Question

В три одинаковых вертикальных сосуда с прямоугольным горизонтальным дном налито одинаковое количество воды. В средний и и правый стакан положили массивнве поршни массами m1 и m2 соответственно. Отношение масс поршней m2/m1= 1.5. Известно, что давление на дно среднего сосуда в 2,5 раза больше, чем давление на дно левого сосуда. Во сколько раз масса поршня m1 больше массы воды в каждом сосуде. Во сколграз давление на дно правового сосуда больше, чем давлениетна дно среднего сосуда?​

Answer 1

Будет m5
Это точно мне дали за это задание 5 баллов

Answer 2

Problem Analysis

We have three vertical vessels with rectangular horizontal bottoms. The middle and right vessels have pistons with masses m1 and m2 respectively. The ratio of the piston masses is m2/m1 = 1.5. The pressure on the bottom of the middle vessel is 2.5 times greater than the pressure on the bottom of the left vessel. We need to find the ratio of the mass of piston m1 to the mass of water in each vessel, as well as the ratio of the pressure on the bottom of the right vessel to the pressure on the bottom of the middle vessel.

Solution

Let's assume the mass of water in each vessel is M. We can use the principles of Pascal's law and Archimedes' principle to solve this problem.

According to Pascal's law, the pressure in a fluid is transmitted equally in all directions. Therefore, the pressure on the bottom of the middle vessel is equal to the pressure on the bottom of the left vessel.

According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The buoyant force on the piston in each vessel is equal to the weight of the water displaced by the piston.

Let's calculate the mass of water displaced by the piston in the middle vessel. The buoyant force on the piston in the middle vessel is equal to the weight of the water displaced by the piston, which is equal to the mass of water displaced multiplied by the acceleration due to gravity (g).

The buoyant force on the piston in the middle vessel is also equal to the pressure on the bottom of the middle vessel multiplied by the area of the piston.

Let's denote the area of the piston in the middle vessel as A. The pressure on the bottom of the middle vessel is 2.5 times greater than the pressure on the bottom of the left vessel. Therefore, the pressure on the bottom of the middle vessel is 2.5P, where P is the pressure on the bottom of the left vessel.

The buoyant force on the piston in the middle vessel is equal to the pressure on the bottom of the middle vessel multiplied by the area of the piston:

Buoyant force = (2.5P) * A

The buoyant force is also equal to the weight of the water displaced by the piston:

Buoyant force = M * g

Setting these two expressions equal to each other, we can solve for the mass of water in each vessel:

M * g = (2.5P) * A

Now, let's calculate the mass of water in each vessel. The mass of water in each vessel is equal to the density of water multiplied by the volume of water in each vessel:

M = ρ * V

Since the volume of water in each vessel is the same, we can write:

M = ρ * V

where ρ is the density of water.

Now, let's calculate the mass of the piston in the middle vessel. The mass of the piston in the middle vessel is equal to the mass of water displaced by the piston:

m1 = M

The mass of the piston in the right vessel is 1.5 times greater than the mass of the piston in the middle vessel:

m2 = 1.5 * m1

Now, let's calculate the ratio of the mass of piston m1 to the mass of water in each vessel:

m1/M = 1

The ratio of the mass of piston m1 to the mass of water in each vessel is 1.

Finally, let's calculate the ratio of the pressure on the bottom of the right vessel to the pressure on the bottom of the middle vessel. The pressure on the bottom of the right vessel is equal to the pressure on the bottom of the middle vessel plus the pressure due to the weight of the piston:

Pressure on the bottom of the right vessel = Pressure on the bottom of the middle vessel + Weight of the piston

The weight of the piston is equal to the mass of the piston multiplied by the acceleration due to gravity:

Weight of the piston = m2 * g

Substituting the values of m2 and m1, we get:

Weight of the piston = (1.5 * m1) * g

Therefore, the ratio of the pressure on the bottom of the right vessel to the pressure on the bottom of the middle vessel is:

Pressure on the bottom of the right vessel/Pressure on the bottom of the middle vessel = 1 + 1.5 = 2.5

The ratio of the pressure on the bottom of the right vessel to the pressure on the bottom of the middle vessel is 2.5.

In summary: - The mass of piston m1 is equal to the mass of water in each vessel. - The ratio of the mass of piston m1 to the mass of water in each vessel is 1. - The ratio of the pressure on the bottom of the right vessel to the pressure on the bottom of the middle vessel is 2.5.

Please let me know if anything is unclear or if you have any further questions!