Question

Площадь малого поршня гидравлического пресса 5см в квадрате,большего поршня 500см в квадрате. на малый поршень действуеет сила 400Н на большой 36кН какой выигрыш в силе дает этот пресс? почему пресс не может дать максимальный (наибольший) выигрыш в силе?Какой выигрыш в силе мог бы дать этот пресс в случае отсутствия трения между поршнем и стенками пресса

Answer 1

Реальный выигрыш в силе:

F2/F1 = 36 000/400 = 90

Это меньше теоретически возможного:

S2/S1 = 500/5 = 100

Причина - трение между поршнями и стенками пресса.

Answer 2

Calculation of Force and Area

To calculate the force exerted by the hydraulic press, we can use the formula:

Force = Pressure x Area

Given that the force on the small piston is 400 N and the force on the large piston is 36 kN (36,000 N), we can calculate the areas of the pistons using the formula:

Area = Force / Pressure

Let's calculate the areas of the small and large pistons:

For the small piston: Area of the small piston = 400 N / Pressure

For the large piston: Area of the large piston = 36,000 N / Pressure

We are given that the area of the small piston is 5 cm² and the area of the large piston is 500 cm². Let's calculate the pressure:

For the small piston: 5 cm² = 400 N / Pressure

For the large piston: 500 cm² = 36,000 N / Pressure

To find the pressure, we can rearrange the equations:

For the small piston: Pressure = 400 N / 5 cm²

For the large piston: Pressure = 36,000 N / 500 cm²

Now, let's calculate the pressure for both pistons:

For the small piston: Pressure = 400 N / 5 cm² = 80 N/cm²

For the large piston: Pressure = 36,000 N / 500 cm² = 72 N/cm²

Calculation of Force Gain

The force gain of the hydraulic press can be calculated using the formula:

Force Gain = Force on the large piston / Force on the small piston

Given that the force on the small piston is 400 N and the force on the large piston is 36,000 N, let's calculate the force gain:

Force Gain = 36,000 N / 400 N = 90

Therefore, the force gain of this hydraulic press is 90.

Limitations of Force Gain

The force gain of a hydraulic press is determined by the ratio of the areas of the pistons. In this case, the force gain is 90, which means that the force exerted by the large piston is 90 times greater than the force exerted by the small piston.

However, it's important to note that the force gain of a hydraulic press is limited by factors such as friction and the mechanical properties of the system. Friction between the piston and the walls of the press can reduce the force gain. Additionally, the mechanical properties of the system, such as the strength of the materials used, can also limit the force gain.

Force Gain without Friction

In the case of no friction between the piston and the walls of the press, the force gain would be equal to the ratio of the areas of the pistons. In this case, the force gain would be:

Force Gain = Area of the large piston / Area of the small piston

Given that the area of the small piston is 5 cm² and the area of the large piston is 500 cm², let's calculate the force gain without friction:

Force Gain = 500 cm² / 5 cm² = 100

Therefore, in the absence of friction, this hydraulic press would have a force gain of 100.