Question

Великий поршень гідравлічного преса стискає деталь із силою 8,2 кН. Яка сила дії на малий поршень,якщо його площа є меншою за площу великого поршня в 41 раз?Если что,вот на русском:Большой поршень гидравлического пресса сжимает деталь с силой 8,2 кН. Какая сила действует на малый поршень, если его площадь является меньше площади большого поршня в 41 раз?

Answer 1

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Answer 2

Calculation of Force on the Small Piston

To calculate the force acting on the small piston of a hydraulic press, we can use the principle of Pascal's law. According to Pascal's law, the pressure exerted on a fluid in a closed system is transmitted equally in all directions.

In this case, the force exerted on the large piston is given as 8.2 kN. We need to find the force acting on the small piston, given that its area is 41 times smaller than the area of the large piston.

Let's denote the force on the small piston as F_small and the force on the large piston as F_large. Similarly, let's denote the area of the small piston as A_small and the area of the large piston as A_large.

According to Pascal's law, the pressure exerted on the fluid is the same on both pistons. Therefore, we can write the following equation:

Pressure on the large piston = Pressure on the small piston

The pressure on a piston is defined as the force divided by the area:

Pressure = Force / Area

Using this equation, we can write:

F_large / A_large = F_small / A_small

We are given that the area of the small piston is 41 times smaller than the area of the large piston. Mathematically, we can express this as:

A_small = (1/41) * A_large

Substituting this into the equation above, we get:

F_large / A_large = F_small / [(1/41) * A_large]

Simplifying the equation, we find:

F_small = (F_large * A_small) / A_large

Now we can substitute the given values into the equation to find the force on the small piston.

Given: - F_large = 8.2 kN - A_small = (1/41) * A_large

Substituting these values, we get:

F_small = (8.2 kN * (1/41) * A_large) / A_large

Simplifying further, we find:

F_small = 0.2 kN

Therefore, the force acting on the small piston is 0.2 kN.

Please note that the above calculation assumes ideal conditions and neglects factors such as friction and losses in the hydraulic system.