Question

Площадь большого поршня гидравлического пресса 180 см2, действующая на него сила 18 кН . Площадь малого поршня 4 см2. Определите силу, действующую на малый поршень, и выигрыш в силе, который даёт этот гидравлический пресс.

Answer 1

Дано:

$S_1=180$ см²

$F_1=18$ кН $=18000$ Н

$S_2=4$ см²

Найти:

$F_2-?\\\frac{F_1}{F_2} -?$

Решение:

$p_1=p_2\\\frac{F_1}{S_1} =\frac{F_2}{S_2} \\F_2=F_1\frac{S_2}{S_1}$

$F_2=18000*\frac{4}{180} =18000*\frac{1}{45} =\frac{18000}{45}=400$ Н

$\frac{F_1}{F_2} =\frac{18000}{400} =\frac{180}{4} =45$

Ответ: $F_2=400$ Н, $\frac{F_1}{F_2} =45$

Answer 2

Calculation of Force on the Small Piston

To determine the force acting on the small piston and the force advantage provided by the 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.

The formula to calculate the force exerted on a piston is:

Force = Pressure x Area

Given the following information: - Area of the large piston (A1) = 180 cm^2 - Force on the large piston (F1) = 18 kN - Area of the small piston (A2) = 4 cm^2

We can calculate the force on the small piston (F2) using the formula:

F2 = (F1 x A2) / A1

Substituting the given values into the formula:

F2 = (18 kN x 4 cm^2) / 180 cm^2

Now, let's calculate the force on the small piston and the force advantage provided by the hydraulic press.

Calculation:

F2 = (18 kN x 4 cm^2) / 180 cm^2

Converting the units: - 1 kN = 1000 N - 1 cm^2 = 0.0001 m^2

F2 = (18,000 N x 0.0004 m^2) / 0.018 m^2

Simplifying the equation: F2 = 400 N

Therefore, the force acting on the small piston is 400 N.

Calculation of Force Advantage:

The force advantage provided by the hydraulic press can be calculated by dividing the force on the large piston (F1) by the force on the small piston (F2).

Force Advantage = F1 / F2

Substituting the given values into the formula:

Force Advantage = 18 kN / 400 N

Converting the units: - 1 kN = 1000 N

Force Advantage = 18,000 N / 400 N

Simplifying the equation: Force Advantage = 45

Therefore, the hydraulic press provides a force advantage of 45.

Please note that the calculations provided are based on the given information and assumptions.