The hydraulic press gives a 100 times strength gain. Find the area of the larger piston and its force

The hydraulic press gives a 100 times strength gain. Find the area of the larger piston and its force if a force of 100N acts on the smaller piston with an area of 1 cm2.

Let the hydraulic press be given. From the condition of the problem it is known that it gives a gain in force 100 times, that is, the pressure force exerted on the larger piston exceeds the pressure force exerted on the smaller piston a hundred times: F₁: F₂ = 100. To find the area of ​​the larger piston S₁ and the force acting from its side F₁ on external bodies, if a force F₂ = 100 N acts on a smaller piston with an area of ​​S₂ = 1 cm² = 0.0001 m², we use Pascal’s law, according to which the pressure created at some point in the liquid is transmitted through all directions are the same. This means that the pressure on both pistons will be the same: p₁ = p₂. By definition, the pressure p is equal to the ratio of the pressure force to the area on which this pressure is exerted, that is: p = F: S. For the first and second pistons, we get: p₁ = F₁: S₁ and p₂ = F₂: S₂. Then it turns out that: F₁: S₁ = F₂: S₂.

Calculation of piston area and pressure force
Since F₁: F₂ = 100, then F₁ = 100 ∙ F₂ and (100 ∙ F₂): S₁ = F₂: S₂, or S₁ = 100 ∙ S₂. Substitute the values ​​of physical quantities in the calculation formulas and find the area of ​​the larger piston:

S₁ = 100 ∙ 0.0001 m²;

S₁ = 0.01 m²;

and the force of pressure created by it:

F₁ = 100 ∙ 100 N;

F₁ = 10000 N = 10 kN.

Answer: The area of ​​the larger piston is 0.01 m²; and the pressure force generated by it is 10 kN.