Assess how much pressure the mosquito’s proboscis can put on human skin. For calculations

Assess how much pressure the mosquito’s proboscis can put on human skin. For calculations, take the diameter of his piercing tool approximately equal to 0.01 mm, the mass of the mosquito equal to 5 mg. To assess the possible force of pressing on the proboscis, let us assume that a mosquito is able to press on the proboscis with a force 5 times its weight.

d = 0.01 mm = 0.01 * 10 ^ -3 m.

m = 5 mg = 5 * 10 ^ -3 kg.

F = 5 * Fв.

g = 9.8 m / s ^ 2.

P -?

The pressure P of the trunk is determined by the formula: P = F / S, where F is the pressing force of the proboscis, S is the area on which this force acts.

The proboscis has a circular cross-section, therefore S = п * d ^ 2/4, where п is the number pi, d is the diameter of the proboscis.

Let’s find the weight of the mosquito: Fв = m * g, where m is the mass of the mosquito, g is the acceleration of gravity.

The formula for the pressing force of the proboscis will be: F = 5 * m * g.

P = 5 * m * g * 4 / п * d ^ 2.

P = 5 * 5 * 10 ^ -3 kg * 9.8 m / s ^ 2 * 4 / 3.14 * (0.01 * 10 ^ -3 m) = 3161290322 N.

Answer: the pressure of the hobodka on human skin is P = 3161290322 N.