Solution

Statement

$2.3.3.$ To test equipment under conditions of extreme acceleration and weightlessness, a container with it is tossed to a height of $125\text{ m}$ by a pneumatic piston device located at the bottom of a vacuum shaft. With what force does the piston act while tossing the container, if it extends by a length $h = 1\text{ m}$ in the process, and the mass of the container with the equipment is $m = 2\text{ t}$?

Solution

The piston device imparts a certain amount of kinetic energy to the equipment, which, according to the law of conservation of mechanical energy (since the shaft is a vacuum), converts into potential energy. Therefore, the work done by the force of the piston device is equal to the change in potential energy:
$$Fh = mgH \implies F = mg\frac{H}{h}$$

Let's substitute the numerical values:
$$F = 2 \cdot 10^3\text{ kg} \cdot 10\text{ }\frac{\text{N}}{\text{kg}} \cdot \frac{125\text{ m}}{1\text{ m}} = 2.5 \cdot 10^6\text{ N}$$