Question

Actividad: Sitúese en el siglo III a.c. el rey de Siracusa, Hierón II, le pide

Answer 1

Answer:

ρ_c < ρ_gold        the crown is not gold

Explanation:

For this exercise we use the translational equilibrium condition

           ∑ F = 0

in the air

           T₁ - W = 0

            T₁ = W

in water  

           T + B - W = 0

where T is the scale reading, B the liquid thrust and W the weight

           B = W -T

           B = 7.84 - 6.84

           B = 1 N

thrust is

            B = ρ g V_water

             V_water = $\frac{B}{\rho g}$

             V_water = $\frac{1}{1000 \ 9.8}$

             V_water = 1.02 10⁻⁴ m³

how the crown is totally submerged

            V_c = V_water

             V_c = 1.02 10⁻⁴ m³

now we can calculate the density of the crown

               ρ_c = m_c / Vc

               W = mg

                m = W / g

we substitute

               ρ_c = $\frac{W}{g \ V_c}$

               ρ_c = $\frac{7.84}{ 9.8 \ 1.02 \ 10^{-4}}$

               ρ_c = 0.784 10⁴ kg / m³

               ρ_c = 7.84 10³ kg / m³

We can see that this density is less than the density of gold

              ρ_c < ρ_gold

therefore the crown is not gold