's use density

          ρ = m / V

           

We replace

         ρ = 14.7 / 0.0013

         ρ = 1.13 10⁴  km/m³