Physics

Question

En un recipiente con mercurio (13.6 gr/cm3) se sumerge completamente un cuerpo de 900 gramos de masa. AL medir su peso aparente este marca 2.94 newton en el dinamómetro. Cual es la densidad del cuerpo (kg/m3)

1 Answer

  • Answer:

          ρ = 20.4 kg / m³

    Explanation:

    For this exercise we use Archimedes' principle, the thrust on a submerged body is equal to the weight of the released liquid

               B = ρ g V_liquid           (1)

    let's write the equilibrium equation

               F -W + B = 0

               B = W -F

    let's calculate

               B = 0.900 9.8 - 2.94

                B = 5.88 N

    From equation 1

                V_{liquid} =  [tex]\frac{B}{\rho_{Hg} g}[/tex]

                V_{liquid} = [tex]\frac{5.88}{13.6 \ 10^3 \ 9.8}[/tex]

                V_{liquid} = 4.41176 10⁻⁵ m³

           

    in this case it is indicated that the body is completely submerged

               V_body = V_liquid = V

         the definition of density is

               ρ = m / V

               ρ = [tex]\frac{0.900 \ 10^{-3}}{ 4.41176 \ 10^{-5} }[/tex]

               ρ = 2.04 10¹ kg / m³

               ρ = 20.4 kg / m³

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