The solid weight was weighed using a dynamometer. First, it was completely immersed in water, and then in kerosene

The solid weight was weighed using a dynamometer. First, it was completely immersed in water, and then in kerosene. In the first case, the readings of the device were P1 = 2.9 N, and in the second – P2 = 3.3 N. Determine the density of the substance from which the load is made. Express your answer in kg / m3, rounded to the nearest whole number. The density of water and kerosene is 1000 kg / m3 and 800 kg / m3, respectively.

P1 = 2.9 N.

P2 = 3.3 N.

ρ1 = 1000 kg / m3.

ρ2 = 800 kg / m3.

g = 9.8 m / s2.

ρ -?

Two forces act on a body immersed in a liquid: the force of gravity Ft, directed vertically downward, and the buoyant force of Archimedes Farkh, directed vertically upward.

The force of gravity is determined by the formula: Ft = m * g, where m is the mass of the body, g is the acceleration of gravity.

The buoyancy force of Archimedes is determined by the formula: Farkh = ρzh * g * V. Where ρzh is the density of the fluid in which the body is immersed, g is the acceleration of gravity, V is the volume of the immersed part of the body in the fluid.

The body weight P will be determined by the formula: P = Ft – Farch = m * g – ρzh * g * V.

Р1 = m * g – ρ1 * V * g.

P2 = m * g – ρ2 * V * g.

P2 – P1 = m * g – ρ2 * V * g – m * g + ρ1 * V * g = V * g * (ρ1 – ρ2).

V = (P2 – P1) / g * (ρ1 – ρ2).

V = (3.3 N – 2.9 N) / 9.8 m / s2 * (1000 kg / m3 – 800 kg / m3) = 0.0002 m3.

Р1 = V * ρ * g – ρ1 * V * g.

V * ρ * g = Р1 + ρ1 * V * g.

ρ = (P1 + ρ1 * V * g) / V * g.

ρ = (2.9 N + 1000 kg / m3 * 0.0002 m3 * 9.8 m / s2) / 0.0002 m3 * 9.8 m / s2 = 1580 kg / m3.

Answer: the density of the substance from which the body is made is ρ = 1580 kg / m3.