Standing on the lunar surface, an American astronaut exerts pressure on the lunar soil with

Standing on the lunar surface, an American astronaut exerts pressure on the lunar soil with a force equal to 21.3 kPa. Determine the mass of the astronaut (along with the equipment) if there are footprints left from his boots, the area of each of which is 410 cm2.

Given:

P = 21.3 kPa is the astronaut’s pressure on the lunar soil;

s = 410 cm2 = 0.041 m2 (square meter) is the reference area of ​​one cosmonaut’s boot;

n = 2 is the total number of boots.

It is required to determine m (kilogram) – the mass of the astronaut together with the equipment.

Let’s convert the units of measurement of pressure to the SI system:

P = 21.3 kPa = 21.3 * 10 ^ 3 = 21.3 * 1000 = 21300 Pascal.

The total reference area of ​​the astronaut will be equal to:

S = n * s = 2 * 0.041 = 0.082 m2.

Then the force with which the astronaut presses on the surface will be equal to:

F = P * S = 21300 * 0.082 = 1746.6 Newton.

This force is numerically equal to the force of gravity with which the Moon acts on the astronaut:

F = m * g, where g = 1.6 Newton / kilogram (acceleration of gravity on the surface of the Moon);

m = F / g = 1746.6 / 1.6 = 1091 kilograms.

Answer: the mass of the astronaut together with the equipment is 1091 kilograms.