Question

Прямоугольный сосуд вместимостью 2 л наполовину наполнен водой, а наполовину керосином, чему равен вес жидкостей в сосуде? Дно сосуда имеет форму квадрата сo стороной 10 см.

Answer 1

Сразу спешу заметить, что я не буду писать здесь "Дано", а предоставлю вам только решение. Оно выглядит так:

Р = $Р_{1}$ + $Р_{2}$; $Р_{1}$ = $m_{1}$g = ρ₁V₁g; P₂ = $m_{2}$g = ρ₂V₂g;

P = ρ₁V₁g + ρ₂V₂g = V₁g(ρ₁+ρ₂) = 1 ˣ $10^{-3} кг/$м$^{3}$ ˣ 10 Н/кг ˣ (1ˣ$10^{3}$ кг/м$^{3}$ + 0,8 ˣ $10^{-3}$кг/м$^{3}$) = 18 Н. 

Answer 2

Calculation of the Weight of Liquids in the Vessel

To calculate the weight of the liquids in the vessel, we need to determine the volume of water and kerosene present in the vessel and then calculate their respective weights.

Given: - The vessel has a capacity of 2 liters. - The vessel is half-filled with water and half-filled with kerosene. - The bottom of the vessel has the shape of a square with sides measuring 10 cm.

To find the volume of water and kerosene, we need to calculate the volume of the square base and multiply it by the height of the liquid in the vessel.

Calculation of the Volume of Water and Kerosene

The volume of the square base can be calculated using the formula for the area of a square: Area = side^2.

Given that the side of the square base is 10 cm, the area of the base is:

Area = 10 cm * 10 cm = 100 cm^2.

Since the vessel is half-filled with water, the height of the water is 1 liter (1000 cm^3) and the height of the kerosene is also 1 liter (1000 cm^3).

Therefore, the volume of water and kerosene in the vessel is:

Volume of Water = Area * Height of Water = 100 cm^2 * 1000 cm = 100,000 cm^3

Volume of Kerosene = Area * Height of Kerosene = 100 cm^2 * 1000 cm = 100,000 cm^3

Calculation of the Weight of Water and Kerosene

To calculate the weight of the liquids, we need to know the density of water and kerosene. The density of water is approximately 1 g/cm^3, and the density of kerosene is approximately 0.8 g/cm^3.

Therefore, the weight of water in the vessel is:

Weight of Water = Volume of Water * Density of Water = 100,000 cm^3 * 1 g/cm^3 = 100,000 g = 100 kg

And the weight of kerosene in the vessel is:

Weight of Kerosene = Volume of Kerosene * Density of Kerosene = 100,000 cm^3 * 0.8 g/cm^3 = 80,000 g = 80 kg

Therefore, the total weight of the liquids in the vessel (water + kerosene) is:

Total Weight of Liquids = Weight of Water + Weight of Kerosene = 100 kg + 80 kg = 180 kg.

So, the weight of the liquids in the vessel is 180 kg.