Calculate the weight of a child that can hold on to a cork rescue harness that weighs 4.5 kg

Calculate the weight of a child that can hold on to a cork rescue harness that weighs 4.5 kg and has a cork density of 240 kg / m3.

mp = 4.5 kg.

g = 9.8 m / s2.

ρp = 240 kg / m3.

ρw = 1000 kg / m3.

mр -?

Let us find the resulting force F from the action of the force of Archimedes Farkh and the force of gravity m * g on the rescue belt.

F = Farch – mp * g.

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

Vп = mp / ρп.

Farch = ρw * g * mp / ρp.

F = ρw * g * mp / ρp – mp * g = (ρw * mp / ρp – mp) * g.

F = (1000 kg / m3 * 4.5 kg / 240 kg / m3 – 4.5 kg) * 9.8 m / s2 = 139.65 N.

F = mр * g.

mр = F / g.

mр = 139.65 N / 9.8 m / s2 = 14.25 kg.

Answer: the rescue harness can support a child weighing no more than mr = 14.25 kg.