The silver water spider builds an air house in the water, transferring bubbles of atmospheric air on its legs

The silver water spider builds an air house in the water, transferring bubbles of atmospheric air on its legs and abdomen and placing them under the dome of a cobweb attached by its ends to aquatic plants. How many trips does a spider need to make in order to build a house with a volume of 1 cm3 at a depth of 50 cm, if each time it takes 5 mm3 of air under atmospheric pressure?

V1 = 5 mm ^ 3 = 5 * 10 ^ -9 m ^ 3 – the volume of air that the spider carries at one time;

P1 = 101325 Pascal – the air pressure that the spider carries;

V2 = 1 cm ^ 3 = 10 ^ -6 m ^ 3 – the required volume of the house;

h = 50 centimeters = 0.5 meters – the depth at which the house is located;

g = 10 N / kg – acceleration of gravity;

ro = 1000 kg / m ^ 3 is the density of water.

It is required to determine how many flights N a spider must make to build a house.

Let’s find the pressure of the water column at the depth h:

P2 = ro * g * h = 1000 * 10 * 0.5 = 5000 Pascal.

That is, the total pressure at this depth will be:

P = P2 + P1 = 101325 + 5000 = 106325.

Then, in order to fill the volume V2 at a depth h, air must be taken above the water, with a volume:

V = P * V2 / P1 = 106325 * 10 ^ -6 / 101325 = 1.05 * 10 ^ -6 m ^ 3.

Then the number of flights will be:

N = V / V1 = 1.05 * 10 ^ -6 / (5 * 10 ^ -9) = 0.21 * 10 ^ 3 = 210 flights.

Answer: the spider will have to make 210 flights.