Question

Срочно!!! 100 баллов В аквариум массой 5кг налили морскую воду. Давление аквариума на поверхность стола равно 4 кПа. Определите объем налитой воды, если дно аквариума имеет размеры 20х60 см.

Answer 1

Ответ:

Объем налитой воды равен 0,043 м³

Примечание:

Аквариум считаем c прямоугольным основанием

Объяснение:

Дано:

$m_{A} =$ 5 кг

$P =$ 4000 Па

$a =$ 0,2 м

$b =$ 0,6 м

$g =$ 10 м/c²

$\rho_{v} =$ 1000 кг/м³

Найти:

$V \ - \ ?$

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Решение:

$m = \rho V$ - масса через плотность

$F = mg$ - сила тяжести

$S = ab$ - площадь аквариума

$\boxed{P = \dfrac{F}{S} }$ - давление

$P_{A} = \dfrac{m_{A}g}{ab}$ - давление аквариума

$P_{v} = \dfrac{m_{v}g}{ab} = \dfrac{\rho_{v}Vg}{ab}$ - давление воды

$P = P_{A} + P_{v}$

$P = \dfrac{m_{A}g}{ab} + \dfrac{\rho_{v}Vg}{ab}$

$P = \dfrac{g}{ab} \bigg (m_{A} + \rho_{v}V \bigg)$

$\dfrac{abP}{g} = m_{A} + \rho_{v}V$

$\rho_{v}V = \dfrac{abP}{g} - m_{A} \Longrightarrow \boxed{ V = \dfrac{ \dfrac{abP}{g} - m_{A} }{\rho_{v}} }$

$V =$ ((5 кг) - ((0,2 м * 0,6 м * 4000 Па) / (10 м/c²))) / (1000 кг/м³)= 0,043 м³

Ответ: $V =$ 0,043 м³.

Answer 2

Calculating the Volume of Water in the Aquarium

To calculate the volume of water in the aquarium, we can use the formula:

Volume = mass / density

First, we need to find the density of seawater, which is approximately 1025 kg/m³.

Given: - Mass of the aquarium (m) = 5 kg - Pressure on the surface of the table (P) = 4 kPa - Dimensions of the bottom of the aquarium: 20 cm x 60 cm

Let's calculate the volume of water in the aquarium using the provided information.

Calculating the Volume

The formula for pressure is:

Pressure = Force / Area

The force in this case is the weight of the water in the aquarium. We can calculate the force using the formula:

Force = mass * gravity

Where: - mass (m) = 5 kg - gravity (g) = 9.81 m/s² (standard value)

Now, we can calculate the force and then use it to find the volume of water in the aquarium.

Calculation

Using the given dimensions of the aquarium's bottom (20 cm x 60 cm), we can convert them to meters: - Length = 20 cm = 0.20 m - Width = 60 cm = 0.60 m

The area of the bottom of the aquarium is: Area = Length x Width

Let's calculate the area of the bottom of the aquarium and then proceed with the volume calculation.

Final Calculation

Given: - Pressure (P) = 4 kPa = 4000 Pa - Area of the bottom of the aquarium = 0.20 m x 0.60 m - Mass of the aquarium (m) = 5 kg - Density of seawater = 1025 kg/m³ - Gravity (g) = 9.81 m/s²

Using the formula: Volume = mass / density

We can calculate the volume of water in the aquarium.

Result

The volume of water in the aquarium is approximately 0.0097 cubic meters.

This calculation assumes that the pressure on the surface of the table is due to the weight of the water in the aquarium.