Question

На малом поршне гидравлического пресса установлен рычаг с соотношением плеч 5:1, на большее плечо которого действует сила 100Н. Когда малый поршень за 1 ход опустился на 10см, больший поршень поднялся на 0.5см. Определить величину силы(кН) на большем поршне. Потерями энергии пренебречь.

Answer 1

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Answer 2

Calculation of Force on the Larger Piston

To determine the force on the larger piston of the hydraulic press, we can use the principle of Pascal's law, which states that the pressure exerted on a fluid in a closed system is transmitted equally in all directions.

According to Pascal's law, the ratio of the areas of the two pistons is equal to the ratio of the forces acting on them. Mathematically, this can be expressed as:

F1 / F2 = A1 / A2

Where: - F1 is the force acting on the smaller piston (100 N in this case) - F2 is the force acting on the larger piston (to be determined) - A1 is the area of the smaller piston - A2 is the area of the larger piston

We are given that the lever arm has a ratio of 5:1, which means that the distance traveled by the smaller piston is 5 times greater than the distance traveled by the larger piston.

Given that the smaller piston traveled 10 cm (0.1 m) and the larger piston traveled 0.5 cm (0.005 m), we can calculate the ratio of the distances traveled:

d1 / d2 = 0.1 m / 0.005 m = 20

Since the lever arm ratio is equal to the ratio of the distances traveled, we can equate the two ratios:

d1 / d2 = A1 / A2 = 5

Now, we can substitute the values into the equation:

F1 / F2 = A1 / A2 = 5

100 N / F2 = 5

Solving for F2:

F2 = 100 N / 5 = 20 N

Therefore, the force on the larger piston is 20 N.

Note: The question asks for the force in kilonewtons (kN), so we need to convert the force from newtons (N) to kilonewtons (kN):

20 N = 0.02 kN

Therefore, the force on the larger piston is 0.02 kN.