# A piece of copper and zinc alloy weighing 5.16 kg in water weighs 45.6 N. How much copper is contained in this alloy?

It is known that a piece of an alloy of copper and zinc in water weighs P (s) = 45.6 N. In air, its weight is P = m ∙ g, where g = 9.8 ≈ 10 N / kg is the proportionality coefficient. In water, the weight decreases due to the action of the buoyancy force, which we find according to Archimedes’ law F (A) = ρ (b) ∙ g ∙ V, where the density of water ρ (b) = 1000 kg / cubic meter. Let us find the volume of the alloy from the ratio Р (в) = Р – F (А) or Р (в) = m ∙ g – ρ (в) ∙ g ∙ V, we get V = (m ∙ g – Р (в)): ( ρ (c) ∙ g). Substitute the values of V = (5.16 ∙ 10 – 45.6): (1000 ∙ 10) = 0.0006 (cubic meters). Alloy density ρ = m / V = 5.16: 0.0006 = 8600 (kg / m3).

The density of a piece of copper and zinc alloy can be calculated using the formula: ρ = (m1 + m2): (V1 + V2) = m: (m1 / ρ1 + m2 / ρ2), where the value of the density of metals is found from the reference tables: for copper ρ1 = 8900 kg / m3 for zinc ρ2 = 7100 kg / m3. Since m2 = m – m1, we get the equation:

m1 / ρ1 + (m – m1) / ρ2 = m / ρ or m1 / 8900 + (5.16 – m1) / 7100 = 5.16 / 8600; m1 = 4.45 (kg).

Answer: copper alloy 4.45 kg.