# With what acceleration will a paraffin ball weighing 30 g float up in water? Density of paraffin 900 kg / m ^ 3?

m = 30 g = 0.03 kg.

g = 10 m / s2.

ρp = 900 kg / m3.

ρw = 1000 kg / m3.

a – ?

Two forces act on a paraffin ball in water: the force of gravity Ft, directed vertically downward, and the buoyancy 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 Farch is determined by the formula: Farch = ρw * g * V. Where ρw is the density of the liquid 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 liquid.

2 Newton’s law will have the form: m * a = Farch – Ft.

a = (ρw * g * V – m * g) / m = ρw * g * V / m – g.

The volume of the ball V is found by the formula: V = m / ρп.

a = ρw * g * m / m * ρp – g = ρw * g / ρp – g.

a = 1000 kg / m3 * 10 m / s2 / 900 kg / m3 – 10 m / s2 = 1.1 m / s2.

Answer: the paraffin ball will move with acceleration a = 1.1 m / s2.

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